task_name
string | rows
int64 | cols
int64 | rules
string | visual_elements
string | initial_board
string | solution
string | initial_observation
string | solution_reference
string | description
string | title
string | hint
string |
|---|---|---|---|---|---|---|---|---|---|---|---|
sudoku_normal_hard_100
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.94.5..16.2..19...1.54..9..4.9...1...5.14.69....97.4355...9.7..98......12....1..9
|
394857216628319547175426983439685172752143698861972435513298764987564321246731859
|
. 9 4 . 5 . . 1 6
. 2 . . 1 9 . . .
1 . 5 4 . . 9 . .
4 . 9 . . . 1 . .
. 5 . 1 4 . 6 9 .
. . . 9 7 . 4 3 5
5 . . . 9 . 7 . .
9 8 . . . . . . 1
2 . . . . 1 . . 9
|
3 9 4 8 5 7 2 1 6
6 2 8 3 1 9 5 4 7
1 7 5 4 2 6 9 8 3
4 3 9 6 8 5 1 7 2
7 5 2 1 4 3 6 9 8
8 6 1 9 7 2 4 3 5
5 1 3 2 9 8 7 6 4
9 8 7 5 6 4 3 2 1
2 4 6 7 3 1 8 5 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4732_hard
|
394857216628319547175426983439685172752143698861972435513298764987564321246731859 #1 Extreme (31972) bf
Hidden Single: r2c5=1
Hidden Single: r6c4=9
Hidden Single: r6c7=4
Hidden Single: r4c7=1
Locked Candidates Type 1 (Pointing): 4 in b3 => r2c3<>4
Hidden Rectangle: 1/6 in r6c23,r7c23 => r7c3<>6
Brute Force: r5c7=6
Forcing Net Verity => r5c8<>7
r3c8=2 (r3c9<>2) (r3c5<>2) r1c7<>2 r8c7=2 (r7c9<>2) r8c5<>2 r4c5=2 r4c9<>2 r5c9=2 r5c9<>9 r5c8=9 r5c8<>7
r3c8=7 r5c8<>7
r3c8=8 (r2c9<>8) (r3c9<>8) (r3c5<>8) (r1c7<>8) r2c7<>8 r9c7=8 (r7c9<>8) (r9c9<>8) r9c5<>8 r4c5=8 r4c9<>8 r5c9=8 r5c9<>9 r5c8=9 r5c8<>7
Forcing Chain Contradiction in c2 => r1c3<>7
r1c3=7 r1c2<>7
r1c3=7 r3c2<>7
r1c3=7 r1c3<>4 r1c2=4 r1c2<>9 r9c2=9 r9c9<>9 r5c9=9 r5c9<>7 r4c89=7 r4c2<>7
r1c3=7 r1c3<>4 r1c2=4 r1c2<>9 r9c2=9 r9c2<>7
Brute Force: r5c8=9
Hidden Single: r9c9=9
Hidden Single: r8c1=9
Hidden Single: r1c2=9
Hidden Single: r1c3=4
Finned Franken Swordfish: 2 c57b6 r348 fr1c7 fr5c9 => r3c9<>2
Finned Franken Swordfish: 8 c57b6 r349 fr1c7 fr2c7 fr5c9 => r3c9<>8
Forcing Chain Contradiction in c2 => r2c9<>3
r2c9=3 r3c9<>3 r3c9=7 r3c2<>7
r2c9=3 r3c9<>3 r3c9=7 r5c9<>7 r4c89=7 r4c2<>7
r2c9=3 r2c9<>4 r2c8=4 r9c8<>4 r9c2=4 r9c2<>7
Forcing Net Verity => r2c4<>7
r3c2=7 r1c1<>7 r1c46=7 r2c4<>7
r4c2=7 (r3c2<>7) (r5c1<>7) r5c3<>7 r5c9=7 r3c9<>7 r3c9=3 r3c2<>3 r3c2=6 (r2c1<>6) r2c3<>6 r2c4=6 r2c4<>7
r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>7 r8c4=7 r2c4<>7
Forcing Net Contradiction in r4c2 => r2c9<>8
r2c9=8 (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c5<>8 r3c5=8 r3c5<>2) (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c8<>7) r2c9<>4 r2c8=4 r2c8<>7 r3c8=7 r3c8<>2 r3c6=2 (r5c6<>2) r6c6<>2 r6c3=2 r5c3<>2 r5c9=2 r5c9<>7 r4c89=7 r4c2<>7
r2c9=8 (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c8<>7) r2c9<>4 r2c8=4 (r9c8<>4 r9c2=4 r9c2<>7) r2c8<>7 r3c8=7 r3c2<>7 r4c2=7
Forcing Net Contradiction in r2c1 => r3c2<>3
r3c2=3 (r4c2<>3) r3c9<>3 r3c9=7 (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r4c2=6 r6c1<>6 r2c1=6
r3c2=3 (r3c9<>3 r3c9=7 r2c8<>7) (r3c9<>3 r3c9=7 r2c9<>7) (r3c9<>3 r3c9=7 r5c9<>7) (r1c1<>3) r2c1<>3 r5c1=3 r5c1<>7 r5c3=7 r2c3<>7 r2c1=7
Forcing Chain Contradiction in r4c2 => r3c6<>3
r3c6=3 r5c6<>3 r4c456=3 r4c2<>3
r3c6=3 r3c9<>3 r3c9=7 r3c2<>7 r3c2=6 r4c2<>6
r3c6=3 r3c9<>3 r3c9=7 r5c9<>7 r4c89=7 r4c2<>7
Forcing Net Contradiction in c4 => r3c9=3
r3c9<>3 r3c5=3 r1c4<>3
r3c9<>3 r3c5=3 r2c4<>3
r3c9<>3 r3c9=7 (r3c2<>7 r3c2=6 r4c2<>6) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r4c2=3 r4c4<>3
r3c9<>3 r7c9=3 r7c4<>3
r3c9<>3 r3c9=7 (r3c2<>7) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>7 r8c4=7 r8c4<>3
r3c9<>3 r3c9=7 (r3c2<>7) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 (r8c6<>5 r4c6=5 r4c4<>5) r8c6<>7 r8c4=7 r8c4<>5 r9c4=5 r9c4<>3
Finned Swordfish: 3 c257 r489 fr7c2 => r89c3<>3
Locked Pair: 6,7 in r89c3 => r26c3,r79c2<>6, r25c3,r9c2<>7
Almost Locked Set Chain: 8- r2c13789 {345678} -6- r3c2 {67} -7- r126c1 {3678} -3- r289c3 {3678} -8 => r2c4<>8
Forcing Chain Contradiction in c6 => r4c6<>2
r4c6=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r4c6=2 r4c6<>3
r4c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r4c6=2 r4c6<>5 r8c6=5 r8c6<>4 r7c6=4 r7c6<>3
r4c6=2 r4c6<>5 r8c6=5 r8c6<>3
Forcing Chain Contradiction in r4 => r7c4<>3
r7c4=3 r2c4<>3 r2c4=6 r2c1<>6 r6c1=6 r4c2<>6
r7c4=3 r2c4<>3 r2c4=6 r4c4<>6
r7c4=3 r89c5<>3 r4c5=3 r4c5<>6
r7c4=3 r7c23<>3 r9c2=3 r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>5 r4c6=5 r4c6<>6
Forcing Chain Contradiction in c6 => r7c6<>2
r7c6=2 r56c6<>2 r4c45=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r7c6=2 r7c6<>4 r8c6=4 r8c6<>5 r4c6=5 r4c6<>3
r7c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r7c6=2 r7c6<>3
r7c6=2 r7c6<>4 r8c6=4 r8c6<>3
Empty Rectangle: 2 in b8 (r18c7) => r1c4<>2
Forcing Chain Contradiction in c5 => r2c8<>8
r2c8=8 r2c3<>8 r2c3=3 r12c1<>3 r5c1=3 r5c1<>7 r5c9=7 r5c9<>2 r4c89=2 r4c45<>2 r56c6=2 r13c6<>2 r3c5=2 r3c5<>8
r2c8=8 r2c3<>8 r2c3=3 r12c1<>3 r5c1=3 r5c1<>7 r5c9=7 r5c9<>8 r4c89=8 r4c5<>8
r2c8=8 r12c7<>8 r9c7=8 r9c5<>8
Forcing Chain Contradiction in c6 => r8c6<>2
r8c6=2 r78c4<>2 r4c4=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r8c6=2 r8c6<>5 r4c6=5 r4c6<>3
r8c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r8c6=2 r8c6<>4 r7c6=4 r7c6<>3
r8c6=2 r8c6<>3
Forcing Chain Contradiction in r8c5 => r9c4<>3
r9c4=3 r2c4<>3 r2c4=6 r2c1<>6 r3c2=6 r3c2<>7 r4c2=7 r5c1<>7 r5c9=7 r5c9<>2 r4c89=2 r4c4<>2 r78c4=2 r8c5<>2
r9c4=3 r8c5<>3
r9c4=3 r9c4<>7 r9c3=7 r9c3<>6 r8c3=6 r8c5<>6
Forcing Net Contradiction in r4 => r1c7=2
r1c7<>2 (r1c7=8 r2c7<>8 r2c7=5 r9c7<>5 r9c7=3 r9c2<>3 r9c2=4 r7c2<>4) r1c6=2 r6c6<>2 r6c3=2 r6c3<>1 r6c2=1 r7c2<>1 r7c2=3 r4c2<>3
r1c7<>2 r1c6=2 r1c6<>3 r12c4=3 r4c4<>3
r1c7<>2 (r1c6=2 r3c5<>2) r8c7=2 r8c5<>2 r4c5=2 r4c5<>3
r1c7<>2 r1c6=2 (r1c6<>7) (r1c6<>7) (r5c6<>2) r6c6<>2 r6c3=2 r5c3<>2 r5c9=2 r5c9<>7 r5c1=7 r1c1<>7 r1c4=7 r3c6<>7 r8c6=7 r8c6<>5 r4c6=5 r4c6<>3
Grouped Discontinuous Nice Loop: 8 r3c5 -8- r3c8 -7- r3c2 =7= r4c2 -7- r5c1 =7= r5c9 =2= r4c89 -2- r4c45 =2= r56c6 -2- r3c6 =2= r3c5 => r3c5<>8
Empty Rectangle: 8 in b5 (r3c68) => r4c8<>8
Locked Candidates Type 1 (Pointing): 8 in b6 => r7c9<>8
Finned Jellyfish: 8 r1367 c1468 fr6c3 => r5c1<>8
XYZ-Wing: 3/7/8 in r15c1,r2c3 => r2c1<>3
Multi Colors 1: 8 (r2c7,r3c6) / (r3c8,r9c7), (r4c5) / (r9c5) => r456c6<>8
Locked Candidates Type 1 (Pointing): 8 in b5 => r4c9<>8
Hidden Single: r5c9=8
Hidden Single: r5c1=7
Hidden Single: r3c2=7
Naked Single: r3c8=8
Naked Single: r2c7=5
Naked Single: r8c7=3
Full House: r9c7=8
Hidden Single: r1c1=3
Naked Single: r2c3=8
Full House: r2c1=6
Full House: r6c1=8
Naked Single: r2c4=3
Hidden Single: r4c5=8
Hidden Single: r9c5=3
Naked Single: r9c2=4
Locked Candidates Type 1 (Pointing): 2 in b6 => r4c4<>2
Locked Candidates Type 1 (Pointing): 2 in b5 => r3c6<>2
Naked Single: r3c6=6
Full House: r3c5=2
Full House: r8c5=6
Naked Single: r6c6=2
Naked Single: r8c3=7
Naked Single: r5c6=3
Full House: r5c3=2
Naked Single: r6c3=1
Full House: r6c2=6
Full House: r4c2=3
Full House: r7c2=1
Naked Single: r9c3=6
Full House: r7c3=3
Naked Single: r4c6=5
Full House: r4c4=6
Naked Single: r9c8=5
Full House: r9c4=7
Naked Single: r8c6=4
Naked Single: r1c4=8
Full House: r1c6=7
Full House: r7c6=8
Naked Single: r8c8=2
Full House: r8c4=5
Full House: r7c4=2
Naked Single: r4c8=7
Full House: r4c9=2
Naked Single: r7c9=4
Full House: r2c9=7
Full House: r2c8=4
Full House: r7c8=6
|
sudoku_normal_extremely_hard_100
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
....5..16.2...9...1.54..9..4.9.......5.14........7..355...9.7...8......12....1...
|
394857216628319547175426983439685172752143698861972435513298764987564321246731859
|
. . . . 5 . . 1 6
. 2 . . . 9 . . .
1 . 5 4 . . 9 . .
4 . 9 . . . . . .
. 5 . 1 4 . . . .
. . . . 7 . . 3 5
5 . . . 9 . 7 . .
. 8 . . . . . . 1
2 . . . . 1 . . .
|
3 9 4 8 5 7 2 1 6
6 2 8 3 1 9 5 4 7
1 7 5 4 2 6 9 8 3
4 3 9 6 8 5 1 7 2
7 5 2 1 4 3 6 9 8
8 6 1 9 7 2 4 3 5
5 1 3 2 9 8 7 6 4
9 8 7 5 6 4 3 2 1
2 4 6 7 3 1 8 5 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4732_hard
|
394857216628319547175426983439685172752143698861972435513298764987564321246731859 #1 Extreme (31972) bf
Hidden Single: r2c5=1
Hidden Single: r6c4=9
Hidden Single: r6c7=4
Hidden Single: r4c7=1
Locked Candidates Type 1 (Pointing): 4 in b3 => r2c3<>4
Hidden Rectangle: 1/6 in r6c23,r7c23 => r7c3<>6
Brute Force: r5c7=6
Forcing Net Verity => r5c8<>7
r3c8=2 (r3c9<>2) (r3c5<>2) r1c7<>2 r8c7=2 (r7c9<>2) r8c5<>2 r4c5=2 r4c9<>2 r5c9=2 r5c9<>9 r5c8=9 r5c8<>7
r3c8=7 r5c8<>7
r3c8=8 (r2c9<>8) (r3c9<>8) (r3c5<>8) (r1c7<>8) r2c7<>8 r9c7=8 (r7c9<>8) (r9c9<>8) r9c5<>8 r4c5=8 r4c9<>8 r5c9=8 r5c9<>9 r5c8=9 r5c8<>7
Forcing Chain Contradiction in c2 => r1c3<>7
r1c3=7 r1c2<>7
r1c3=7 r3c2<>7
r1c3=7 r1c3<>4 r1c2=4 r1c2<>9 r9c2=9 r9c9<>9 r5c9=9 r5c9<>7 r4c89=7 r4c2<>7
r1c3=7 r1c3<>4 r1c2=4 r1c2<>9 r9c2=9 r9c2<>7
Brute Force: r5c8=9
Hidden Single: r9c9=9
Hidden Single: r8c1=9
Hidden Single: r1c2=9
Hidden Single: r1c3=4
Finned Franken Swordfish: 2 c57b6 r348 fr1c7 fr5c9 => r3c9<>2
Finned Franken Swordfish: 8 c57b6 r349 fr1c7 fr2c7 fr5c9 => r3c9<>8
Forcing Chain Contradiction in c2 => r2c9<>3
r2c9=3 r3c9<>3 r3c9=7 r3c2<>7
r2c9=3 r3c9<>3 r3c9=7 r5c9<>7 r4c89=7 r4c2<>7
r2c9=3 r2c9<>4 r2c8=4 r9c8<>4 r9c2=4 r9c2<>7
Forcing Net Verity => r2c4<>7
r3c2=7 r1c1<>7 r1c46=7 r2c4<>7
r4c2=7 (r3c2<>7) (r5c1<>7) r5c3<>7 r5c9=7 r3c9<>7 r3c9=3 r3c2<>3 r3c2=6 (r2c1<>6) r2c3<>6 r2c4=6 r2c4<>7
r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>7 r8c4=7 r2c4<>7
Forcing Net Contradiction in r4c2 => r2c9<>8
r2c9=8 (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c5<>8 r3c5=8 r3c5<>2) (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c8<>7) r2c9<>4 r2c8=4 r2c8<>7 r3c8=7 r3c8<>2 r3c6=2 (r5c6<>2) r6c6<>2 r6c3=2 r5c3<>2 r5c9=2 r5c9<>7 r4c89=7 r4c2<>7
r2c9=8 (r2c7<>8 r9c7=8 r9c8<>8 r4c8=8 r4c8<>7) r2c9<>4 r2c8=4 (r9c8<>4 r9c2=4 r9c2<>7) r2c8<>7 r3c8=7 r3c2<>7 r4c2=7
Forcing Net Contradiction in r2c1 => r3c2<>3
r3c2=3 (r4c2<>3) r3c9<>3 r3c9=7 (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r4c2=6 r6c1<>6 r2c1=6
r3c2=3 (r3c9<>3 r3c9=7 r2c8<>7) (r3c9<>3 r3c9=7 r2c9<>7) (r3c9<>3 r3c9=7 r5c9<>7) (r1c1<>3) r2c1<>3 r5c1=3 r5c1<>7 r5c3=7 r2c3<>7 r2c1=7
Forcing Chain Contradiction in r4c2 => r3c6<>3
r3c6=3 r5c6<>3 r4c456=3 r4c2<>3
r3c6=3 r3c9<>3 r3c9=7 r3c2<>7 r3c2=6 r4c2<>6
r3c6=3 r3c9<>3 r3c9=7 r5c9<>7 r4c89=7 r4c2<>7
Forcing Net Contradiction in c4 => r3c9=3
r3c9<>3 r3c5=3 r1c4<>3
r3c9<>3 r3c5=3 r2c4<>3
r3c9<>3 r3c9=7 (r3c2<>7 r3c2=6 r4c2<>6) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r4c2=3 r4c4<>3
r3c9<>3 r7c9=3 r7c4<>3
r3c9<>3 r3c9=7 (r3c2<>7) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>7 r8c4=7 r8c4<>3
r3c9<>3 r3c9=7 (r3c2<>7) (r2c8<>7) r3c8<>7 r4c8=7 r4c2<>7 r9c2=7 (r8c3<>7) r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 (r8c6<>5 r4c6=5 r4c4<>5) r8c6<>7 r8c4=7 r8c4<>5 r9c4=5 r9c4<>3
Finned Swordfish: 3 c257 r489 fr7c2 => r89c3<>3
Locked Pair: 6,7 in r89c3 => r26c3,r79c2<>6, r25c3,r9c2<>7
Almost Locked Set Chain: 8- r2c13789 {345678} -6- r3c2 {67} -7- r126c1 {3678} -3- r289c3 {3678} -8 => r2c4<>8
Forcing Chain Contradiction in c6 => r4c6<>2
r4c6=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r4c6=2 r4c6<>3
r4c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r4c6=2 r4c6<>5 r8c6=5 r8c6<>4 r7c6=4 r7c6<>3
r4c6=2 r4c6<>5 r8c6=5 r8c6<>3
Forcing Chain Contradiction in r4 => r7c4<>3
r7c4=3 r2c4<>3 r2c4=6 r2c1<>6 r6c1=6 r4c2<>6
r7c4=3 r2c4<>3 r2c4=6 r4c4<>6
r7c4=3 r89c5<>3 r4c5=3 r4c5<>6
r7c4=3 r7c23<>3 r9c2=3 r9c2<>4 r9c8=4 r8c8<>4 r8c6=4 r8c6<>5 r4c6=5 r4c6<>6
Forcing Chain Contradiction in c6 => r7c6<>2
r7c6=2 r56c6<>2 r4c45=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r7c6=2 r7c6<>4 r8c6=4 r8c6<>5 r4c6=5 r4c6<>3
r7c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r7c6=2 r7c6<>3
r7c6=2 r7c6<>4 r8c6=4 r8c6<>3
Empty Rectangle: 2 in b8 (r18c7) => r1c4<>2
Forcing Chain Contradiction in c5 => r2c8<>8
r2c8=8 r2c3<>8 r2c3=3 r12c1<>3 r5c1=3 r5c1<>7 r5c9=7 r5c9<>2 r4c89=2 r4c45<>2 r56c6=2 r13c6<>2 r3c5=2 r3c5<>8
r2c8=8 r2c3<>8 r2c3=3 r12c1<>3 r5c1=3 r5c1<>7 r5c9=7 r5c9<>8 r4c89=8 r4c5<>8
r2c8=8 r12c7<>8 r9c7=8 r9c5<>8
Forcing Chain Contradiction in c6 => r8c6<>2
r8c6=2 r78c4<>2 r4c4=2 r4c89<>2 r5c9=2 r5c9<>7 r5c1=7 r4c2<>7 r3c2=7 r3c2<>6 r2c1=6 r2c4<>6 r2c4=3 r1c6<>3
r8c6=2 r8c6<>5 r4c6=5 r4c6<>3
r8c6=2 r6c6<>2 r6c3=2 r6c3<>1 r7c3=1 r7c3<>3 r79c2=3 r4c2<>3 r4c456=3 r5c6<>3
r8c6=2 r8c6<>4 r7c6=4 r7c6<>3
r8c6=2 r8c6<>3
Forcing Chain Contradiction in r8c5 => r9c4<>3
r9c4=3 r2c4<>3 r2c4=6 r2c1<>6 r3c2=6 r3c2<>7 r4c2=7 r5c1<>7 r5c9=7 r5c9<>2 r4c89=2 r4c4<>2 r78c4=2 r8c5<>2
r9c4=3 r8c5<>3
r9c4=3 r9c4<>7 r9c3=7 r9c3<>6 r8c3=6 r8c5<>6
Forcing Net Contradiction in r4 => r1c7=2
r1c7<>2 (r1c7=8 r2c7<>8 r2c7=5 r9c7<>5 r9c7=3 r9c2<>3 r9c2=4 r7c2<>4) r1c6=2 r6c6<>2 r6c3=2 r6c3<>1 r6c2=1 r7c2<>1 r7c2=3 r4c2<>3
r1c7<>2 r1c6=2 r1c6<>3 r12c4=3 r4c4<>3
r1c7<>2 (r1c6=2 r3c5<>2) r8c7=2 r8c5<>2 r4c5=2 r4c5<>3
r1c7<>2 r1c6=2 (r1c6<>7) (r1c6<>7) (r5c6<>2) r6c6<>2 r6c3=2 r5c3<>2 r5c9=2 r5c9<>7 r5c1=7 r1c1<>7 r1c4=7 r3c6<>7 r8c6=7 r8c6<>5 r4c6=5 r4c6<>3
Grouped Discontinuous Nice Loop: 8 r3c5 -8- r3c8 -7- r3c2 =7= r4c2 -7- r5c1 =7= r5c9 =2= r4c89 -2- r4c45 =2= r56c6 -2- r3c6 =2= r3c5 => r3c5<>8
Empty Rectangle: 8 in b5 (r3c68) => r4c8<>8
Locked Candidates Type 1 (Pointing): 8 in b6 => r7c9<>8
Finned Jellyfish: 8 r1367 c1468 fr6c3 => r5c1<>8
XYZ-Wing: 3/7/8 in r15c1,r2c3 => r2c1<>3
Multi Colors 1: 8 (r2c7,r3c6) / (r3c8,r9c7), (r4c5) / (r9c5) => r456c6<>8
Locked Candidates Type 1 (Pointing): 8 in b5 => r4c9<>8
Hidden Single: r5c9=8
Hidden Single: r5c1=7
Hidden Single: r3c2=7
Naked Single: r3c8=8
Naked Single: r2c7=5
Naked Single: r8c7=3
Full House: r9c7=8
Hidden Single: r1c1=3
Naked Single: r2c3=8
Full House: r2c1=6
Full House: r6c1=8
Naked Single: r2c4=3
Hidden Single: r4c5=8
Hidden Single: r9c5=3
Naked Single: r9c2=4
Locked Candidates Type 1 (Pointing): 2 in b6 => r4c4<>2
Locked Candidates Type 1 (Pointing): 2 in b5 => r3c6<>2
Naked Single: r3c6=6
Full House: r3c5=2
Full House: r8c5=6
Naked Single: r6c6=2
Naked Single: r8c3=7
Naked Single: r5c6=3
Full House: r5c3=2
Naked Single: r6c3=1
Full House: r6c2=6
Full House: r4c2=3
Full House: r7c2=1
Naked Single: r9c3=6
Full House: r7c3=3
Naked Single: r4c6=5
Full House: r4c4=6
Naked Single: r9c8=5
Full House: r9c4=7
Naked Single: r8c6=4
Naked Single: r1c4=8
Full House: r1c6=7
Full House: r7c6=8
Naked Single: r8c8=2
Full House: r8c4=5
Full House: r7c4=2
Naked Single: r4c8=7
Full House: r4c9=2
Naked Single: r7c9=4
Full House: r2c9=7
Full House: r2c8=4
Full House: r7c8=6
|
sudoku_normal_hard_101
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..1..7..2....1..5.9..3..1...95683...624179....834526...4.79...1.19..4.7.5..8.19..
|
851967432436218759972345168795683214624179385183452697348796521219534876567821943
|
. . 1 . . 7 . . 2
. . . . 1 . . 5 .
9 . . 3 . . 1 . .
. 9 5 6 8 3 . . .
6 2 4 1 7 9 . . .
. 8 3 4 5 2 6 . .
. 4 . 7 9 . . . 1
. 1 9 . . 4 . 7 .
5 . . 8 . 1 9 . .
|
8 5 1 9 6 7 4 3 2
4 3 6 2 1 8 7 5 9
9 7 2 3 4 5 1 6 8
7 9 5 6 8 3 2 1 4
6 2 4 1 7 9 3 8 5
1 8 3 4 5 2 6 9 7
3 4 8 7 9 6 5 2 1
2 1 9 5 3 4 8 7 6
5 6 7 8 2 1 9 4 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4370_hard
|
851967432436218759972345168795683214624179385183452697348796521219534876567821943 #1 Extreme (23442) bf
Brute Force: r5c5=7
Hidden Single: r7c4=7
Locked Candidates Type 1 (Pointing): 7 in b4 => r2c1<>7
Forcing Net Contradiction in r3 => r4c8<>8
r4c8=8 r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r3c3<>4
r4c8=8 r4c5<>8 r4c5=4 r3c5<>4
r4c8=8 (r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r5c7<>4) (r4c9<>8) r4c5<>8 r4c5=4 (r4c7<>4) r4c9<>4 r4c9=7 r4c7<>7 r2c7=7 r2c7<>4 r1c7=4 r3c8<>4
r4c8=8 (r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r5c7<>4) (r4c9<>8) r4c5<>8 r4c5=4 (r4c7<>4) r4c9<>4 r4c9=7 r4c7<>7 r2c7=7 r2c7<>4 r1c7=4 r3c9<>4
Forcing Net Contradiction in c8 => r5c9<>4
r5c9=4 r5c9<>5 (r8c9=5 r8c4<>5 r1c4=5 r1c4<>9) r5c7=5 r7c7<>5 r7c6=5 r7c6<>9 r7c5=9 r1c5<>9 r1c8=9
r5c9=4 (r6c8<>4) r5c3<>4 r5c3=2 r5c2<>2 r5c2=1 r4c1<>1 r4c8=1 r6c8<>1 r6c8=9
Brute Force: r5c4=1
Naked Single: r5c2=2
Naked Single: r5c3=4
Hidden Single: r9c6=1
Hidden Single: r8c2=1
Finned Swordfish: 4 r349 c589 fr4c7 => r6c89<>4
Hidden Single: r6c4=4
Naked Single: r4c5=8
Full House: r5c6=9
Hidden Single: r7c5=9
Discontinuous Nice Loop: 4 r1c8 -4- r9c8 =4= r9c9 -4- r4c9 -7- r6c9 -9- r6c8 =9= r1c8 => r1c8<>4
Discontinuous Nice Loop: 2 r2c1 -2- r2c4 =2= r3c5 =4= r1c5 -4- r1c1 =4= r2c1 => r2c1<>2
Locked Candidates Type 1 (Pointing): 2 in b1 => r79c3<>2
Continuous Nice Loop: 2/3/4/6/7 4= r9c8 =2= r9c5 -2- r3c5 =2= r2c4 =9= r2c9 -9- r6c9 -7- r4c9 -4- r9c9 =4= r9c8 =2 => r8c5<>2, r9c8<>3, r3c9<>4, r9c8<>6, r3c9,r4c7<>7
Hidden Single: r2c7=7
Hidden Rectangle: 6/7 in r3c23,r9c23 => r3c2<>6
Sue de Coq: r3c56 - {24568} (r3c89 - {468}, r12c4 - {259}) => r3c3<>6, r3c3<>8
AIC: 6 6- r1c5 -4- r1c7 =4= r4c7 =2= r4c8 -2- r9c8 =2= r9c5 -2- r8c4 -5- r7c6 -6 => r23c6,r89c5<>6
Naked Single: r2c6=8
Naked Single: r8c5=3
Naked Single: r3c6=5
Full House: r7c6=6
Naked Single: r9c5=2
Full House: r8c4=5
Naked Single: r1c4=9
Full House: r2c4=2
Naked Single: r3c2=7
Naked Single: r7c3=8
Naked Single: r9c8=4
Naked Single: r2c3=6
Naked Single: r3c3=2
Full House: r9c3=7
Naked Single: r8c1=2
Naked Single: r2c2=3
Naked Single: r7c1=3
Full House: r9c2=6
Full House: r1c2=5
Full House: r9c9=3
Naked Single: r8c7=8
Full House: r8c9=6
Naked Single: r2c1=4
Full House: r1c1=8
Full House: r2c9=9
Naked Single: r7c8=2
Full House: r7c7=5
Naked Single: r3c9=8
Naked Single: r6c9=7
Naked Single: r4c8=1
Naked Single: r5c7=3
Naked Single: r3c8=6
Full House: r3c5=4
Full House: r1c5=6
Naked Single: r5c9=5
Full House: r4c9=4
Full House: r5c8=8
Naked Single: r6c1=1
Full House: r4c1=7
Full House: r6c8=9
Full House: r1c8=3
Full House: r1c7=4
Full House: r4c7=2
|
sudoku_normal_extremely_hard_101
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..1..7..2....1..5.9..3..1...956.3...6.........83.526...4......1..9..4.7.5..8..9..
|
851967432436218759972345168795683214624179385183452697348796521219534876567821943
|
. . 1 . . 7 . . 2
. . . . 1 . . 5 .
9 . . 3 . . 1 . .
. 9 5 6 . 3 . . .
6 . . . . . . . .
. 8 3 . 5 2 6 . .
. 4 . . . . . . 1
. . 9 . . 4 . 7 .
5 . . 8 . . 9 . .
|
8 5 1 9 6 7 4 3 2
4 3 6 2 1 8 7 5 9
9 7 2 3 4 5 1 6 8
7 9 5 6 8 3 2 1 4
6 2 4 1 7 9 3 8 5
1 8 3 4 5 2 6 9 7
3 4 8 7 9 6 5 2 1
2 1 9 5 3 4 8 7 6
5 6 7 8 2 1 9 4 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4370_hard
|
851967432436218759972345168795683214624179385183452697348796521219534876567821943 #1 Extreme (23442) bf
Brute Force: r5c5=7
Hidden Single: r7c4=7
Locked Candidates Type 1 (Pointing): 7 in b4 => r2c1<>7
Forcing Net Contradiction in r3 => r4c8<>8
r4c8=8 r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r3c3<>4
r4c8=8 r4c5<>8 r4c5=4 r3c5<>4
r4c8=8 (r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r5c7<>4) (r4c9<>8) r4c5<>8 r4c5=4 (r4c7<>4) r4c9<>4 r4c9=7 r4c7<>7 r2c7=7 r2c7<>4 r1c7=4 r3c8<>4
r4c8=8 (r4c8<>1 r4c1=1 r5c2<>1 r5c2=2 r5c3<>2 r5c3=4 r5c7<>4) (r4c9<>8) r4c5<>8 r4c5=4 (r4c7<>4) r4c9<>4 r4c9=7 r4c7<>7 r2c7=7 r2c7<>4 r1c7=4 r3c9<>4
Forcing Net Contradiction in c8 => r5c9<>4
r5c9=4 r5c9<>5 (r8c9=5 r8c4<>5 r1c4=5 r1c4<>9) r5c7=5 r7c7<>5 r7c6=5 r7c6<>9 r7c5=9 r1c5<>9 r1c8=9
r5c9=4 (r6c8<>4) r5c3<>4 r5c3=2 r5c2<>2 r5c2=1 r4c1<>1 r4c8=1 r6c8<>1 r6c8=9
Brute Force: r5c4=1
Naked Single: r5c2=2
Naked Single: r5c3=4
Hidden Single: r9c6=1
Hidden Single: r8c2=1
Finned Swordfish: 4 r349 c589 fr4c7 => r6c89<>4
Hidden Single: r6c4=4
Naked Single: r4c5=8
Full House: r5c6=9
Hidden Single: r7c5=9
Discontinuous Nice Loop: 4 r1c8 -4- r9c8 =4= r9c9 -4- r4c9 -7- r6c9 -9- r6c8 =9= r1c8 => r1c8<>4
Discontinuous Nice Loop: 2 r2c1 -2- r2c4 =2= r3c5 =4= r1c5 -4- r1c1 =4= r2c1 => r2c1<>2
Locked Candidates Type 1 (Pointing): 2 in b1 => r79c3<>2
Continuous Nice Loop: 2/3/4/6/7 4= r9c8 =2= r9c5 -2- r3c5 =2= r2c4 =9= r2c9 -9- r6c9 -7- r4c9 -4- r9c9 =4= r9c8 =2 => r8c5<>2, r9c8<>3, r3c9<>4, r9c8<>6, r3c9,r4c7<>7
Hidden Single: r2c7=7
Hidden Rectangle: 6/7 in r3c23,r9c23 => r3c2<>6
Sue de Coq: r3c56 - {24568} (r3c89 - {468}, r12c4 - {259}) => r3c3<>6, r3c3<>8
AIC: 6 6- r1c5 -4- r1c7 =4= r4c7 =2= r4c8 -2- r9c8 =2= r9c5 -2- r8c4 -5- r7c6 -6 => r23c6,r89c5<>6
Naked Single: r2c6=8
Naked Single: r8c5=3
Naked Single: r3c6=5
Full House: r7c6=6
Naked Single: r9c5=2
Full House: r8c4=5
Naked Single: r1c4=9
Full House: r2c4=2
Naked Single: r3c2=7
Naked Single: r7c3=8
Naked Single: r9c8=4
Naked Single: r2c3=6
Naked Single: r3c3=2
Full House: r9c3=7
Naked Single: r8c1=2
Naked Single: r2c2=3
Naked Single: r7c1=3
Full House: r9c2=6
Full House: r1c2=5
Full House: r9c9=3
Naked Single: r8c7=8
Full House: r8c9=6
Naked Single: r2c1=4
Full House: r1c1=8
Full House: r2c9=9
Naked Single: r7c8=2
Full House: r7c7=5
Naked Single: r3c9=8
Naked Single: r6c9=7
Naked Single: r4c8=1
Naked Single: r5c7=3
Naked Single: r3c8=6
Full House: r3c5=4
Full House: r1c5=6
Naked Single: r5c9=5
Full House: r4c9=4
Full House: r5c8=8
Naked Single: r6c1=1
Full House: r4c1=7
Full House: r6c8=9
Full House: r1c8=3
Full House: r1c7=4
Full House: r4c7=2
|
sudoku_normal_hard_102
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7....8..3..5....6....65..1.3....4..8..7936.2..2.81.3...48..97..9.........73.....9
|
716298543835471962492653817369524178187936425524817396248369751951782634673145289
|
7 . . . . 8 . . 3
. . 5 . . . . 6 .
. . . 6 5 . . 1 .
3 . . . . 4 . . 8
. . 7 9 3 6 . 2 .
. 2 . 8 1 . 3 . .
. 4 8 . . 9 7 . .
9 . . . . . . . .
. 7 3 . . . . . 9
|
7 1 6 2 9 8 5 4 3
8 3 5 4 7 1 9 6 2
4 9 2 6 5 3 8 1 7
3 6 9 5 2 4 1 7 8
1 8 7 9 3 6 4 2 5
5 2 4 8 1 7 3 9 6
2 4 8 3 6 9 7 5 1
9 5 1 7 8 2 6 3 4
6 7 3 1 4 5 2 8 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4294_hard
|
716298543835471962492653817369524178187936425524817396248369751951782634673145289 #1 Extreme (39912) bf
Locked Candidates Type 1 (Pointing): 7 in b3 => r6c9<>7
Locked Candidates Type 1 (Pointing): 8 in b3 => r89c7<>8
Brute Force: r5c5=3
Locked Candidates Type 1 (Pointing): 8 in b5 => r89c4<>8
Brute Force: r5c6=6
Brute Force: r5c4=9
Hidden Single: r6c4=8
Forcing Net Contradiction in r9c8 => r6c8<>4
r6c8=4 r9c8<>4
r6c8=4 (r5c9<>4 r5c1=4 r5c1<>8 r5c2=8 r5c2<>5) r6c8<>7 r6c6=7 (r6c6<>5) r6c6<>5 r4c4=5 r4c2<>5 r8c2=5 r8c6<>5 r9c6=5 r9c8<>5
r6c8=4 (r6c8<>9) r6c8<>7 r6c6=7 (r4c4<>7) r4c5<>7 (r4c5=2 r9c5<>2) (r4c5=2 r7c5<>2 r7c5=6 r9c5<>6) (r4c5=2 r1c5<>2) r4c8=7 r4c8<>9 r1c8=9 r1c5<>9 r1c5=4 r9c5<>4 r9c5=8 r9c8<>8
Forcing Net Verity => r9c1<>1
r9c1=6 r9c1<>1
r9c5=6 r7c5<>6 r7c5=2 (r9c6<>2) r4c5<>2 r4c5=7 r6c6<>7 r6c6=5 r9c6<>5 r9c6=1 r9c1<>1
r9c7=6 (r9c7<>2) (r9c1<>6) (r7c9<>6) r8c9<>6 r6c9=6 r6c1<>6 r7c1=6 r7c5<>6 r7c5=2 (r9c4<>2) (r9c5<>2) r9c6<>2 r9c1=2 r9c1<>1
Forcing Chain Verity => r7c4<>1
r2c1=1 r2c6<>1 r12c4=1 r7c4<>1
r5c1=1 r5c9<>1 r45c7=1 r9c7<>1 r9c46=1 r7c4<>1
r7c1=1 r7c4<>1
Forcing Net Contradiction in c1 => r6c8<>5
r6c8=5 (r6c6<>5 r6c6=7 r4c5<>7 r4c8=7 r4c8<>9) r6c8<>9 r6c3=9 (r4c2<>9) r4c3<>9 r4c7=9 r4c7<>6 r6c9=6 r6c1<>6
r6c8=5 r6c6<>5 r6c6=7 r4c5<>7 r4c5=2 r7c5<>2 r7c5=6 r7c1<>6
r6c8=5 (r1c8<>5 r1c7=5 r1c7<>2) (r7c8<>5 r7c8=3 r7c4<>3) r6c6<>5 (r6c6=7 r4c5<>7 r4c5=2 r1c5<>2) r4c4=5 r7c4<>5 r7c4=2 (r7c1<>2) r1c4<>2 r1c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>6
Forcing Net Contradiction in c1 => r8c3<>6
r8c3=6 (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 (r6c9<>6) r6c9<>6 r7c9=6 r7c5<>6 r7c5=2 r4c5<>2 r4c5=7 r6c6<>7 r6c6=5 r6c9<>5 r6c9=4 (r5c7<>4) r5c9<>4 r5c1=4 r5c1<>5
r8c3=6 (r7c1<>6) r9c1<>6 r6c1=6 r6c1<>5
r8c3=6 (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 r6c9<>6 r7c9=6 r7c9<>1 r7c1=1 r7c1<>5
r8c3=6 (r8c2<>6) (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 r6c9<>6 r7c9=6 r7c9<>1 r7c1=1 r8c2<>1 r8c2=5 r9c1<>5
Forcing Net Contradiction in c7 => r6c1<>6
r6c1=6 (r6c3<>6 r1c3=6 r1c3<>2) (r7c1<>6) (r9c1<>6) (r4c2<>6) r4c3<>6 r4c7=6 r9c7<>6 r9c5=6 r7c5<>6 r7c9=6 r7c5<>6 r7c5=2 (r1c5<>2) r4c5<>2 r4c4=2 r1c4<>2 r1c7=2
r6c1=6 (r7c1<>6) (r9c1<>6) (r4c2<>6) r4c3<>6 r4c7=6 r9c7<>6 r9c5=6 (r9c5<>2) r7c5<>6 (r7c5=2 r9c4<>2) (r7c5=2 r9c6<>2) r7c9=6 r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r9c1<>2 r9c7=2
Locked Candidates Type 2 (Claiming): 6 in c1 => r8c2<>6
Discontinuous Nice Loop: 6 r7c9 -6- r7c5 -2- r4c5 -7- r4c8 =7= r6c8 =9= r6c3 =6= r6c9 -6- r7c9 => r7c9<>6
Forcing Net Contradiction in c6 => r5c2<>5
r5c2=5 (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r2c9=2 r2c6<>2
r5c2=5 (r6c1<>5 r6c1=4 r3c1<>4) r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c6<>2
r5c2=5 r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r8c6<>2
r5c2=5 (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c7<>2) (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r2c9=2 (r1c7<>2) r2c7<>2 r9c7=2 r9c6<>2
Turbot Fish: 5 r6c6 =5= r4c4 -5- r4c2 =5= r8c2 => r8c6<>5
Forcing Chain Contradiction in r8c9 => r8c7<>5
r8c7=5 r8c2<>5 r8c2=1 r8c9<>1
r8c7=5 r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r8c9<>2
r8c7=5 r1c7<>5 r1c8=5 r1c8<>4 r89c8=4 r8c9<>4
r8c7=5 r8c9<>5
r8c7=5 r8c2<>5 r4c2=5 r4c4<>5 r6c6=5 r6c6<>7 r6c8=7 r6c8<>9 r6c3=9 r6c3<>6 r6c9=6 r8c9<>6
Forcing Net Contradiction in r1c2 => r1c3<>9
r1c3=9 (r1c8<>9) (r3c2<>9 r4c2=9 r4c2<>5 r8c2=5 r7c1<>5) (r3c2<>9 r4c2=9 r4c2<>5 r8c2=5 r8c9<>5) (r1c3<>6 r1c2=6 r1c2<>1 r1c4=1 r9c4<>1) r6c3<>9 r6c8=9 r6c8<>7 r6c6=7 (r4c5<>7 r4c5=2 r1c5<>2) (r4c5<>7 r4c5=2 r1c5<>2 r1c7=2 r8c7<>2) (r4c5<>7 r4c5=2 r1c5<>2 r1c7=2 r9c7<>2) r6c6<>5 r9c6=5 r9c6<>1 r9c7=1 (r8c9<>1 r5c9=1 r5c9<>5) r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r8c9<>2 r7c9=2 (r7c9<>5) r7c9<>5 r6c9=5 r6c6<>5 r9c6=5 r7c4<>5 r7c8=5 r1c8<>5 r1c8=4 r1c5<>4 r1c5=9 r1c3<>9
Forcing Net Verity => r1c7<>2
r7c8=5 r1c8<>5 r1c7=5 r1c7<>2
r7c9=5 (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c4<>2) (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c5<>2) (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c6<>2) r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r9c1<>2 r9c7=2 r1c7<>2
r8c8=5 r1c8<>5 r1c7=5 r1c7<>2
r8c9=5 (r8c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) r7c1<>1 r7c9=1 r7c9<>2 r9c7=2 r1c7<>2
r9c7=5 (r4c7<>5) (r1c7<>5 r1c8=5 r4c8<>5) r9c6<>5 r6c6=5 r4c4<>5 r4c2=5 r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r9c7=2 r1c7<>2
r9c8=5 r1c8<>5 r1c7=5 r1c7<>2
Grouped Discontinuous Nice Loop: 5 r9c1 -5- r8c2 -1- r8c3 -2- r1c3 =2= r1c45 -2- r23c6 =2= r89c6 -2- r7c5 -6- r7c1 =6= r9c1 => r9c1<>5
Forcing Chain Contradiction in r7c4 => r8c2=5
r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r1c3<>2 r1c45=2 r23c6<>2 r89c6=2 r7c4<>2
r8c2<>5 r7c1=5 r7c8<>5 r7c8=3 r7c4<>3
r8c2<>5 r7c1=5 r7c4<>5
Finned Swordfish: 5 r147 c478 fr7c9 => r9c78<>5
Locked Candidates Type 1 (Pointing): 5 in b9 => r7c4<>5
Hidden Rectangle: 4/8 in r8c58,r9c58 => r8c5<>4
Discontinuous Nice Loop: 2 r8c5 -2- r7c4 -3- r7c8 =3= r8c8 =8= r8c5 => r8c5<>2
Discontinuous Nice Loop: 6 r8c5 -6- r7c5 -2- r7c4 -3- r7c8 =3= r8c8 =8= r8c5 => r8c5<>6
Locked Candidates Type 2 (Claiming): 6 in r8 => r9c7<>6
Uniqueness Test 6: 2/6 in r7c15,r9c15 => r7c1,r9c5<>6
Hidden Single: r7c5=6
Hidden Single: r9c1=6
Grouped AIC: 2 2- r4c5 =2= r4c4 =5= r4c78 -5- r56c9 =5= r7c9 -5- r7c8 -3- r7c4 -2 => r4c4,r9c5<>2
Hidden Single: r4c5=2
Naked Pair: 4,8 in r9c58 => r9c47<>4
Naked Triple: 4,5,9 in r1c578 => r1c2<>9, r1c34<>4
Turbot Fish: 2 r1c4 =2= r1c3 -2- r8c3 =2= r7c1 => r7c4<>2
Naked Single: r7c4=3
Naked Single: r7c8=5
Hidden Single: r8c8=3
Hidden Single: r1c7=5
Hidden Single: r8c5=8
Naked Single: r9c5=4
Naked Single: r1c5=9
Full House: r2c5=7
Naked Single: r9c8=8
Naked Single: r1c8=4
Naked Single: r2c9=2
Naked Single: r3c9=7
Naked Single: r7c9=1
Full House: r7c1=2
Full House: r8c3=1
Naked Single: r9c7=2
Hidden Single: r4c4=5
Full House: r6c6=7
Naked Single: r9c4=1
Full House: r9c6=5
Naked Single: r6c8=9
Full House: r4c8=7
Naked Single: r8c6=2
Full House: r8c4=7
Naked Single: r1c4=2
Full House: r2c4=4
Naked Single: r3c6=3
Full House: r2c6=1
Naked Single: r1c3=6
Full House: r1c2=1
Naked Single: r2c1=8
Naked Single: r4c3=9
Naked Single: r6c3=4
Full House: r3c3=2
Naked Single: r5c2=8
Naked Single: r2c7=9
Full House: r2c2=3
Full House: r3c7=8
Naked Single: r3c1=4
Full House: r3c2=9
Full House: r4c2=6
Full House: r4c7=1
Naked Single: r6c1=5
Full House: r5c1=1
Full House: r6c9=6
Naked Single: r5c7=4
Full House: r5c9=5
Full House: r8c9=4
Full House: r8c7=6
|
sudoku_normal_extremely_hard_102
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7....8..3..5....6....65..1.3....4..8..7....2..2..1.3...48..97..9.........73.....9
|
716298543835471962492653817369524178187936425524817396248369751951782634673145289
|
7 . . . . 8 . . 3
. . 5 . . . . 6 .
. . . 6 5 . . 1 .
3 . . . . 4 . . 8
. . 7 . . . . 2 .
. 2 . . 1 . 3 . .
. 4 8 . . 9 7 . .
9 . . . . . . . .
. 7 3 . . . . . 9
|
7 1 6 2 9 8 5 4 3
8 3 5 4 7 1 9 6 2
4 9 2 6 5 3 8 1 7
3 6 9 5 2 4 1 7 8
1 8 7 9 3 6 4 2 5
5 2 4 8 1 7 3 9 6
2 4 8 3 6 9 7 5 1
9 5 1 7 8 2 6 3 4
6 7 3 1 4 5 2 8 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4294_hard
|
716298543835471962492653817369524178187936425524817396248369751951782634673145289 #1 Extreme (39912) bf
Locked Candidates Type 1 (Pointing): 7 in b3 => r6c9<>7
Locked Candidates Type 1 (Pointing): 8 in b3 => r89c7<>8
Brute Force: r5c5=3
Locked Candidates Type 1 (Pointing): 8 in b5 => r89c4<>8
Brute Force: r5c6=6
Brute Force: r5c4=9
Hidden Single: r6c4=8
Forcing Net Contradiction in r9c8 => r6c8<>4
r6c8=4 r9c8<>4
r6c8=4 (r5c9<>4 r5c1=4 r5c1<>8 r5c2=8 r5c2<>5) r6c8<>7 r6c6=7 (r6c6<>5) r6c6<>5 r4c4=5 r4c2<>5 r8c2=5 r8c6<>5 r9c6=5 r9c8<>5
r6c8=4 (r6c8<>9) r6c8<>7 r6c6=7 (r4c4<>7) r4c5<>7 (r4c5=2 r9c5<>2) (r4c5=2 r7c5<>2 r7c5=6 r9c5<>6) (r4c5=2 r1c5<>2) r4c8=7 r4c8<>9 r1c8=9 r1c5<>9 r1c5=4 r9c5<>4 r9c5=8 r9c8<>8
Forcing Net Verity => r9c1<>1
r9c1=6 r9c1<>1
r9c5=6 r7c5<>6 r7c5=2 (r9c6<>2) r4c5<>2 r4c5=7 r6c6<>7 r6c6=5 r9c6<>5 r9c6=1 r9c1<>1
r9c7=6 (r9c7<>2) (r9c1<>6) (r7c9<>6) r8c9<>6 r6c9=6 r6c1<>6 r7c1=6 r7c5<>6 r7c5=2 (r9c4<>2) (r9c5<>2) r9c6<>2 r9c1=2 r9c1<>1
Forcing Chain Verity => r7c4<>1
r2c1=1 r2c6<>1 r12c4=1 r7c4<>1
r5c1=1 r5c9<>1 r45c7=1 r9c7<>1 r9c46=1 r7c4<>1
r7c1=1 r7c4<>1
Forcing Net Contradiction in c1 => r6c8<>5
r6c8=5 (r6c6<>5 r6c6=7 r4c5<>7 r4c8=7 r4c8<>9) r6c8<>9 r6c3=9 (r4c2<>9) r4c3<>9 r4c7=9 r4c7<>6 r6c9=6 r6c1<>6
r6c8=5 r6c6<>5 r6c6=7 r4c5<>7 r4c5=2 r7c5<>2 r7c5=6 r7c1<>6
r6c8=5 (r1c8<>5 r1c7=5 r1c7<>2) (r7c8<>5 r7c8=3 r7c4<>3) r6c6<>5 (r6c6=7 r4c5<>7 r4c5=2 r1c5<>2) r4c4=5 r7c4<>5 r7c4=2 (r7c1<>2) r1c4<>2 r1c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>6
Forcing Net Contradiction in c1 => r8c3<>6
r8c3=6 (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 (r6c9<>6) r6c9<>6 r7c9=6 r7c5<>6 r7c5=2 r4c5<>2 r4c5=7 r6c6<>7 r6c6=5 r6c9<>5 r6c9=4 (r5c7<>4) r5c9<>4 r5c1=4 r5c1<>5
r8c3=6 (r7c1<>6) r9c1<>6 r6c1=6 r6c1<>5
r8c3=6 (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 r6c9<>6 r7c9=6 r7c9<>1 r7c1=1 r7c1<>5
r8c3=6 (r8c2<>6) (r8c9<>6) (r7c1<>6) r9c1<>6 r6c1=6 r6c9<>6 r7c9=6 r7c9<>1 r7c1=1 r8c2<>1 r8c2=5 r9c1<>5
Forcing Net Contradiction in c7 => r6c1<>6
r6c1=6 (r6c3<>6 r1c3=6 r1c3<>2) (r7c1<>6) (r9c1<>6) (r4c2<>6) r4c3<>6 r4c7=6 r9c7<>6 r9c5=6 r7c5<>6 r7c9=6 r7c5<>6 r7c5=2 (r1c5<>2) r4c5<>2 r4c4=2 r1c4<>2 r1c7=2
r6c1=6 (r7c1<>6) (r9c1<>6) (r4c2<>6) r4c3<>6 r4c7=6 r9c7<>6 r9c5=6 (r9c5<>2) r7c5<>6 (r7c5=2 r9c4<>2) (r7c5=2 r9c6<>2) r7c9=6 r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r9c1<>2 r9c7=2
Locked Candidates Type 2 (Claiming): 6 in c1 => r8c2<>6
Discontinuous Nice Loop: 6 r7c9 -6- r7c5 -2- r4c5 -7- r4c8 =7= r6c8 =9= r6c3 =6= r6c9 -6- r7c9 => r7c9<>6
Forcing Net Contradiction in c6 => r5c2<>5
r5c2=5 (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r2c9=2 r2c6<>2
r5c2=5 (r6c1<>5 r6c1=4 r3c1<>4) r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c6<>2
r5c2=5 r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r8c6<>2
r5c2=5 (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c7<>2) (r5c2<>8 r5c1=8 r3c1<>8 r3c1=2 r3c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r2c9=2 (r1c7<>2) r2c7<>2 r9c7=2 r9c6<>2
Turbot Fish: 5 r6c6 =5= r4c4 -5- r4c2 =5= r8c2 => r8c6<>5
Forcing Chain Contradiction in r8c9 => r8c7<>5
r8c7=5 r8c2<>5 r8c2=1 r8c9<>1
r8c7=5 r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r8c9<>2
r8c7=5 r1c7<>5 r1c8=5 r1c8<>4 r89c8=4 r8c9<>4
r8c7=5 r8c9<>5
r8c7=5 r8c2<>5 r4c2=5 r4c4<>5 r6c6=5 r6c6<>7 r6c8=7 r6c8<>9 r6c3=9 r6c3<>6 r6c9=6 r8c9<>6
Forcing Net Contradiction in r1c2 => r1c3<>9
r1c3=9 (r1c8<>9) (r3c2<>9 r4c2=9 r4c2<>5 r8c2=5 r7c1<>5) (r3c2<>9 r4c2=9 r4c2<>5 r8c2=5 r8c9<>5) (r1c3<>6 r1c2=6 r1c2<>1 r1c4=1 r9c4<>1) r6c3<>9 r6c8=9 r6c8<>7 r6c6=7 (r4c5<>7 r4c5=2 r1c5<>2) (r4c5<>7 r4c5=2 r1c5<>2 r1c7=2 r8c7<>2) (r4c5<>7 r4c5=2 r1c5<>2 r1c7=2 r9c7<>2) r6c6<>5 r9c6=5 r9c6<>1 r9c7=1 (r8c9<>1 r5c9=1 r5c9<>5) r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r8c9<>2 r7c9=2 (r7c9<>5) r7c9<>5 r6c9=5 r6c6<>5 r9c6=5 r7c4<>5 r7c8=5 r1c8<>5 r1c8=4 r1c5<>4 r1c5=9 r1c3<>9
Forcing Net Verity => r1c7<>2
r7c8=5 r1c8<>5 r1c7=5 r1c7<>2
r7c9=5 (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c4<>2) (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c5<>2) (r7c8<>5 r7c8=3 r7c4<>3 r7c4=2 r9c6<>2) r7c9<>1 r7c1=1 r8c3<>1 r8c3=2 r9c1<>2 r9c7=2 r1c7<>2
r8c8=5 r1c8<>5 r1c7=5 r1c7<>2
r8c9=5 (r8c9<>2) r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) r7c1<>1 r7c9=1 r7c9<>2 r9c7=2 r1c7<>2
r9c7=5 (r4c7<>5) (r1c7<>5 r1c8=5 r4c8<>5) r9c6<>5 r6c6=5 r4c4<>5 r4c2=5 r8c2<>5 r8c2=1 (r8c3<>1 r8c3=2 r8c7<>2) (r8c3<>1 r8c3=2 r8c9<>2) r7c1<>1 r7c9=1 r7c9<>2 r9c7=2 r1c7<>2
r9c8=5 r1c8<>5 r1c7=5 r1c7<>2
Grouped Discontinuous Nice Loop: 5 r9c1 -5- r8c2 -1- r8c3 -2- r1c3 =2= r1c45 -2- r23c6 =2= r89c6 -2- r7c5 -6- r7c1 =6= r9c1 => r9c1<>5
Forcing Chain Contradiction in r7c4 => r8c2=5
r8c2<>5 r8c2=1 r8c3<>1 r8c3=2 r1c3<>2 r1c45=2 r23c6<>2 r89c6=2 r7c4<>2
r8c2<>5 r7c1=5 r7c8<>5 r7c8=3 r7c4<>3
r8c2<>5 r7c1=5 r7c4<>5
Finned Swordfish: 5 r147 c478 fr7c9 => r9c78<>5
Locked Candidates Type 1 (Pointing): 5 in b9 => r7c4<>5
Hidden Rectangle: 4/8 in r8c58,r9c58 => r8c5<>4
Discontinuous Nice Loop: 2 r8c5 -2- r7c4 -3- r7c8 =3= r8c8 =8= r8c5 => r8c5<>2
Discontinuous Nice Loop: 6 r8c5 -6- r7c5 -2- r7c4 -3- r7c8 =3= r8c8 =8= r8c5 => r8c5<>6
Locked Candidates Type 2 (Claiming): 6 in r8 => r9c7<>6
Uniqueness Test 6: 2/6 in r7c15,r9c15 => r7c1,r9c5<>6
Hidden Single: r7c5=6
Hidden Single: r9c1=6
Grouped AIC: 2 2- r4c5 =2= r4c4 =5= r4c78 -5- r56c9 =5= r7c9 -5- r7c8 -3- r7c4 -2 => r4c4,r9c5<>2
Hidden Single: r4c5=2
Naked Pair: 4,8 in r9c58 => r9c47<>4
Naked Triple: 4,5,9 in r1c578 => r1c2<>9, r1c34<>4
Turbot Fish: 2 r1c4 =2= r1c3 -2- r8c3 =2= r7c1 => r7c4<>2
Naked Single: r7c4=3
Naked Single: r7c8=5
Hidden Single: r8c8=3
Hidden Single: r1c7=5
Hidden Single: r8c5=8
Naked Single: r9c5=4
Naked Single: r1c5=9
Full House: r2c5=7
Naked Single: r9c8=8
Naked Single: r1c8=4
Naked Single: r2c9=2
Naked Single: r3c9=7
Naked Single: r7c9=1
Full House: r7c1=2
Full House: r8c3=1
Naked Single: r9c7=2
Hidden Single: r4c4=5
Full House: r6c6=7
Naked Single: r9c4=1
Full House: r9c6=5
Naked Single: r6c8=9
Full House: r4c8=7
Naked Single: r8c6=2
Full House: r8c4=7
Naked Single: r1c4=2
Full House: r2c4=4
Naked Single: r3c6=3
Full House: r2c6=1
Naked Single: r1c3=6
Full House: r1c2=1
Naked Single: r2c1=8
Naked Single: r4c3=9
Naked Single: r6c3=4
Full House: r3c3=2
Naked Single: r5c2=8
Naked Single: r2c7=9
Full House: r2c2=3
Full House: r3c7=8
Naked Single: r3c1=4
Full House: r3c2=9
Full House: r4c2=6
Full House: r4c7=1
Naked Single: r6c1=5
Full House: r5c1=1
Full House: r6c9=6
Naked Single: r5c7=4
Full House: r5c9=5
Full House: r8c9=4
Full House: r8c7=6
|
sudoku_normal_hard_103
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....4..2..812..3..7..689..5....92......8.....6..3...4.3..7.5....18.....4....3.2.
|
153794862698125437274368951517649283349281675862537194936472518721856349485913726
|
. . . . . 4 . . 2
. . 8 1 2 . . 3 .
. 7 . . 6 8 9 . .
5 . . . . 9 2 . .
. . . . 8 . . . .
. 6 . . 3 . . . 4
. 3 . . 7 . 5 . .
. . 1 8 . . . . .
4 . . . . 3 . 2 .
|
1 5 3 7 9 4 8 6 2
6 9 8 1 2 5 4 3 7
2 7 4 3 6 8 9 5 1
5 1 7 6 4 9 2 8 3
3 4 9 2 8 1 6 7 5
8 6 2 5 3 7 1 9 4
9 3 6 4 7 2 5 1 8
7 2 1 8 5 6 3 4 9
4 8 5 9 1 3 7 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7559_hard
|
153794862698125437274368951517649283349281675862537194936472518721856349485913726 #1 Extreme (24512) bf
AIC: 3/4 4- r3c3 =4= r3c8 -4- r2c7 =4= r8c7 =3= r8c9 -3- r4c9 =3= r4c3 -3 => r3c3<>3, r4c3<>4
Brute Force: r5c5=8
Hidden Single: r3c6=8
Finned X-Wing: 8 c29 r49 fr7c9 => r9c7<>8
Forcing Net Contradiction in r8 => r1c2<>9
r1c2=9 (r8c2<>9) (r2c1<>9) r2c2<>9 r2c5=9 r2c5<>2 r8c5=2 r8c2<>2 r8c2=5
r1c2=9 (r2c1<>9) r2c2<>9 r2c5=9 (r9c5<>9 r9c5=1 r7c6<>1) r2c5<>2 r8c5=2 (r8c6<>2) r7c6<>2 r7c6=6 r8c6<>6 r8c6=5
Forcing Net Verity => r1c1<>9
r4c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
r4c5=1 r4c5<>4 r8c5=4 r8c5<>2 r2c5=2 r2c5<>9 r1c45=9 r1c1<>9
r4c8=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
r4c9=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
Forcing Net Verity => r1c3<>9
r4c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
r4c5=1 r4c5<>4 r8c5=4 r8c5<>2 r2c5=2 r2c5<>9 r1c45=9 r1c3<>9
r4c8=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
r4c9=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r2c5<>9
Forcing Net Contradiction in c4 => r1c7<>1
r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c4<>9
r1c7=1 (r3c8<>1) r3c9<>1 r3c9=5 r3c8<>5 r3c8=4 r7c8<>4 r7c4=4 r7c4<>9
r1c7=1 (r1c2<>1 r1c2=5 r9c2<>5) r1c7<>8 (r1c8=8 r4c8<>8) r6c7=8 r4c9<>8 r4c2=8 r9c2<>8 r9c2=9 r9c4<>9
Sashimi X-Wing: 1 c57 r49 fr5c7 fr6c7 => r4c89<>1
Discontinuous Nice Loop: 5 r3c3 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 -4- r8c7 =4= r2c7 -4- r2c2 =4= r3c3 => r3c3<>5
Discontinuous Nice Loop: 9 r8c5 -9- r1c5 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 => r8c5<>9
Grouped Discontinuous Nice Loop: 6 r8c1 -6- r12c1 =6= r1c3 =5= r9c3 =7= r8c1 => r8c1<>6
Grouped Discontinuous Nice Loop: 6 r7c6 -6- r7c13 =6= r9c3 =5= r1c3 -5- r1c2 -1- r4c2 =1= r4c5 -1- r9c5 =1= r7c6 => r7c6<>6
AIC: 2 2- r2c5 =2= r8c5 =4= r4c5 =1= r9c5 -1- r7c6 -2 => r2c6,r8c5<>2
Hidden Single: r2c5=2
Finned X-Wing: 5 c35 r19 fr8c5 => r9c4<>5
Discontinuous Nice Loop: 2 r6c1 -2- r3c1 =2= r3c3 =4= r3c8 -4- r7c8 =4= r7c4 -4- r8c5 =4= r4c5 =1= r4c2 =8= r6c1 => r6c1<>2
Discontinuous Nice Loop: 2 r7c1 -2- r7c6 -1- r9c5 =1= r4c5 =4= r8c5 -4- r8c7 =4= r2c7 -4- r2c2 =4= r3c3 =2= r3c1 -2- r7c1 => r7c1<>2
Discontinuous Nice Loop: 2 r8c1 -2- r3c1 =2= r3c3 =4= r3c8 -4- r7c8 =4= r7c4 -4- r8c5 =4= r4c5 =1= r4c2 -1- r1c2 -5- r1c3 =5= r9c3 =7= r8c1 => r8c1<>2
Grouped Discontinuous Nice Loop: 5 r1c8 -5- r1c23 =5= r2c2 =4= r3c3 =2= r3c1 =3= r3c4 =5= r3c89 -5- r1c8 => r1c8<>5
Grouped Discontinuous Nice Loop: 6 r7c8 -6- r7c13 =6= r9c3 =5= r1c3 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 -4- r7c4 =4= r7c8 => r7c8<>6
Forcing Chain Contradiction in r9c5 => r1c4<>5
r1c4=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r9c5<>1
r1c4=5 r1c3<>5 r9c3=5 r9c5<>5
r1c4=5 r1c4<>9 r1c5=9 r9c5<>9
Forcing Chain Contradiction in r9c5 => r5c2<>1
r5c2=1 r4c2<>1 r4c5=1 r9c5<>1
r5c2=1 r5c2<>2 r8c2=2 r8c2<>5 r8c56=5 r9c5<>5
r5c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r9c5<>9
Forcing Chain Contradiction in r8 => r5c6<>2
r5c6=2 r5c2<>2 r8c2=2 r8c2<>5
r5c6=2 r56c4<>2 r7c4=2 r7c4<>4 r8c5=4 r8c5<>5
r5c6=2 r5c6<>6 r8c6=6 r8c6<>5
Forcing Chain Contradiction in r5c2 => r5c6<>5
r5c6=5 r5c6<>6 r8c6=6 r8c6<>2 r8c2=2 r5c2<>2
r5c6=5 r56c4<>5 r3c4=5 r3c4<>3 r3c1=3 r3c1<>2 r3c3=2 r3c3<>4 r5c3=4 r5c2<>4
r5c6=5 r5c89<>5 r6c8=5 r6c8<>9 r5c89=9 r5c2<>9
Forcing Chain Verity => r7c8<>9
r8c1=9 r8c1<>7 r9c3=7 r9c3<>5 r1c3=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r4c5<>4 r8c5=4 r7c4<>4 r7c8=4 r7c8<>9
r8c2=9 r8c2<>2 r8c6=2 r7c6<>2 r7c6=1 r9c5<>1 r4c5=1 r4c5<>4 r8c5=4 r7c4<>4 r7c8=4 r7c8<>9
r8c8=9 r7c8<>9
r8c9=9 r7c8<>9
Forcing Chain Contradiction in r8 => r7c9<>6
r7c9=6 r8c789<>6 r8c6=6 r8c6<>2 r8c2=2 r8c2<>5
r7c9=6 r7c13<>6 r9c3=6 r9c3<>5 r1c3=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r4c5<>4 r8c5=4 r8c5<>5
r7c9=6 r8c789<>6 r8c6=6 r8c6<>5
Forcing Chain Contradiction in r7c9 => r6c1<>9
r6c1=9 r6c1<>8 r4c2=8 r4c2<>1 r4c5=1 r9c5<>1 r7c6=1 r7c9<>1
r6c1=9 r6c1<>8 r7c1=8 r7c9<>8
r6c1=9 r56c3<>9 r79c3=9 r8c12<>9 r8c89=9 r7c9<>9
Forcing Chain Contradiction in r2c2 => r8c2<>9
r8c2=9 r8c2<>2 r7c3=2 r3c3<>2 r3c3=4 r2c2<>4
r8c2=9 r8c2<>2 r8c6=2 r8c6<>5 r89c5=5 r1c5<>5 r1c23=5 r2c2<>5
r8c2=9 r2c2<>9
Almost Locked Set XY-Wing: A=r8c256789 {2345679}, B=r9c23457 {156789}, C=r278c1 {6789}, X,Y=7,8, Z=9 => r9c9<>9
Forcing Chain Contradiction in r2c9 => r8c9<>7
r8c9=7 r8c9<>3 r8c7=3 r8c7<>4 r2c7=4 r2c2<>4 r3c3=4 r3c3<>2 r3c1=2 r3c1<>3 r3c4=3 r3c4<>5 r3c89=5 r2c9<>5
r8c9=7 r8c1<>7 r8c1=9 r2c1<>9 r2c1=6 r2c9<>6
r8c9=7 r2c9<>7
Forcing Chain Contradiction in r9c5 => r9c2<>5
r9c2=5 r9c2<>8 r4c2=8 r4c2<>1 r4c5=1 r9c5<>1
r9c2=5 r9c5<>5
r9c2=5 r9c3<>5 r1c3=5 r1c5<>5 r1c5=9 r9c5<>9
XYZ-Wing: 6/8/9 in r27c1,r9c2 => r8c1<>9
Naked Single: r8c1=7
Locked Candidates Type 2 (Claiming): 9 in r8 => r7c9<>9
AIC: 1/8 1- r4c2 =1= r4c5 -1- r9c5 =1= r7c6 -1- r7c9 -8- r7c1 =8= r6c1 -8 => r6c1<>1, r4c2<>8
Naked Single: r6c1=8
Hidden Single: r9c2=8
Hidden Single: r1c7=8
Naked Pair: 1,4 in r4c25 => r4c4<>4
Naked Pair: 6,9 in r27c1 => r1c1<>6, r5c1<>9
Discontinuous Nice Loop: 6/7 r2c7 =4= r2c2 =9= r5c2 -9- r5c9 =9= r8c9 =3= r8c7 =4= r2c7 => r2c7<>6, r2c7<>7
Naked Single: r2c7=4
Hidden Single: r3c3=4
Hidden Single: r3c1=2
Hidden Single: r3c4=3
Locked Candidates Type 1 (Pointing): 1 in b1 => r1c8<>1
Locked Candidates Type 2 (Claiming): 5 in r3 => r2c9<>5
Locked Candidates Type 2 (Claiming): 5 in c4 => r6c6<>5
Naked Triple: 6,7,9 in r149c4 => r57c4<>6, r56c4<>7, r7c4<>9
Locked Candidates Type 1 (Pointing): 9 in b8 => r9c3<>9
Locked Candidates Type 2 (Claiming): 6 in r7 => r9c3<>6
Naked Single: r9c3=5
Naked Single: r8c2=2
2-String Kite: 7 in r2c9,r4c4 (connected by r1c4,r2c6) => r4c9<>7
W-Wing: 6/7 in r2c9,r4c4 connected by 7 in r1c48 => r4c9<>6
2-String Kite: 6 in r4c8,r8c6 (connected by r4c4,r5c6) => r8c8<>6
XY-Wing: 3/6/7 in r1c38,r4c3 => r4c8<>7
XY-Wing: 5/7/6 in r2c69,r8c6 => r8c9<>6
Finned Swordfish: 1 r367 c689 fr6c7 => r5c89<>1
XY-Chain: 3 3- r4c9 -8- r7c9 -1- r7c6 -2- r7c4 -4- r8c5 -5- r1c5 -9- r9c5 -1- r4c5 -4- r4c2 -1- r5c1 -3 => r4c3,r5c79<>3
Naked Single: r4c3=7
Naked Single: r4c4=6
Naked Single: r4c8=8
Naked Single: r9c4=9
Naked Single: r4c9=3
Naked Single: r1c4=7
Naked Single: r9c5=1
Naked Single: r8c9=9
Naked Single: r1c8=6
Naked Single: r2c6=5
Full House: r1c5=9
Naked Single: r4c5=4
Full House: r4c2=1
Full House: r8c5=5
Naked Single: r7c6=2
Naked Single: r8c8=4
Naked Single: r1c3=3
Naked Single: r2c9=7
Naked Single: r2c2=9
Full House: r2c1=6
Naked Single: r8c6=6
Full House: r7c4=4
Full House: r8c7=3
Naked Single: r1c2=5
Full House: r1c1=1
Full House: r5c2=4
Naked Single: r5c1=3
Full House: r7c1=9
Full House: r7c3=6
Naked Single: r7c8=1
Full House: r7c9=8
Naked Single: r9c9=6
Full House: r9c7=7
Naked Single: r3c8=5
Full House: r3c9=1
Full House: r5c9=5
Naked Single: r6c7=1
Full House: r5c7=6
Naked Single: r5c4=2
Full House: r6c4=5
Naked Single: r6c6=7
Full House: r5c6=1
Naked Single: r5c3=9
Full House: r5c8=7
Full House: r6c8=9
Full House: r6c3=2
|
sudoku_normal_extremely_hard_103
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....4..2..81...3..7..6.9..5....92............6..3...4.3..7.5....18.....4....3.2.
|
153794862698125437274368951517649283349281675862537194936472518721856349485913726
|
. . . . . 4 . . 2
. . 8 1 . . . 3 .
. 7 . . 6 . 9 . .
5 . . . . 9 2 . .
. . . . . . . . .
. 6 . . 3 . . . 4
. 3 . . 7 . 5 . .
. . 1 8 . . . . .
4 . . . . 3 . 2 .
|
1 5 3 7 9 4 8 6 2
6 9 8 1 2 5 4 3 7
2 7 4 3 6 8 9 5 1
5 1 7 6 4 9 2 8 3
3 4 9 2 8 1 6 7 5
8 6 2 5 3 7 1 9 4
9 3 6 4 7 2 5 1 8
7 2 1 8 5 6 3 4 9
4 8 5 9 1 3 7 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7559_hard
|
153794862698125437274368951517649283349281675862537194936472518721856349485913726 #1 Extreme (24512) bf
AIC: 3/4 4- r3c3 =4= r3c8 -4- r2c7 =4= r8c7 =3= r8c9 -3- r4c9 =3= r4c3 -3 => r3c3<>3, r4c3<>4
Brute Force: r5c5=8
Hidden Single: r3c6=8
Finned X-Wing: 8 c29 r49 fr7c9 => r9c7<>8
Forcing Net Contradiction in r8 => r1c2<>9
r1c2=9 (r8c2<>9) (r2c1<>9) r2c2<>9 r2c5=9 r2c5<>2 r8c5=2 r8c2<>2 r8c2=5
r1c2=9 (r2c1<>9) r2c2<>9 r2c5=9 (r9c5<>9 r9c5=1 r7c6<>1) r2c5<>2 r8c5=2 (r8c6<>2) r7c6<>2 r7c6=6 r8c6<>6 r8c6=5
Forcing Net Verity => r1c1<>9
r4c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
r4c5=1 r4c5<>4 r8c5=4 r8c5<>2 r2c5=2 r2c5<>9 r1c45=9 r1c1<>9
r4c8=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
r4c9=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c1<>9
Forcing Net Verity => r1c3<>9
r4c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
r4c5=1 r4c5<>4 r8c5=4 r8c5<>2 r2c5=2 r2c5<>9 r1c45=9 r1c3<>9
r4c8=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
r4c9=1 (r5c7<>1) (r6c7<>1) r4c5<>1 r9c5=1 r9c7<>1 r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c3<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r2c5<>9
Forcing Net Contradiction in c4 => r1c7<>1
r1c7=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r1c4<>9
r1c7=1 (r3c8<>1) r3c9<>1 r3c9=5 r3c8<>5 r3c8=4 r7c8<>4 r7c4=4 r7c4<>9
r1c7=1 (r1c2<>1 r1c2=5 r9c2<>5) r1c7<>8 (r1c8=8 r4c8<>8) r6c7=8 r4c9<>8 r4c2=8 r9c2<>8 r9c2=9 r9c4<>9
Sashimi X-Wing: 1 c57 r49 fr5c7 fr6c7 => r4c89<>1
Discontinuous Nice Loop: 5 r3c3 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 -4- r8c7 =4= r2c7 -4- r2c2 =4= r3c3 => r3c3<>5
Discontinuous Nice Loop: 9 r8c5 -9- r1c5 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 => r8c5<>9
Grouped Discontinuous Nice Loop: 6 r8c1 -6- r12c1 =6= r1c3 =5= r9c3 =7= r8c1 => r8c1<>6
Grouped Discontinuous Nice Loop: 6 r7c6 -6- r7c13 =6= r9c3 =5= r1c3 -5- r1c2 -1- r4c2 =1= r4c5 -1- r9c5 =1= r7c6 => r7c6<>6
AIC: 2 2- r2c5 =2= r8c5 =4= r4c5 =1= r9c5 -1- r7c6 -2 => r2c6,r8c5<>2
Hidden Single: r2c5=2
Finned X-Wing: 5 c35 r19 fr8c5 => r9c4<>5
Discontinuous Nice Loop: 2 r6c1 -2- r3c1 =2= r3c3 =4= r3c8 -4- r7c8 =4= r7c4 -4- r8c5 =4= r4c5 =1= r4c2 =8= r6c1 => r6c1<>2
Discontinuous Nice Loop: 2 r7c1 -2- r7c6 -1- r9c5 =1= r4c5 =4= r8c5 -4- r8c7 =4= r2c7 -4- r2c2 =4= r3c3 =2= r3c1 -2- r7c1 => r7c1<>2
Discontinuous Nice Loop: 2 r8c1 -2- r3c1 =2= r3c3 =4= r3c8 -4- r7c8 =4= r7c4 -4- r8c5 =4= r4c5 =1= r4c2 -1- r1c2 -5- r1c3 =5= r9c3 =7= r8c1 => r8c1<>2
Grouped Discontinuous Nice Loop: 5 r1c8 -5- r1c23 =5= r2c2 =4= r3c3 =2= r3c1 =3= r3c4 =5= r3c89 -5- r1c8 => r1c8<>5
Grouped Discontinuous Nice Loop: 6 r7c8 -6- r7c13 =6= r9c3 =5= r1c3 -5- r1c2 -1- r4c2 =1= r4c5 =4= r8c5 -4- r7c4 =4= r7c8 => r7c8<>6
Forcing Chain Contradiction in r9c5 => r1c4<>5
r1c4=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r9c5<>1
r1c4=5 r1c3<>5 r9c3=5 r9c5<>5
r1c4=5 r1c4<>9 r1c5=9 r9c5<>9
Forcing Chain Contradiction in r9c5 => r5c2<>1
r5c2=1 r4c2<>1 r4c5=1 r9c5<>1
r5c2=1 r5c2<>2 r8c2=2 r8c2<>5 r8c56=5 r9c5<>5
r5c2=1 r1c2<>1 r1c2=5 r1c5<>5 r1c5=9 r9c5<>9
Forcing Chain Contradiction in r8 => r5c6<>2
r5c6=2 r5c2<>2 r8c2=2 r8c2<>5
r5c6=2 r56c4<>2 r7c4=2 r7c4<>4 r8c5=4 r8c5<>5
r5c6=2 r5c6<>6 r8c6=6 r8c6<>5
Forcing Chain Contradiction in r5c2 => r5c6<>5
r5c6=5 r5c6<>6 r8c6=6 r8c6<>2 r8c2=2 r5c2<>2
r5c6=5 r56c4<>5 r3c4=5 r3c4<>3 r3c1=3 r3c1<>2 r3c3=2 r3c3<>4 r5c3=4 r5c2<>4
r5c6=5 r5c89<>5 r6c8=5 r6c8<>9 r5c89=9 r5c2<>9
Forcing Chain Verity => r7c8<>9
r8c1=9 r8c1<>7 r9c3=7 r9c3<>5 r1c3=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r4c5<>4 r8c5=4 r7c4<>4 r7c8=4 r7c8<>9
r8c2=9 r8c2<>2 r8c6=2 r7c6<>2 r7c6=1 r9c5<>1 r4c5=1 r4c5<>4 r8c5=4 r7c4<>4 r7c8=4 r7c8<>9
r8c8=9 r7c8<>9
r8c9=9 r7c8<>9
Forcing Chain Contradiction in r8 => r7c9<>6
r7c9=6 r8c789<>6 r8c6=6 r8c6<>2 r8c2=2 r8c2<>5
r7c9=6 r7c13<>6 r9c3=6 r9c3<>5 r1c3=5 r1c2<>5 r1c2=1 r4c2<>1 r4c5=1 r4c5<>4 r8c5=4 r8c5<>5
r7c9=6 r8c789<>6 r8c6=6 r8c6<>5
Forcing Chain Contradiction in r7c9 => r6c1<>9
r6c1=9 r6c1<>8 r4c2=8 r4c2<>1 r4c5=1 r9c5<>1 r7c6=1 r7c9<>1
r6c1=9 r6c1<>8 r7c1=8 r7c9<>8
r6c1=9 r56c3<>9 r79c3=9 r8c12<>9 r8c89=9 r7c9<>9
Forcing Chain Contradiction in r2c2 => r8c2<>9
r8c2=9 r8c2<>2 r7c3=2 r3c3<>2 r3c3=4 r2c2<>4
r8c2=9 r8c2<>2 r8c6=2 r8c6<>5 r89c5=5 r1c5<>5 r1c23=5 r2c2<>5
r8c2=9 r2c2<>9
Almost Locked Set XY-Wing: A=r8c256789 {2345679}, B=r9c23457 {156789}, C=r278c1 {6789}, X,Y=7,8, Z=9 => r9c9<>9
Forcing Chain Contradiction in r2c9 => r8c9<>7
r8c9=7 r8c9<>3 r8c7=3 r8c7<>4 r2c7=4 r2c2<>4 r3c3=4 r3c3<>2 r3c1=2 r3c1<>3 r3c4=3 r3c4<>5 r3c89=5 r2c9<>5
r8c9=7 r8c1<>7 r8c1=9 r2c1<>9 r2c1=6 r2c9<>6
r8c9=7 r2c9<>7
Forcing Chain Contradiction in r9c5 => r9c2<>5
r9c2=5 r9c2<>8 r4c2=8 r4c2<>1 r4c5=1 r9c5<>1
r9c2=5 r9c5<>5
r9c2=5 r9c3<>5 r1c3=5 r1c5<>5 r1c5=9 r9c5<>9
XYZ-Wing: 6/8/9 in r27c1,r9c2 => r8c1<>9
Naked Single: r8c1=7
Locked Candidates Type 2 (Claiming): 9 in r8 => r7c9<>9
AIC: 1/8 1- r4c2 =1= r4c5 -1- r9c5 =1= r7c6 -1- r7c9 -8- r7c1 =8= r6c1 -8 => r6c1<>1, r4c2<>8
Naked Single: r6c1=8
Hidden Single: r9c2=8
Hidden Single: r1c7=8
Naked Pair: 1,4 in r4c25 => r4c4<>4
Naked Pair: 6,9 in r27c1 => r1c1<>6, r5c1<>9
Discontinuous Nice Loop: 6/7 r2c7 =4= r2c2 =9= r5c2 -9- r5c9 =9= r8c9 =3= r8c7 =4= r2c7 => r2c7<>6, r2c7<>7
Naked Single: r2c7=4
Hidden Single: r3c3=4
Hidden Single: r3c1=2
Hidden Single: r3c4=3
Locked Candidates Type 1 (Pointing): 1 in b1 => r1c8<>1
Locked Candidates Type 2 (Claiming): 5 in r3 => r2c9<>5
Locked Candidates Type 2 (Claiming): 5 in c4 => r6c6<>5
Naked Triple: 6,7,9 in r149c4 => r57c4<>6, r56c4<>7, r7c4<>9
Locked Candidates Type 1 (Pointing): 9 in b8 => r9c3<>9
Locked Candidates Type 2 (Claiming): 6 in r7 => r9c3<>6
Naked Single: r9c3=5
Naked Single: r8c2=2
2-String Kite: 7 in r2c9,r4c4 (connected by r1c4,r2c6) => r4c9<>7
W-Wing: 6/7 in r2c9,r4c4 connected by 7 in r1c48 => r4c9<>6
2-String Kite: 6 in r4c8,r8c6 (connected by r4c4,r5c6) => r8c8<>6
XY-Wing: 3/6/7 in r1c38,r4c3 => r4c8<>7
XY-Wing: 5/7/6 in r2c69,r8c6 => r8c9<>6
Finned Swordfish: 1 r367 c689 fr6c7 => r5c89<>1
XY-Chain: 3 3- r4c9 -8- r7c9 -1- r7c6 -2- r7c4 -4- r8c5 -5- r1c5 -9- r9c5 -1- r4c5 -4- r4c2 -1- r5c1 -3 => r4c3,r5c79<>3
Naked Single: r4c3=7
Naked Single: r4c4=6
Naked Single: r4c8=8
Naked Single: r9c4=9
Naked Single: r4c9=3
Naked Single: r1c4=7
Naked Single: r9c5=1
Naked Single: r8c9=9
Naked Single: r1c8=6
Naked Single: r2c6=5
Full House: r1c5=9
Naked Single: r4c5=4
Full House: r4c2=1
Full House: r8c5=5
Naked Single: r7c6=2
Naked Single: r8c8=4
Naked Single: r1c3=3
Naked Single: r2c9=7
Naked Single: r2c2=9
Full House: r2c1=6
Naked Single: r8c6=6
Full House: r7c4=4
Full House: r8c7=3
Naked Single: r1c2=5
Full House: r1c1=1
Full House: r5c2=4
Naked Single: r5c1=3
Full House: r7c1=9
Full House: r7c3=6
Naked Single: r7c8=1
Full House: r7c9=8
Naked Single: r9c9=6
Full House: r9c7=7
Naked Single: r3c8=5
Full House: r3c9=1
Full House: r5c9=5
Naked Single: r6c7=1
Full House: r5c7=6
Naked Single: r5c4=2
Full House: r6c4=5
Naked Single: r6c6=7
Full House: r5c6=1
Naked Single: r5c3=9
Full House: r5c8=7
Full House: r6c8=9
Full House: r6c3=2
|
sudoku_normal_hard_104
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7..4...95.5.7.82....2.5....5...8.7..9.36.4581.1...5...2...4.95....5.3....45....6.
|
786432195159768234432159678564381729923674581817295346271846953698523417345917862
|
7 . . 4 . . . 9 5
. 5 . 7 . 8 2 . .
. . 2 . 5 . . . .
5 . . . 8 . 7 . .
9 . 3 6 . 4 5 8 1
. 1 . . . 5 . . .
2 . . . 4 . 9 5 .
. . . 5 . 3 . . .
. 4 5 . . . . 6 .
|
7 8 6 4 3 2 1 9 5
1 5 9 7 6 8 2 3 4
4 3 2 1 5 9 6 7 8
5 6 4 3 8 1 7 2 9
9 2 3 6 7 4 5 8 1
8 1 7 2 9 5 3 4 6
2 7 1 8 4 6 9 5 3
6 9 8 5 2 3 4 1 7
3 4 5 9 1 7 8 6 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_6940_hard
|
786432195159768234432159678564381729923674581817295346271846953698523417345917862 #1 Extreme (39004) bf
Brute Force: r5c7=5
Hidden Single: r1c9=5
Hidden Single: r6c6=5
Hidden Single: r7c8=5
Brute Force: r5c6=4
Locked Candidates Type 1 (Pointing): 7 in b5 => r89c5<>7
Discontinuous Nice Loop: 9 r4c2 -9- r5c1 -8- r5c8 -2- r5c2 =2= r4c2 => r4c2<>9
Brute Force: r5c8=8
Naked Single: r5c1=9
Locked Candidates Type 1 (Pointing): 9 in b7 => r8c5<>9
Forcing Chain Contradiction in r9 => r8c2<>6
r8c2=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r46c4<>2 r9c4=2 r9c4<>9
r8c2=6 r8c2<>9 r8c3=9 r2c3<>9 r2c5=9 r9c5<>9
r8c2=6 r8c5<>6 r7c6=6 r7c6<>7 r9c6=7 r9c6<>9
Forcing Net Contradiction in r7c3 => r2c3<>4
r2c3=4 (r2c3<>9 r2c5=9 r9c5<>9) r4c3<>4 r4c3=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r9c5<>2 r9c5=1 (r7c4<>1) r7c6<>1 r7c3=1
r2c3=4 (r2c3<>9 r8c3=9 r8c3<>7) (r2c1<>4) r3c1<>4 r6c1=4 r6c1<>8 r6c3=8 r6c3<>7 r7c3=7
Locked Candidates Type 1 (Pointing): 4 in b1 => r6c1<>4
Forcing Net Contradiction in r9 => r3c1<>8
r3c1=8 (r3c1<>3) r3c1<>4 r2c1=4 r2c1<>3 r9c1=3
r3c1=8 (r3c1<>4 r2c1=4 r2c9<>4) r6c1<>8 r6c1=6 (r4c2<>6) r4c3<>6 r4c9=6 r2c9<>6 r2c9=3 r79c9<>3 r9c7=3
Forcing Net Contradiction in c5 => r9c1<>8
r9c1=8 (r6c1<>8 r6c1=6 r2c1<>6) (r6c1<>8 r6c1=6 r4c3<>6 r4c9=6 r2c9<>6) (r6c1<>8 r6c1=6 r8c1<>6 r8c1=1 r7c3<>1) (r7c3<>8) (r9c4<>8 r7c4=8 r7c9<>8) r9c1<>3 r7c2=3 r7c9<>3 r7c9=7 r7c3<>7 r7c3=6 r2c3<>6 r2c5=6
r9c1=8 r6c1<>8 (r6c1=6 r8c1<>6 r8c1=1 r8c5<>1) r6c3=8 r6c3<>7 r6c5=7 r5c5<>7 r5c5=2 r8c5<>2 r8c5=6
Forcing Net Contradiction in r8c5 => r6c1=8
r6c1<>8 (r8c1=8 r8c7<>8) r6c1=6 (r6c7<>6) (r4c2<>6 r4c2=2 r4c8<>2) r4c3<>6 r4c3=4 r4c8<>4 r4c8=3 r6c7<>3 r6c7=4 r8c7<>4 r8c7=1 r8c5<>1
r6c1<>8 r6c1=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r8c5<>2
r6c1<>8 (r6c1=6 r2c1<>6) (r6c1=6 r4c3<>6 r4c9=6 r2c9<>6) (r8c1=8 r8c2<>8) r6c3=8 r6c3<>7 r6c5=7 r5c5<>7 r5c2=7 r8c2<>7 r8c2=9 r8c3<>9 r2c3=9 r2c3<>6 r2c5=6 r8c5<>6
Grouped Discontinuous Nice Loop: 1 r9c6 -1- r9c7 =1= r8c78 -1- r8c1 -6- r8c5 =6= r7c6 =7= r9c6 => r9c6<>1
Forcing Chain Contradiction in r3 => r9c6=7
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r3c1<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c4<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c6<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r8c8<>1 r89c7=1 r3c7<>1
r9c6<>7 r9c9=7 r3c9<>7 r3c8=7 r3c8<>1
Forcing Chain Contradiction in r3c4 => r6c9<>3
r6c9=3 r7c9<>3 r7c2=3 r9c1<>3 r9c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c4<>1
r6c9=3 r6c5<>3 r46c4=3 r3c4<>3
r6c9=3 r6c9<>9 r4c9=9 r4c6<>9 r3c6=9 r3c4<>9
Forcing Chain Contradiction in r7 => r7c2<>8
r7c2=8 r7c2<>7
r7c2=8 r7c4<>8 r9c4=8 r9c4<>2 r46c4=2 r5c5<>2 r5c5=7 r5c2<>7 r6c3=7 r7c3<>7
r7c2=8 r7c2<>3 r7c9=3 r7c9<>7
Forcing Chain Contradiction in r7 => r7c9<>8
r7c9=8 r7c9<>3 r7c2=3 r7c2<>7
r7c9=8 r7c4<>8 r9c4=8 r9c4<>2 r46c4=2 r5c5<>2 r5c5=7 r5c2<>7 r6c3=7 r7c3<>7
r7c9=8 r7c9<>7
Almost Locked Set XY-Wing: A=r7c9 {37}, B=r9c17 {138}, C=r8c15789 {124678}, X,Y=7,8, Z=3 => r9c9<>3
Forcing Chain Verity => r8c2<>7
r7c3=8 r7c4<>8 r7c4=1 r4c4<>1 r4c6=1 r4c6<>9 r3c6=9 r3c2<>9 r8c2=9 r8c2<>7
r8c2=8 r8c2<>7
r8c3=8 r8c3<>9 r8c2=9 r8c2<>7
Forcing Chain Contradiction in r8c5 => r7c9=3
r7c9<>3 r9c7=3 r9c7<>1 r8c78=1 r8c5<>1
r7c9<>3 r7c9=7 r7c2<>7 r5c2=7 r5c2<>2 r5c5=2 r8c5<>2
r7c9<>3 r7c2=3 r9c1<>3 r9c1=1 r8c1<>1 r8c1=6 r8c5<>6
Hidden Single: r9c1=3
Locked Candidates Type 1 (Pointing): 7 in b9 => r8c3<>7
Naked Triple: 2,6,7 in r457c2 => r13c2<>6
Skyscraper: 3 in r2c5,r4c4 (connected by r24c8) => r3c4,r6c5<>3
XYZ-Wing: 1/6/9 in r3c46,r7c6 => r1c6<>1
Sashimi Swordfish: 1 r179 c357 fr7c4 fr7c6 fr9c4 => r8c5<>1
Sue de Coq: r89c5 - {1269} (r56c5 - {279}, r7c46 - {168}) => r9c4<>1, r9c4<>8, r1c5<>2, r2c5<>9
Hidden Single: r7c4=8
Hidden Single: r1c6=2
Hidden Single: r2c3=9
Hidden Single: r8c2=9
Hidden Single: r8c3=8
2-String Kite: 6 in r3c6,r8c1 (connected by r7c6,r8c5) => r3c1<>6
Turbot Fish: 1 r1c3 =1= r7c3 -1- r7c6 =1= r9c5 => r1c5<>1
Turbot Fish: 6 r1c3 =6= r2c1 -6- r8c1 =6= r8c5 => r1c5<>6
Naked Single: r1c5=3
Naked Single: r1c2=8
Naked Single: r3c2=3
Hidden Single: r2c8=3
Hidden Single: r6c7=3
Hidden Single: r4c4=3
Hidden Single: r4c6=1
Naked Single: r7c6=6
Full House: r3c6=9
Naked Single: r7c2=7
Full House: r7c3=1
Full House: r8c1=6
Naked Single: r8c5=2
Naked Single: r3c4=1
Full House: r2c5=6
Naked Single: r5c2=2
Full House: r5c5=7
Full House: r4c2=6
Naked Single: r1c3=6
Full House: r1c7=1
Naked Single: r9c4=9
Full House: r6c4=2
Full House: r6c5=9
Full House: r9c5=1
Naked Single: r3c1=4
Full House: r2c1=1
Full House: r2c9=4
Naked Single: r4c3=4
Full House: r6c3=7
Naked Single: r8c7=4
Naked Single: r9c7=8
Full House: r3c7=6
Full House: r9c9=2
Naked Single: r6c8=4
Full House: r6c9=6
Naked Single: r3c8=7
Full House: r3c9=8
Naked Single: r8c9=7
Full House: r4c9=9
Full House: r4c8=2
Full House: r8c8=1
|
sudoku_normal_extremely_hard_104
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7..4...9..5.7.82....2.5....5...8.7....36....1.1.......2...4.9.....5.3....45....6.
|
786432195159768234432159678564381729923674581817295346271846953698523417345917862
|
7 . . 4 . . . 9 .
. 5 . 7 . 8 2 . .
. . 2 . 5 . . . .
5 . . . 8 . 7 . .
. . 3 6 . . . . 1
. 1 . . . . . . .
2 . . . 4 . 9 . .
. . . 5 . 3 . . .
. 4 5 . . . . 6 .
|
7 8 6 4 3 2 1 9 5
1 5 9 7 6 8 2 3 4
4 3 2 1 5 9 6 7 8
5 6 4 3 8 1 7 2 9
9 2 3 6 7 4 5 8 1
8 1 7 2 9 5 3 4 6
2 7 1 8 4 6 9 5 3
6 9 8 5 2 3 4 1 7
3 4 5 9 1 7 8 6 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_6940_hard
|
786432195159768234432159678564381729923674581817295346271846953698523417345917862 #1 Extreme (39004) bf
Brute Force: r5c7=5
Hidden Single: r1c9=5
Hidden Single: r6c6=5
Hidden Single: r7c8=5
Brute Force: r5c6=4
Locked Candidates Type 1 (Pointing): 7 in b5 => r89c5<>7
Discontinuous Nice Loop: 9 r4c2 -9- r5c1 -8- r5c8 -2- r5c2 =2= r4c2 => r4c2<>9
Brute Force: r5c8=8
Naked Single: r5c1=9
Locked Candidates Type 1 (Pointing): 9 in b7 => r8c5<>9
Forcing Chain Contradiction in r9 => r8c2<>6
r8c2=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r46c4<>2 r9c4=2 r9c4<>9
r8c2=6 r8c2<>9 r8c3=9 r2c3<>9 r2c5=9 r9c5<>9
r8c2=6 r8c5<>6 r7c6=6 r7c6<>7 r9c6=7 r9c6<>9
Forcing Net Contradiction in r7c3 => r2c3<>4
r2c3=4 (r2c3<>9 r2c5=9 r9c5<>9) r4c3<>4 r4c3=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r9c5<>2 r9c5=1 (r7c4<>1) r7c6<>1 r7c3=1
r2c3=4 (r2c3<>9 r8c3=9 r8c3<>7) (r2c1<>4) r3c1<>4 r6c1=4 r6c1<>8 r6c3=8 r6c3<>7 r7c3=7
Locked Candidates Type 1 (Pointing): 4 in b1 => r6c1<>4
Forcing Net Contradiction in r9 => r3c1<>8
r3c1=8 (r3c1<>3) r3c1<>4 r2c1=4 r2c1<>3 r9c1=3
r3c1=8 (r3c1<>4 r2c1=4 r2c9<>4) r6c1<>8 r6c1=6 (r4c2<>6) r4c3<>6 r4c9=6 r2c9<>6 r2c9=3 r79c9<>3 r9c7=3
Forcing Net Contradiction in c5 => r9c1<>8
r9c1=8 (r6c1<>8 r6c1=6 r2c1<>6) (r6c1<>8 r6c1=6 r4c3<>6 r4c9=6 r2c9<>6) (r6c1<>8 r6c1=6 r8c1<>6 r8c1=1 r7c3<>1) (r7c3<>8) (r9c4<>8 r7c4=8 r7c9<>8) r9c1<>3 r7c2=3 r7c9<>3 r7c9=7 r7c3<>7 r7c3=6 r2c3<>6 r2c5=6
r9c1=8 r6c1<>8 (r6c1=6 r8c1<>6 r8c1=1 r8c5<>1) r6c3=8 r6c3<>7 r6c5=7 r5c5<>7 r5c5=2 r8c5<>2 r8c5=6
Forcing Net Contradiction in r8c5 => r6c1=8
r6c1<>8 (r8c1=8 r8c7<>8) r6c1=6 (r6c7<>6) (r4c2<>6 r4c2=2 r4c8<>2) r4c3<>6 r4c3=4 r4c8<>4 r4c8=3 r6c7<>3 r6c7=4 r8c7<>4 r8c7=1 r8c5<>1
r6c1<>8 r6c1=6 r4c2<>6 r4c2=2 r5c2<>2 r5c5=2 r8c5<>2
r6c1<>8 (r6c1=6 r2c1<>6) (r6c1=6 r4c3<>6 r4c9=6 r2c9<>6) (r8c1=8 r8c2<>8) r6c3=8 r6c3<>7 r6c5=7 r5c5<>7 r5c2=7 r8c2<>7 r8c2=9 r8c3<>9 r2c3=9 r2c3<>6 r2c5=6 r8c5<>6
Grouped Discontinuous Nice Loop: 1 r9c6 -1- r9c7 =1= r8c78 -1- r8c1 -6- r8c5 =6= r7c6 =7= r9c6 => r9c6<>1
Forcing Chain Contradiction in r3 => r9c6=7
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r3c1<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c4<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c6<>1
r9c6<>7 r7c6=7 r7c6<>6 r8c5=6 r8c1<>6 r8c1=1 r8c8<>1 r89c7=1 r3c7<>1
r9c6<>7 r9c9=7 r3c9<>7 r3c8=7 r3c8<>1
Forcing Chain Contradiction in r3c4 => r6c9<>3
r6c9=3 r7c9<>3 r7c2=3 r9c1<>3 r9c1=1 r7c3<>1 r7c46=1 r89c5<>1 r12c5=1 r3c4<>1
r6c9=3 r6c5<>3 r46c4=3 r3c4<>3
r6c9=3 r6c9<>9 r4c9=9 r4c6<>9 r3c6=9 r3c4<>9
Forcing Chain Contradiction in r7 => r7c2<>8
r7c2=8 r7c2<>7
r7c2=8 r7c4<>8 r9c4=8 r9c4<>2 r46c4=2 r5c5<>2 r5c5=7 r5c2<>7 r6c3=7 r7c3<>7
r7c2=8 r7c2<>3 r7c9=3 r7c9<>7
Forcing Chain Contradiction in r7 => r7c9<>8
r7c9=8 r7c9<>3 r7c2=3 r7c2<>7
r7c9=8 r7c4<>8 r9c4=8 r9c4<>2 r46c4=2 r5c5<>2 r5c5=7 r5c2<>7 r6c3=7 r7c3<>7
r7c9=8 r7c9<>7
Almost Locked Set XY-Wing: A=r7c9 {37}, B=r9c17 {138}, C=r8c15789 {124678}, X,Y=7,8, Z=3 => r9c9<>3
Forcing Chain Verity => r8c2<>7
r7c3=8 r7c4<>8 r7c4=1 r4c4<>1 r4c6=1 r4c6<>9 r3c6=9 r3c2<>9 r8c2=9 r8c2<>7
r8c2=8 r8c2<>7
r8c3=8 r8c3<>9 r8c2=9 r8c2<>7
Forcing Chain Contradiction in r8c5 => r7c9=3
r7c9<>3 r9c7=3 r9c7<>1 r8c78=1 r8c5<>1
r7c9<>3 r7c9=7 r7c2<>7 r5c2=7 r5c2<>2 r5c5=2 r8c5<>2
r7c9<>3 r7c2=3 r9c1<>3 r9c1=1 r8c1<>1 r8c1=6 r8c5<>6
Hidden Single: r9c1=3
Locked Candidates Type 1 (Pointing): 7 in b9 => r8c3<>7
Naked Triple: 2,6,7 in r457c2 => r13c2<>6
Skyscraper: 3 in r2c5,r4c4 (connected by r24c8) => r3c4,r6c5<>3
XYZ-Wing: 1/6/9 in r3c46,r7c6 => r1c6<>1
Sashimi Swordfish: 1 r179 c357 fr7c4 fr7c6 fr9c4 => r8c5<>1
Sue de Coq: r89c5 - {1269} (r56c5 - {279}, r7c46 - {168}) => r9c4<>1, r9c4<>8, r1c5<>2, r2c5<>9
Hidden Single: r7c4=8
Hidden Single: r1c6=2
Hidden Single: r2c3=9
Hidden Single: r8c2=9
Hidden Single: r8c3=8
2-String Kite: 6 in r3c6,r8c1 (connected by r7c6,r8c5) => r3c1<>6
Turbot Fish: 1 r1c3 =1= r7c3 -1- r7c6 =1= r9c5 => r1c5<>1
Turbot Fish: 6 r1c3 =6= r2c1 -6- r8c1 =6= r8c5 => r1c5<>6
Naked Single: r1c5=3
Naked Single: r1c2=8
Naked Single: r3c2=3
Hidden Single: r2c8=3
Hidden Single: r6c7=3
Hidden Single: r4c4=3
Hidden Single: r4c6=1
Naked Single: r7c6=6
Full House: r3c6=9
Naked Single: r7c2=7
Full House: r7c3=1
Full House: r8c1=6
Naked Single: r8c5=2
Naked Single: r3c4=1
Full House: r2c5=6
Naked Single: r5c2=2
Full House: r5c5=7
Full House: r4c2=6
Naked Single: r1c3=6
Full House: r1c7=1
Naked Single: r9c4=9
Full House: r6c4=2
Full House: r6c5=9
Full House: r9c5=1
Naked Single: r3c1=4
Full House: r2c1=1
Full House: r2c9=4
Naked Single: r4c3=4
Full House: r6c3=7
Naked Single: r8c7=4
Naked Single: r9c7=8
Full House: r3c7=6
Full House: r9c9=2
Naked Single: r6c8=4
Full House: r6c9=6
Naked Single: r3c8=7
Full House: r3c9=8
Naked Single: r8c9=7
Full House: r4c9=9
Full House: r4c8=2
Full House: r8c8=1
|
sudoku_normal_hard_105
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7...15..3..24...1..1...25....79...51...18...6.6125..9.17...9.4...9......42.7.....
|
794615283532478619816392574287946351945183726361257498173569842659824137428731965
|
7 . . . 1 5 . . 3
. . 2 4 . . . 1 .
. 1 . . . 2 5 . .
. . 7 9 . . . 5 1
. . . 1 8 . . . 6
. 6 1 2 5 . . 9 .
1 7 . . . 9 . 4 .
. . 9 . . . . . .
4 2 . 7 . . . . .
|
7 9 4 6 1 5 2 8 3
5 3 2 4 7 8 6 1 9
8 1 6 3 9 2 5 7 4
2 8 7 9 4 6 3 5 1
9 4 5 1 8 3 7 2 6
3 6 1 2 5 7 4 9 8
1 7 3 5 6 9 8 4 2
6 5 9 8 2 4 1 3 7
4 2 8 7 3 1 9 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9172_hard
|
794615283532478619816392574287946351945183726361257498173569842659824137428731965 #1 Extreme (20538) bf
Finned X-Wing: 2 c69 r38 fr7c9 => r8c78<>2
Brute Force: r5c4=1
Hidden Single: r1c5=1
Hidden Single: r6c5=5
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c89<>2
Locked Candidates Type 1 (Pointing): 7 in b5 => r23c6<>7
Locked Candidates Type 2 (Claiming): 2 in c9 => r7c7<>2
Naked Triple: 3,6,8 in r13c4,r2c6 => r23c5,r3c6<>3, r23c5,r3c6<>6, r3c6<>8
Naked Single: r3c6=2
Grouped Discontinuous Nice Loop: 3 r4c1 -3- r6c1 -8- r4c12 =8= r4c7 =2= r4c1 => r4c1<>3
Forcing Chain Contradiction in r5 => r4c1=2
r4c1<>2 r5c1=2 r5c1<>5
r4c1<>2 r5c1=2 r5c1<>9 r5c2=9 r5c2<>5
r4c1<>2 r5c1=2 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5
Forcing Chain Contradiction in r5 => r5c1<>3
r5c1=3 r5c1<>5
r5c1=3 r5c1<>9 r5c2=9 r5c2<>5
r5c1=3 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5
Forcing Net Contradiction in r5 => r1c2<>8
r1c2=8 (r1c4<>8 r1c4=6 r1c3<>6 r1c3=4 r5c3<>4) r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5 r5c3=3
r1c2=8 (r4c2<>8 r4c7=8 r6c9<>8) (r1c3<>8) r1c4<>8 r1c4=6 (r1c8<>6 r1c8=2 r5c8<>2) r1c3<>6 r1c3=4 r3c3<>4 r3c9=4 r6c9<>4 r6c9=7 r5c8<>7 r5c8=3
Forcing Net Contradiction in r4c7 => r1c7<>8
r1c7=8 (r1c7<>2 r1c8=2 r5c8<>2) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>9) r1c7<>9 r1c2=9 r3c1<>9 r3c5=9 r3c5<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r1c7=8 (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>9) r1c7<>9 r1c2=9 r3c1<>9 r3c5=9 r2c5<>9 r2c5=7 r2c9<>7 r8c9=7 r8c9<>2 r8c5=2 r8c5<>4 r4c5=4 r4c7<>4
r1c7=8 r4c7<>8
Forcing Net Contradiction in r9c7 => r2c1<>9
r2c1=9 (r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r9c3<>3) (r2c1<>3) r2c1<>5 r2c2=5 r2c2<>3 r2c6=3 (r2c6<>6) (r5c6<>3 r5c8=3 r9c8<>3) (r9c6<>3) (r5c6<>3 r5c8=3 r9c8<>3) (r4c6<>3) (r5c6<>3) r6c6<>3 r4c5=3 r9c5<>3 r9c7=3 (r7c7<>3) r9c5<>3 r9c5=6 r9c8<>6 r9c8=8 r7c7<>8 r7c7=6 r2c7<>6 r2c1=6 r2c1<>9
Forcing Net Contradiction in c7 => r2c2<>8
r2c2=8 (r2c2<>3) r2c2<>5 r2c1=5 (r2c1<>6) r2c1<>3 r2c6=3 r2c6<>6 r2c7=6
r2c2=8 (r4c2<>8 r4c7=8 r7c7<>8) (r4c2<>8 r4c7=8 r6c9<>8 r6c1=8 r6c1<>3) (r2c2<>3) r2c2<>5 r2c1=5 r2c1<>3 r2c6=3 r6c6<>3 r6c7=3 r7c7<>3 r7c7=6
Forcing Net Contradiction in r7c7 => r2c2<>9
r2c2=9 (r2c2<>3) (r2c2<>3) (r1c2<>9 r1c2=4 r3c3<>4 r5c3=4 r5c3<>5 r5c2=5 r5c2<>3) (r2c2<>3) r2c2<>5 r2c1=5 r2c1<>3 r2c6=3 (r4c6<>3) (r5c6<>3) r6c6<>3 r4c5=3 r4c2<>3 r8c2=3 (r8c4<>3) r8c2<>8 r4c2=8 r6c1<>8 r6c1=3 r2c1<>3 r2c6=3 (r4c6<>3) (r5c6<>3) r3c4<>3 r7c4=3 r7c7<>3
r2c2=9 (r2c7<>9) (r2c9<>9) r2c5<>9 r2c5=7 (r2c7<>7) r2c9<>7 r2c9=8 r2c7<>8 r2c7=6 r7c7<>6
r2c2=9 (r2c9<>9) r2c5<>9 r2c5=7 r2c9<>7 r2c9=8 r6c9<>8 r46c7=8 r7c7<>8
Forcing Net Contradiction in c3 => r2c1<>8
r2c1=8 r1c3<>8
r2c1=8 r3c3<>8
r2c1=8 (r2c1<>6) (r2c1<>3) r2c1<>5 r2c2=5 r2c2<>3 r2c6=3 (r3c4<>3 r7c4=3 r7c7<>3) r2c6<>6 r2c7=6 r7c7<>6 r7c7=8 r7c3<>8
r2c1=8 (r2c1<>3) r2c1<>5 r2c2=5 (r8c2<>5 r8c2=3 r8c4<>3) r2c2<>3 r2c6=3 r3c4<>3 r7c4=3 (r7c4<>5 r8c4=5 r8c1<>5) r3c4<>3 r2c6=3 r2c2<>3 r2c2=5 (r8c2<>5 r8c2=3 r8c4<>3) r2c1<>5 r5c1=5 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r9c3<>8
Forcing Chain Contradiction in r7 => r3c1<>3
r3c1=3 r3c1<>8 r13c3=8 r7c3<>8
r3c1=3 r3c4<>3 r2c6=3 r2c6<>8 r13c4=8 r7c4<>8
r3c1=3 r6c1<>3 r6c1=8 r6c9<>8 r46c7=8 r7c7<>8
r3c1=3 r3c4<>3 r2c6=3 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Empty Rectangle: 3 in b7 (r3c34) => r8c4<>3
Forcing Chain Contradiction in r7 => r3c4<>8
r3c4=8 r3c1<>8 r13c3=8 r7c3<>8
r3c4=8 r7c4<>8
r3c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c7<>8
r3c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Forcing Chain Contradiction in r7c9 => r8c4<>6
r8c4=6 r789c5<>6 r4c5=6 r4c5<>4 r8c5=4 r8c5<>2 r8c9=2 r7c9<>2
r8c4=6 r8c4<>5 r7c4=5 r7c9<>5
r8c4=6 r1c4<>6 r1c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Forcing Chain Contradiction in r5 => r5c2<>3
r5c2=3 r5c2<>9 r5c1=9 r5c1<>5
r5c2=3 r5c2<>5
r5c2=3 r6c1<>3 r6c1=8 r4c2<>8 r8c2=8 r8c4<>8 r8c4=5 r8c12<>5 r79c3=5 r5c3<>5
Forcing Chain Verity => r8c1<>5
r2c1=3 r6c1<>3 r6c1=8 r4c2<>8 r8c2=8 r8c4<>8 r8c4=5 r8c1<>5
r2c2=3 r2c2<>5 r2c1=5 r8c1<>5
r2c6=3 r2c6<>8 r1c4=8 r8c4<>8 r8c4=5 r8c1<>5
Forcing Chain Contradiction in r3c8 => r3c4=3
r3c4<>3 r3c4=6 r3c8<>6
r3c4<>3 r3c3=3 r2c2<>3 r2c2=5 r2c1<>5 r5c1=5 r5c1<>9 r3c1=9 r3c5<>9 r3c5=7 r3c8<>7
r3c4<>3 r2c6=3 r2c6<>8 r2c79=8 r3c8<>8
Hidden Pair: 3,5 in r2c12 => r2c1<>6
2-String Kite: 6 in r2c7,r7c4 (connected by r1c4,r2c6) => r7c7<>6
W-Wing: 3/8 in r6c1,r7c7 connected by 8 in r4c27 => r6c7<>3
XYZ-Wing: 3/6/8 in r7c7,r9c58 => r9c7<>3
Discontinuous Nice Loop: 3 r8c2 -3- r2c2 =3= r2c1 -3- r6c1 -8- r4c2 =8= r8c2 => r8c2<>3
Naked Pair: 5,8 in r8c24 => r8c16789<>8, r8c9<>5
Sashimi X-Wing: 8 c68 r29 fr1c8 fr3c8 => r2c79<>8
Hidden Single: r2c6=8
Naked Single: r1c4=6
Hidden Single: r2c7=6
W-Wing: 3/6 in r8c1,r9c5 connected by 6 in r7c35 => r8c56,r9c3<>3
Empty Rectangle: 3 in b6 (r57c3) => r7c7<>3
Naked Single: r7c7=8
Naked Single: r7c4=5
Full House: r8c4=8
Naked Single: r7c9=2
Naked Single: r8c2=5
Naked Single: r8c9=7
Naked Single: r2c2=3
Naked Single: r2c9=9
Naked Single: r2c1=5
Full House: r2c5=7
Full House: r3c5=9
Naked Single: r9c9=5
Naked Single: r5c1=9
Naked Single: r5c2=4
Naked Single: r1c2=9
Full House: r4c2=8
Naked Single: r6c1=3
Full House: r5c3=5
Naked Single: r8c1=6
Full House: r3c1=8
Naked Single: r7c3=3
Full House: r9c3=8
Full House: r7c5=6
Naked Single: r8c8=3
Naked Single: r1c3=4
Full House: r3c3=6
Naked Single: r3c8=7
Full House: r3c9=4
Full House: r6c9=8
Naked Single: r9c5=3
Naked Single: r8c7=1
Naked Single: r9c8=6
Full House: r9c7=9
Full House: r9c6=1
Naked Single: r1c7=2
Full House: r1c8=8
Full House: r5c8=2
Naked Single: r4c5=4
Full House: r8c5=2
Full House: r8c6=4
Naked Single: r4c7=3
Full House: r4c6=6
Naked Single: r6c6=7
Full House: r5c6=3
Full House: r5c7=7
Full House: r6c7=4
|
sudoku_normal_extremely_hard_105
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7....5..3..24...1..1....5....79...51....8...6.612...9.17...9.4...9......42.7.....
|
794615283532478619816392574287946351945183726361257498173569842659824137428731965
|
7 . . . . 5 . . 3
. . 2 4 . . . 1 .
. 1 . . . . 5 . .
. . 7 9 . . . 5 1
. . . . 8 . . . 6
. 6 1 2 . . . 9 .
1 7 . . . 9 . 4 .
. . 9 . . . . . .
4 2 . 7 . . . . .
|
7 9 4 6 1 5 2 8 3
5 3 2 4 7 8 6 1 9
8 1 6 3 9 2 5 7 4
2 8 7 9 4 6 3 5 1
9 4 5 1 8 3 7 2 6
3 6 1 2 5 7 4 9 8
1 7 3 5 6 9 8 4 2
6 5 9 8 2 4 1 3 7
4 2 8 7 3 1 9 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9172_hard
|
794615283532478619816392574287946351945183726361257498173569842659824137428731965 #1 Extreme (20538) bf
Finned X-Wing: 2 c69 r38 fr7c9 => r8c78<>2
Brute Force: r5c4=1
Hidden Single: r1c5=1
Hidden Single: r6c5=5
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c89<>2
Locked Candidates Type 1 (Pointing): 7 in b5 => r23c6<>7
Locked Candidates Type 2 (Claiming): 2 in c9 => r7c7<>2
Naked Triple: 3,6,8 in r13c4,r2c6 => r23c5,r3c6<>3, r23c5,r3c6<>6, r3c6<>8
Naked Single: r3c6=2
Grouped Discontinuous Nice Loop: 3 r4c1 -3- r6c1 -8- r4c12 =8= r4c7 =2= r4c1 => r4c1<>3
Forcing Chain Contradiction in r5 => r4c1=2
r4c1<>2 r5c1=2 r5c1<>5
r4c1<>2 r5c1=2 r5c1<>9 r5c2=9 r5c2<>5
r4c1<>2 r5c1=2 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5
Forcing Chain Contradiction in r5 => r5c1<>3
r5c1=3 r5c1<>5
r5c1=3 r5c1<>9 r5c2=9 r5c2<>5
r5c1=3 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5
Forcing Net Contradiction in r5 => r1c2<>8
r1c2=8 (r1c4<>8 r1c4=6 r1c3<>6 r1c3=4 r5c3<>4) r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r5c3<>5 r5c3=3
r1c2=8 (r4c2<>8 r4c7=8 r6c9<>8) (r1c3<>8) r1c4<>8 r1c4=6 (r1c8<>6 r1c8=2 r5c8<>2) r1c3<>6 r1c3=4 r3c3<>4 r3c9=4 r6c9<>4 r6c9=7 r5c8<>7 r5c8=3
Forcing Net Contradiction in r4c7 => r1c7<>8
r1c7=8 (r1c7<>2 r1c8=2 r5c8<>2) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>9) r1c7<>9 r1c2=9 r3c1<>9 r3c5=9 r3c5<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r1c7=8 (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>7) (r4c7<>8 r4c2=8 r6c1<>8 r6c9=8 r6c9<>4 r3c9=4 r3c9<>9) r1c7<>9 r1c2=9 r3c1<>9 r3c5=9 r2c5<>9 r2c5=7 r2c9<>7 r8c9=7 r8c9<>2 r8c5=2 r8c5<>4 r4c5=4 r4c7<>4
r1c7=8 r4c7<>8
Forcing Net Contradiction in r9c7 => r2c1<>9
r2c1=9 (r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r9c3<>3) (r2c1<>3) r2c1<>5 r2c2=5 r2c2<>3 r2c6=3 (r2c6<>6) (r5c6<>3 r5c8=3 r9c8<>3) (r9c6<>3) (r5c6<>3 r5c8=3 r9c8<>3) (r4c6<>3) (r5c6<>3) r6c6<>3 r4c5=3 r9c5<>3 r9c7=3 (r7c7<>3) r9c5<>3 r9c5=6 r9c8<>6 r9c8=8 r7c7<>8 r7c7=6 r2c7<>6 r2c1=6 r2c1<>9
Forcing Net Contradiction in c7 => r2c2<>8
r2c2=8 (r2c2<>3) r2c2<>5 r2c1=5 (r2c1<>6) r2c1<>3 r2c6=3 r2c6<>6 r2c7=6
r2c2=8 (r4c2<>8 r4c7=8 r7c7<>8) (r4c2<>8 r4c7=8 r6c9<>8 r6c1=8 r6c1<>3) (r2c2<>3) r2c2<>5 r2c1=5 r2c1<>3 r2c6=3 r6c6<>3 r6c7=3 r7c7<>3 r7c7=6
Forcing Net Contradiction in r7c7 => r2c2<>9
r2c2=9 (r2c2<>3) (r2c2<>3) (r1c2<>9 r1c2=4 r3c3<>4 r5c3=4 r5c3<>5 r5c2=5 r5c2<>3) (r2c2<>3) r2c2<>5 r2c1=5 r2c1<>3 r2c6=3 (r4c6<>3) (r5c6<>3) r6c6<>3 r4c5=3 r4c2<>3 r8c2=3 (r8c4<>3) r8c2<>8 r4c2=8 r6c1<>8 r6c1=3 r2c1<>3 r2c6=3 (r4c6<>3) (r5c6<>3) r3c4<>3 r7c4=3 r7c7<>3
r2c2=9 (r2c7<>9) (r2c9<>9) r2c5<>9 r2c5=7 (r2c7<>7) r2c9<>7 r2c9=8 r2c7<>8 r2c7=6 r7c7<>6
r2c2=9 (r2c9<>9) r2c5<>9 r2c5=7 r2c9<>7 r2c9=8 r6c9<>8 r46c7=8 r7c7<>8
Forcing Net Contradiction in c3 => r2c1<>8
r2c1=8 r1c3<>8
r2c1=8 r3c3<>8
r2c1=8 (r2c1<>6) (r2c1<>3) r2c1<>5 r2c2=5 r2c2<>3 r2c6=3 (r3c4<>3 r7c4=3 r7c7<>3) r2c6<>6 r2c7=6 r7c7<>6 r7c7=8 r7c3<>8
r2c1=8 (r2c1<>3) r2c1<>5 r2c2=5 (r8c2<>5 r8c2=3 r8c4<>3) r2c2<>3 r2c6=3 r3c4<>3 r7c4=3 (r7c4<>5 r8c4=5 r8c1<>5) r3c4<>3 r2c6=3 r2c2<>3 r2c2=5 (r8c2<>5 r8c2=3 r8c4<>3) r2c1<>5 r5c1=5 r5c1<>9 r5c2=9 r1c2<>9 r1c7=9 r9c7<>9 r9c9=9 r9c9<>5 r9c3=5 r9c3<>8
Forcing Chain Contradiction in r7 => r3c1<>3
r3c1=3 r3c1<>8 r13c3=8 r7c3<>8
r3c1=3 r3c4<>3 r2c6=3 r2c6<>8 r13c4=8 r7c4<>8
r3c1=3 r6c1<>3 r6c1=8 r6c9<>8 r46c7=8 r7c7<>8
r3c1=3 r3c4<>3 r2c6=3 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Empty Rectangle: 3 in b7 (r3c34) => r8c4<>3
Forcing Chain Contradiction in r7 => r3c4<>8
r3c4=8 r3c1<>8 r13c3=8 r7c3<>8
r3c4=8 r7c4<>8
r3c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c7<>8
r3c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Forcing Chain Contradiction in r7c9 => r8c4<>6
r8c4=6 r789c5<>6 r4c5=6 r4c5<>4 r8c5=4 r8c5<>2 r8c9=2 r7c9<>2
r8c4=6 r8c4<>5 r7c4=5 r7c9<>5
r8c4=6 r1c4<>6 r1c4=8 r2c6<>8 r2c79=8 r13c8<>8 r89c8=8 r7c9<>8
Forcing Chain Contradiction in r5 => r5c2<>3
r5c2=3 r5c2<>9 r5c1=9 r5c1<>5
r5c2=3 r5c2<>5
r5c2=3 r6c1<>3 r6c1=8 r4c2<>8 r8c2=8 r8c4<>8 r8c4=5 r8c12<>5 r79c3=5 r5c3<>5
Forcing Chain Verity => r8c1<>5
r2c1=3 r6c1<>3 r6c1=8 r4c2<>8 r8c2=8 r8c4<>8 r8c4=5 r8c1<>5
r2c2=3 r2c2<>5 r2c1=5 r8c1<>5
r2c6=3 r2c6<>8 r1c4=8 r8c4<>8 r8c4=5 r8c1<>5
Forcing Chain Contradiction in r3c8 => r3c4=3
r3c4<>3 r3c4=6 r3c8<>6
r3c4<>3 r3c3=3 r2c2<>3 r2c2=5 r2c1<>5 r5c1=5 r5c1<>9 r3c1=9 r3c5<>9 r3c5=7 r3c8<>7
r3c4<>3 r2c6=3 r2c6<>8 r2c79=8 r3c8<>8
Hidden Pair: 3,5 in r2c12 => r2c1<>6
2-String Kite: 6 in r2c7,r7c4 (connected by r1c4,r2c6) => r7c7<>6
W-Wing: 3/8 in r6c1,r7c7 connected by 8 in r4c27 => r6c7<>3
XYZ-Wing: 3/6/8 in r7c7,r9c58 => r9c7<>3
Discontinuous Nice Loop: 3 r8c2 -3- r2c2 =3= r2c1 -3- r6c1 -8- r4c2 =8= r8c2 => r8c2<>3
Naked Pair: 5,8 in r8c24 => r8c16789<>8, r8c9<>5
Sashimi X-Wing: 8 c68 r29 fr1c8 fr3c8 => r2c79<>8
Hidden Single: r2c6=8
Naked Single: r1c4=6
Hidden Single: r2c7=6
W-Wing: 3/6 in r8c1,r9c5 connected by 6 in r7c35 => r8c56,r9c3<>3
Empty Rectangle: 3 in b6 (r57c3) => r7c7<>3
Naked Single: r7c7=8
Naked Single: r7c4=5
Full House: r8c4=8
Naked Single: r7c9=2
Naked Single: r8c2=5
Naked Single: r8c9=7
Naked Single: r2c2=3
Naked Single: r2c9=9
Naked Single: r2c1=5
Full House: r2c5=7
Full House: r3c5=9
Naked Single: r9c9=5
Naked Single: r5c1=9
Naked Single: r5c2=4
Naked Single: r1c2=9
Full House: r4c2=8
Naked Single: r6c1=3
Full House: r5c3=5
Naked Single: r8c1=6
Full House: r3c1=8
Naked Single: r7c3=3
Full House: r9c3=8
Full House: r7c5=6
Naked Single: r8c8=3
Naked Single: r1c3=4
Full House: r3c3=6
Naked Single: r3c8=7
Full House: r3c9=4
Full House: r6c9=8
Naked Single: r9c5=3
Naked Single: r8c7=1
Naked Single: r9c8=6
Full House: r9c7=9
Full House: r9c6=1
Naked Single: r1c7=2
Full House: r1c8=8
Full House: r5c8=2
Naked Single: r4c5=4
Full House: r8c5=2
Full House: r8c6=4
Naked Single: r4c7=3
Full House: r4c6=6
Naked Single: r6c6=7
Full House: r5c6=3
Full House: r5c7=7
Full House: r6c7=4
|
sudoku_normal_hard_106
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7...816.........51.91........9.47...2.861.4...4..28..39...74.3..1.....4.4....68..
|
753481692824963751691752384569347128238619475147528963982174536316895247475236819
|
7 . . . 8 1 6 . .
. . . . . . . 5 1
. 9 1 . . . . . .
. . 9 . 4 7 . . .
2 . 8 6 1 . 4 . .
. 4 . . 2 8 . . 3
9 . . . 7 4 . 3 .
. 1 . . . . . 4 .
4 . . . . 6 8 . .
|
7 5 3 4 8 1 6 9 2
8 2 4 9 6 3 7 5 1
6 9 1 7 5 2 3 8 4
5 6 9 3 4 7 1 2 8
2 3 8 6 1 9 4 7 5
1 4 7 5 2 8 9 6 3
9 8 2 1 7 4 5 3 6
3 1 6 8 9 5 2 4 7
4 7 5 2 3 6 8 1 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3591_hard
|
753481692824963751691752384569347128238619475147528963982174536316895247475236819 #1 Extreme (30012) bf
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c13<>8
Locked Candidates Type 1 (Pointing): 6 in b9 => r4c9<>6
Brute Force: r5c3=8
Brute Force: r5c5=1
Grouped Discontinuous Nice Loop: 5 r3c3 -5- r1c23 =5= r1c4 -5- r4c4 -3- r5c6 =3= r5c2 =7= r6c3 =1= r3c3 => r3c3<>5
Finned Franken Swordfish: 9 c57b5 r268 fr5c6 fr9c5 => r8c6<>9
Forcing Chain Contradiction in r3c1 => r2c5<>9
r2c5=9 r2c6<>9 r5c6=9 r5c6<>3 r5c2=3 r5c2<>7 r6c3=7 r6c3<>1 r3c3=1 r3c1<>1
r2c5=9 r2c6<>9 r5c6=9 r5c6<>3 r4c4=3 r1c4<>3 r1c23=3 r3c1<>3
r2c5=9 r2c6<>9 r5c6=9 r5c6<>5 r46c4=5 r1c4<>5 r1c23=5 r3c1<>5
r2c5=9 r2c5<>6 r3c5=6 r3c1<>6
Locked Candidates Type 2 (Claiming): 9 in c5 => r89c4<>9
Forcing Chain Contradiction in r3 => r3c1<>3
r3c1=3 r3c1<>6
r3c1=3 r3c1<>1 r3c3=1 r3c3<>6
r3c1=3 r3c7<>3 r2c7=3 r2c5<>3 r2c5=6 r3c5<>6
Forcing Chain Contradiction in r3 => r3c3<>3
r3c3=3 r3c3<>1 r3c1=1 r3c1<>6
r3c3=3 r3c3<>6
r3c3=3 r3c7<>3 r2c7=3 r2c5<>3 r2c5=6 r3c5<>6
Forcing Chain Contradiction in b3 => r3c3<>4
r3c3=4 r3c3<>1 r6c3=1 r6c3<>7 r5c2=7 r5c8<>7 r5c8=9 r1c8<>9
r3c3=4 r3c9<>4 r1c9=4 r1c9<>9
r3c3=4 r2c3<>4 r2c4=4 r2c4<>7 r2c7=7 r2c7<>9
Forcing Chain Contradiction in r1 => r3c8<>7
r3c8=7 r5c8<>7 r5c8=9 r5c6<>9 r2c6=9 r1c4<>9
r3c8=7 r5c8<>7 r5c8=9 r1c8<>9
r3c8=7 r3c8<>8 r3c9=8 r3c9<>4 r1c9=4 r1c9<>9
Hidden Rectangle: 2/8 in r3c89,r4c89 => r4c9<>2
Finned X-Wing: 7 c28 r59 fr6c8 => r5c9<>7
Forcing Chain Contradiction in r1 => r6c7<>7
r6c7=7 r5c8<>7 r5c8=9 r5c6<>9 r2c6=9 r1c4<>9
r6c7=7 r5c8<>7 r5c8=9 r1c8<>9
r6c7=7 r23c7<>7 r3c9=7 r3c9<>4 r1c9=4 r1c9<>9
Locked Candidates Type 1 (Pointing): 7 in b6 => r9c8<>7
Almost Locked Set XZ-Rule: A=r4c124 {1356}, B=r6c147 {1569}, X=6, Z=1 => r6c3<>1
Hidden Single: r3c3=1
Almost Locked Set XY-Wing: A=r2c123567 {2346789}, B=r3c156 {2356}, C=r34678c7 {123579}, X,Y=3,7, Z=2 => r2c4<>2
Forcing Chain Verity => r2c1<>6
r2c1=3 r2c1<>6
r4c1=3 r4c4<>3 r4c4=5 r1c4<>5 r1c23=5 r3c1<>5 r3c1=6 r2c1<>6
r8c1=3 r8c1<>8 r2c1=8 r2c1<>6
Grouped Discontinuous Nice Loop: 3 r8c4 -3- r1c4 =3= r1c23 -3- r2c1 -8- r8c1 =8= r8c4 => r8c4<>3
Grouped Discontinuous Nice Loop: 5 r8c4 -5- r4c4 -3- r1c4 =3= r1c23 -3- r2c1 -8- r8c1 =8= r8c4 => r8c4<>5
Forcing Chain Contradiction in r1 => r2c3<>6
r2c3=6 r3c1<>6 r3c1=5 r1c23<>5 r1c4=5 r4c4<>5 r4c4=3 r4c1<>3 r45c2=3 r1c2<>3
r2c3=6 r2c3<>4 r1c3=4 r1c3<>3
r2c3=6 r2c5<>6 r2c5=3 r1c4<>3
Grouped Discontinuous Nice Loop: 6 r8c1 -6- r3c1 -5- r1c23 =5= r1c4 -5- r4c4 -3- r5c6 =3= r5c2 =7= r6c3 =6= r78c3 -6- r8c1 => r8c1<>6
Forcing Chain Contradiction in r2c2 => r2c6<>2
r2c6=2 r2c2<>2
r2c6=2 r2c6<>9 r5c6=9 r5c6<>3 r5c2=3 r2c2<>3
r2c6=2 r2c6<>9 r5c6=9 r5c6<>5 r46c4=5 r1c4<>5 r1c23=5 r3c1<>5 r3c1=6 r2c2<>6
r2c6=2 r2c6<>9 r5c6=9 r5c6<>3 r4c4=3 r1c4<>3 r1c23=3 r2c1<>3 r2c1=8 r2c2<>8
Forcing Chain Contradiction in r1c2 => r6c1<>6
r6c1=6 r6c8<>6 r4c8=6 r4c8<>2 r4c7=2 r2c7<>2 r2c23=2 r1c2<>2
r6c1=6 r6c1<>1 r4c1=1 r4c1<>3 r45c2=3 r1c2<>3
r6c1=6 r3c1<>6 r3c1=5 r1c2<>5
Naked Triple: 1,5,9 in r6c147 => r6c3<>5, r6c8<>1, r6c8<>9
2-String Kite: 9 in r2c6,r6c7 (connected by r5c6,r6c4) => r2c7<>9
Locked Candidates Type 1 (Pointing): 9 in b3 => r1c4<>9
Discontinuous Nice Loop: 7 r8c7 -7- r2c7 =7= r2c4 =9= r6c4 -9- r6c7 =9= r8c7 => r8c7<>7
Locked Candidates Type 1 (Pointing): 7 in b9 => r3c9<>7
Hidden Pair: 3,7 in r23c7 => r23c7<>2
Locked Candidates Type 2 (Claiming): 2 in r2 => r1c23<>2
Hidden Pair: 6,7 in r8c39 => r8c39<>2, r8c3<>3, r8c39<>5, r8c9<>9
Naked Pair: 6,7 in r68c3 => r7c3<>6, r9c3<>7
W-Wing: 5/3 in r1c2,r4c4 connected by 3 in r5c26 => r1c4,r4c2<>5
Locked Candidates Type 1 (Pointing): 5 in b2 => r3c1<>5
Naked Single: r3c1=6
Hidden Single: r2c5=6
Uniqueness Test 4: 3/7 in r2c47,r3c47 => r23c4<>3
Sue de Coq: r45c2 - {3567} (r1c2 - {35}, r6c3 - {67}) => r29c2<>3, r79c2<>5
AIC: 6 6- r4c2 =6= r7c2 =8= r7c4 =1= r7c7 -1- r9c8 =1= r4c8 =6= r6c8 -6 => r4c8,r6c3<>6
Naked Single: r6c3=7
Naked Single: r6c8=6
Naked Single: r8c3=6
Naked Single: r8c9=7
Hidden Single: r4c2=6
Hidden Single: r5c8=7
Hidden Single: r9c2=7
Hidden Single: r7c9=6
2-String Kite: 3 in r1c2,r4c4 (connected by r4c1,r5c2) => r1c4<>3
Locked Candidates Type 2 (Claiming): 3 in r1 => r2c13<>3
Naked Single: r2c1=8
Naked Single: r2c2=2
Naked Single: r2c3=4
Naked Single: r7c2=8
Hidden Single: r8c4=8
Skyscraper: 3 in r8c1,r9c4 (connected by r4c14) => r8c56,r9c3<>3
Hidden Single: r8c1=3
Hidden Single: r1c3=3
Full House: r1c2=5
Full House: r5c2=3
Hidden Single: r4c4=3
Hidden Single: r9c5=3
Naked Single: r3c5=5
Full House: r8c5=9
Hidden Single: r6c7=9
Naked Single: r5c9=5
Full House: r5c6=9
Full House: r6c4=5
Full House: r6c1=1
Full House: r4c1=5
Naked Single: r4c9=8
Naked Single: r2c6=3
Naked Single: r2c7=7
Full House: r2c4=9
Naked Single: r3c6=2
Full House: r8c6=5
Full House: r8c7=2
Naked Single: r3c7=3
Naked Single: r1c4=4
Full House: r3c4=7
Naked Single: r3c8=8
Full House: r3c9=4
Naked Single: r4c7=1
Full House: r4c8=2
Full House: r7c7=5
Naked Single: r9c9=9
Full House: r1c9=2
Full House: r1c8=9
Full House: r9c8=1
Naked Single: r7c3=2
Full House: r7c4=1
Full House: r9c4=2
Full House: r9c3=5
|
sudoku_normal_extremely_hard_106
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7...816.........51.9.........9.47...2..6..4...4..28..39...74.3..1.....4.4....68..
|
753481692824963751691752384569347128238619475147528963982174536316895247475236819
|
7 . . . 8 1 6 . .
. . . . . . . 5 1
. 9 . . . . . . .
. . 9 . 4 7 . . .
2 . . 6 . . 4 . .
. 4 . . 2 8 . . 3
9 . . . 7 4 . 3 .
. 1 . . . . . 4 .
4 . . . . 6 8 . .
|
7 5 3 4 8 1 6 9 2
8 2 4 9 6 3 7 5 1
6 9 1 7 5 2 3 8 4
5 6 9 3 4 7 1 2 8
2 3 8 6 1 9 4 7 5
1 4 7 5 2 8 9 6 3
9 8 2 1 7 4 5 3 6
3 1 6 8 9 5 2 4 7
4 7 5 2 3 6 8 1 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3591_hard
|
753481692824963751691752384569347128238619475147528963982174536316895247475236819 #1 Extreme (30012) bf
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c13<>8
Locked Candidates Type 1 (Pointing): 6 in b9 => r4c9<>6
Brute Force: r5c3=8
Brute Force: r5c5=1
Grouped Discontinuous Nice Loop: 5 r3c3 -5- r1c23 =5= r1c4 -5- r4c4 -3- r5c6 =3= r5c2 =7= r6c3 =1= r3c3 => r3c3<>5
Finned Franken Swordfish: 9 c57b5 r268 fr5c6 fr9c5 => r8c6<>9
Forcing Chain Contradiction in r3c1 => r2c5<>9
r2c5=9 r2c6<>9 r5c6=9 r5c6<>3 r5c2=3 r5c2<>7 r6c3=7 r6c3<>1 r3c3=1 r3c1<>1
r2c5=9 r2c6<>9 r5c6=9 r5c6<>3 r4c4=3 r1c4<>3 r1c23=3 r3c1<>3
r2c5=9 r2c6<>9 r5c6=9 r5c6<>5 r46c4=5 r1c4<>5 r1c23=5 r3c1<>5
r2c5=9 r2c5<>6 r3c5=6 r3c1<>6
Locked Candidates Type 2 (Claiming): 9 in c5 => r89c4<>9
Forcing Chain Contradiction in r3 => r3c1<>3
r3c1=3 r3c1<>6
r3c1=3 r3c1<>1 r3c3=1 r3c3<>6
r3c1=3 r3c7<>3 r2c7=3 r2c5<>3 r2c5=6 r3c5<>6
Forcing Chain Contradiction in r3 => r3c3<>3
r3c3=3 r3c3<>1 r3c1=1 r3c1<>6
r3c3=3 r3c3<>6
r3c3=3 r3c7<>3 r2c7=3 r2c5<>3 r2c5=6 r3c5<>6
Forcing Chain Contradiction in b3 => r3c3<>4
r3c3=4 r3c3<>1 r6c3=1 r6c3<>7 r5c2=7 r5c8<>7 r5c8=9 r1c8<>9
r3c3=4 r3c9<>4 r1c9=4 r1c9<>9
r3c3=4 r2c3<>4 r2c4=4 r2c4<>7 r2c7=7 r2c7<>9
Forcing Chain Contradiction in r1 => r3c8<>7
r3c8=7 r5c8<>7 r5c8=9 r5c6<>9 r2c6=9 r1c4<>9
r3c8=7 r5c8<>7 r5c8=9 r1c8<>9
r3c8=7 r3c8<>8 r3c9=8 r3c9<>4 r1c9=4 r1c9<>9
Hidden Rectangle: 2/8 in r3c89,r4c89 => r4c9<>2
Finned X-Wing: 7 c28 r59 fr6c8 => r5c9<>7
Forcing Chain Contradiction in r1 => r6c7<>7
r6c7=7 r5c8<>7 r5c8=9 r5c6<>9 r2c6=9 r1c4<>9
r6c7=7 r5c8<>7 r5c8=9 r1c8<>9
r6c7=7 r23c7<>7 r3c9=7 r3c9<>4 r1c9=4 r1c9<>9
Locked Candidates Type 1 (Pointing): 7 in b6 => r9c8<>7
Almost Locked Set XZ-Rule: A=r4c124 {1356}, B=r6c147 {1569}, X=6, Z=1 => r6c3<>1
Hidden Single: r3c3=1
Almost Locked Set XY-Wing: A=r2c123567 {2346789}, B=r3c156 {2356}, C=r34678c7 {123579}, X,Y=3,7, Z=2 => r2c4<>2
Forcing Chain Verity => r2c1<>6
r2c1=3 r2c1<>6
r4c1=3 r4c4<>3 r4c4=5 r1c4<>5 r1c23=5 r3c1<>5 r3c1=6 r2c1<>6
r8c1=3 r8c1<>8 r2c1=8 r2c1<>6
Grouped Discontinuous Nice Loop: 3 r8c4 -3- r1c4 =3= r1c23 -3- r2c1 -8- r8c1 =8= r8c4 => r8c4<>3
Grouped Discontinuous Nice Loop: 5 r8c4 -5- r4c4 -3- r1c4 =3= r1c23 -3- r2c1 -8- r8c1 =8= r8c4 => r8c4<>5
Forcing Chain Contradiction in r1 => r2c3<>6
r2c3=6 r3c1<>6 r3c1=5 r1c23<>5 r1c4=5 r4c4<>5 r4c4=3 r4c1<>3 r45c2=3 r1c2<>3
r2c3=6 r2c3<>4 r1c3=4 r1c3<>3
r2c3=6 r2c5<>6 r2c5=3 r1c4<>3
Grouped Discontinuous Nice Loop: 6 r8c1 -6- r3c1 -5- r1c23 =5= r1c4 -5- r4c4 -3- r5c6 =3= r5c2 =7= r6c3 =6= r78c3 -6- r8c1 => r8c1<>6
Forcing Chain Contradiction in r2c2 => r2c6<>2
r2c6=2 r2c2<>2
r2c6=2 r2c6<>9 r5c6=9 r5c6<>3 r5c2=3 r2c2<>3
r2c6=2 r2c6<>9 r5c6=9 r5c6<>5 r46c4=5 r1c4<>5 r1c23=5 r3c1<>5 r3c1=6 r2c2<>6
r2c6=2 r2c6<>9 r5c6=9 r5c6<>3 r4c4=3 r1c4<>3 r1c23=3 r2c1<>3 r2c1=8 r2c2<>8
Forcing Chain Contradiction in r1c2 => r6c1<>6
r6c1=6 r6c8<>6 r4c8=6 r4c8<>2 r4c7=2 r2c7<>2 r2c23=2 r1c2<>2
r6c1=6 r6c1<>1 r4c1=1 r4c1<>3 r45c2=3 r1c2<>3
r6c1=6 r3c1<>6 r3c1=5 r1c2<>5
Naked Triple: 1,5,9 in r6c147 => r6c3<>5, r6c8<>1, r6c8<>9
2-String Kite: 9 in r2c6,r6c7 (connected by r5c6,r6c4) => r2c7<>9
Locked Candidates Type 1 (Pointing): 9 in b3 => r1c4<>9
Discontinuous Nice Loop: 7 r8c7 -7- r2c7 =7= r2c4 =9= r6c4 -9- r6c7 =9= r8c7 => r8c7<>7
Locked Candidates Type 1 (Pointing): 7 in b9 => r3c9<>7
Hidden Pair: 3,7 in r23c7 => r23c7<>2
Locked Candidates Type 2 (Claiming): 2 in r2 => r1c23<>2
Hidden Pair: 6,7 in r8c39 => r8c39<>2, r8c3<>3, r8c39<>5, r8c9<>9
Naked Pair: 6,7 in r68c3 => r7c3<>6, r9c3<>7
W-Wing: 5/3 in r1c2,r4c4 connected by 3 in r5c26 => r1c4,r4c2<>5
Locked Candidates Type 1 (Pointing): 5 in b2 => r3c1<>5
Naked Single: r3c1=6
Hidden Single: r2c5=6
Uniqueness Test 4: 3/7 in r2c47,r3c47 => r23c4<>3
Sue de Coq: r45c2 - {3567} (r1c2 - {35}, r6c3 - {67}) => r29c2<>3, r79c2<>5
AIC: 6 6- r4c2 =6= r7c2 =8= r7c4 =1= r7c7 -1- r9c8 =1= r4c8 =6= r6c8 -6 => r4c8,r6c3<>6
Naked Single: r6c3=7
Naked Single: r6c8=6
Naked Single: r8c3=6
Naked Single: r8c9=7
Hidden Single: r4c2=6
Hidden Single: r5c8=7
Hidden Single: r9c2=7
Hidden Single: r7c9=6
2-String Kite: 3 in r1c2,r4c4 (connected by r4c1,r5c2) => r1c4<>3
Locked Candidates Type 2 (Claiming): 3 in r1 => r2c13<>3
Naked Single: r2c1=8
Naked Single: r2c2=2
Naked Single: r2c3=4
Naked Single: r7c2=8
Hidden Single: r8c4=8
Skyscraper: 3 in r8c1,r9c4 (connected by r4c14) => r8c56,r9c3<>3
Hidden Single: r8c1=3
Hidden Single: r1c3=3
Full House: r1c2=5
Full House: r5c2=3
Hidden Single: r4c4=3
Hidden Single: r9c5=3
Naked Single: r3c5=5
Full House: r8c5=9
Hidden Single: r6c7=9
Naked Single: r5c9=5
Full House: r5c6=9
Full House: r6c4=5
Full House: r6c1=1
Full House: r4c1=5
Naked Single: r4c9=8
Naked Single: r2c6=3
Naked Single: r2c7=7
Full House: r2c4=9
Naked Single: r3c6=2
Full House: r8c6=5
Full House: r8c7=2
Naked Single: r3c7=3
Naked Single: r1c4=4
Full House: r3c4=7
Naked Single: r3c8=8
Full House: r3c9=4
Naked Single: r4c7=1
Full House: r4c8=2
Full House: r7c7=5
Naked Single: r9c9=9
Full House: r1c9=2
Full House: r1c8=9
Full House: r9c8=1
Naked Single: r7c3=2
Full House: r7c4=1
Full House: r9c4=2
Full House: r9c3=5
|
sudoku_normal_hard_107
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
5....2.6..1.65.4..2.67......6..2.854...5.6.39.5.4896..4.1.6..8..8......66.5...1..
|
574192368819653427236748915967321854148576239352489671421965783783214596695837142
|
5 . . . . 2 . 6 .
. 1 . 6 5 . 4 . .
2 . 6 7 . . . . .
. 6 . . 2 . 8 5 4
. . . 5 . 6 . 3 9
. 5 . 4 8 9 6 . .
4 . 1 . 6 . . 8 .
. 8 . . . . . . 6
6 . 5 . . . 1 . .
|
5 7 4 1 9 2 3 6 8
8 1 9 6 5 3 4 2 7
2 3 6 7 4 8 9 1 5
9 6 7 3 2 1 8 5 4
1 4 8 5 7 6 2 3 9
3 5 2 4 8 9 6 7 1
4 2 1 9 6 5 7 8 3
7 8 3 2 1 4 5 9 6
6 9 5 8 3 7 1 4 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3398_hard
|
574192368819653427236748915967321854148576239352489671421965783783214596695837142 #1 Extreme (21512) bf
Hidden Single: r8c9=6
Hidden Single: r1c1=5
Brute Force: r5c4=5
Hidden Single: r4c8=5
Hidden Single: r5c6=6
Hidden Single: r2c4=6
Hidden Single: r3c3=6
Locked Candidates Type 1 (Pointing): 1 in b6 => r6c14<>1
AIC: 3 3- r2c6 -8- r2c1 =8= r5c1 =1= r5c5 -1- r4c4 -3 => r1c4,r4c6<>3
Locked Candidates Type 1 (Pointing): 3 in b5 => r789c4<>3
Discontinuous Nice Loop: 3 r8c6 -3- r2c6 -8- r3c6 =8= r3c9 =5= r3c7 -5- r8c7 =5= r8c6 => r8c6<>3
Forcing Chain Contradiction in r7c6 => r3c6<>3
r3c6=3 r7c6<>3
r3c6=3 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r3c6=3 r2c6<>3 r2c6=8 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r5c5<>7 r4c6=7 r7c6<>7
Forcing Chain Contradiction in c6 => r8c4<>4
r8c4=4 r89c6<>4 r3c6=4 r3c6<>1
r8c4=4 r6c4<>4 r6c4=3 r4c4<>3 r4c4=1 r4c6<>1
r8c4=4 r89c6<>4 r3c6=4 r3c6<>8 r3c9=8 r3c9<>5 r3c7=5 r8c7<>5 r8c6=5 r8c6<>1
Forcing Chain Contradiction in r7c6 => r9c4<>4
r9c4=4 r9c4<>8 r9c6=8 r2c6<>8 r2c6=3 r7c6<>3
r9c4=4 r9c4<>8 r9c6=8 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r9c4=4 r6c4<>4 r5c5=4 r5c5<>7 r4c6=7 r7c6<>7
Forcing Chain Contradiction in r7c6 => r9c6<>3
r9c6=3 r7c6<>3
r9c6=3 r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r9c6=3 r2c6<>3 r2c6=8 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r5c5<>7 r4c6=7 r7c6<>7
Forcing Net Contradiction in c4 => r4c4=3
r4c4<>3 r4c4=1
r4c4<>3 (r4c4=1 r5c5<>1 r5c1=1 r5c1<>8 r5c3=8 r5c3<>2) (r4c4=1 r4c6<>1 r4c6=7 r5c5<>7 r5c5=4 r5c2<>4) r6c4=3 r6c1<>3 r6c1=7 r5c2<>7 r5c2=2 (r5c7<>2) r6c3<>2 r8c3=2 (r8c4<>2) r8c7<>2 r7c7=2 r7c4<>2 r7c4=9 r8c4<>9 r8c4=1
Naked Single: r6c4=4
Discontinuous Nice Loop: 9 r1c3 -9- r4c3 =9= r4c1 =1= r5c1 =8= r5c3 =4= r1c3 => r1c3<>9
Forcing Chain Contradiction in r2c3 => r8c3<>9
r8c3=9 r4c3<>9 r4c1=9 r4c1<>1 r5c1=1 r5c1<>8 r2c1=8 r2c6<>8 r2c6=3 r2c3<>3
r8c3=9 r4c3<>9 r4c3=7 r2c3<>7
r8c3=9 r4c3<>9 r4c1=9 r4c1<>1 r5c1=1 r5c1<>8 r5c3=8 r2c3<>8
r8c3=9 r2c3<>9
Forcing Net Contradiction in r7c7 => r1c2<>9
r1c2=9 (r1c5<>9 r3c5=9 r3c5<>3) (r9c2<>9) (r1c5<>9 r3c5=9 r9c5<>9) (r2c1<>9) r2c3<>9 r2c8=9 r9c8<>9 r9c4=9 r9c4<>8 r9c6=8 (r2c6<>8 r2c6=3 r7c6<>3) r3c6<>8 r3c9=8 (r3c9<>3) r3c9<>5 (r7c9=5 r7c9<>3) r3c7=5 r3c7<>3 r3c2=3 r7c2<>3 r7c7=3
r1c2=9 (r7c2<>9) (r9c2<>9) (r1c5<>9 r3c5=9 r9c5<>9) (r2c1<>9) r2c3<>9 r2c8=9 r9c8<>9 r9c4=9 r7c4<>9 r7c7=9
Forcing Net Contradiction in c7 => r1c5<>3
r1c5=3 r1c7<>3
r1c5=3 r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 r3c9<>5 r3c7=5 r3c7<>3
r1c5=3 r2c6<>3 r7c6=3 r7c7<>3
r1c5=3 (r3c5<>3) r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 (r3c9<>3) r3c9<>5 r3c7=5 r3c7<>3 r3c2=3 r79c2<>3 r8c13=3 r8c7<>3
Forcing Net Contradiction in r2c1 => r2c1<>3
r2c1=3 r2c1=3
r2c1=3 (r6c1<>3 r6c3=3 r8c3<>3 r8c7=3 r1c7<>3 r1c7=9 r2c8<>9) r2c6<>3 r7c6=3 r7c6<>5 r8c6=5 r8c6<>1 r3c6=1 r4c6<>1 r4c6=7 (r4c6<>1) r4c3<>7 r4c3=9 r2c3<>9 r2c1=9
Forcing Net Contradiction in r1 => r2c1<>7
r2c1=7 (r2c1<>9) (r8c1<>7) r6c1<>7 r6c1=3 r8c1<>3 r8c1=9 (r8c4<>9) (r7c2<>9) r9c2<>9 r3c2=9 (r3c7<>9) r2c3<>9 (r2c8=9 r1c7<>9) r4c3=9 r4c1<>9 r8c1=9 (r8c4<>9) (r7c2<>9) r8c7<>9 r7c7=9 r7c4<>9 r7c4=2 r8c4<>2 r8c4=1 r1c4<>1
r2c1=7 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r1c5<>1
r2c1=7 (r8c1<>7) r6c1<>7 r6c1=3 r8c1<>3 r8c1=9 (r7c2<>9) r9c2<>9 r3c2=9 r3c8<>9 r3c8=1 r1c9<>1
Forcing Net Verity => r2c6=3
r2c3=3 (r6c3<>3 r6c1=3 r8c1<>3 r8c7=3 r8c7<>2) (r8c3<>3) (r6c3<>3 r6c1=3 r8c1<>3) r2c6<>3 (r7c6=3 r7c2<>3 r9c2=3 r9c2<>2) (r7c6=3 r7c2<>3 r9c2=3 r9c2<>9 r7c2=9 r7c2<>2) r2c6=8 r2c1<>8 r2c1=9 r8c1<>9 r8c1=7 r8c3<>7 r8c3=2 r9c2<>2 r5c2=2 r5c7<>2 r7c7=2 r9c9<>2 r9c4=2 (r9c8<>2) r9c4<>8 r9c6=8 r2c6<>8 r2c6=3
r2c6=3 r2c6=3
r2c9=3 (r2c6<>3 r7c6=3 r9c5<>3 r9c2=3 r1c2<>3) (r2c9<>7) r2c9<>2 r2c8=2 r2c8<>7 r2c3=7 r1c2<>7 r1c2=4 (r3c2<>4) r5c2<>4 r5c3=4 r5c3<>8 r5c1=8 r2c1<>8 r2c1=9 r3c2<>9 r3c2=3 r3c5<>3 r2c6=3
Discontinuous Nice Loop: 1 r3c6 -1- r4c6 -7- r7c6 -5- r7c9 =5= r3c9 =8= r3c6 => r3c6<>1
Discontinuous Nice Loop: 2 r8c7 -2- r5c7 -7- r5c5 -1- r4c6 =1= r8c6 =5= r8c7 => r8c7<>2
Grouped Discontinuous Nice Loop: 3 r8c7 -3- r7c79 =3= r7c2 -3- r13c2 =3= r1c3 =4= r5c3 =8= r5c1 =1= r5c5 -1- r4c6 =1= r8c6 =5= r8c7 => r8c7<>3
Grouped Discontinuous Nice Loop: 9 r9c5 -9- r789c4 =9= r1c4 =1= r13c5 -1- r5c5 =1= r5c1 =8= r5c3 =4= r1c3 =3= r13c2 -3- r79c2 =3= r8c13 -3- r8c5 =3= r9c5 => r9c5<>9
Forcing Chain Contradiction in r8c4 => r5c2<>2
r5c2=2 r5c7<>2 r5c7=7 r5c5<>7 r5c5=1 r4c6<>1 r8c6=1 r8c4<>1
r5c2=2 r79c2<>2 r8c3=2 r8c4<>2
r5c2=2 r5c7<>2 r7c7=2 r7c4<>2 r7c4=9 r8c4<>9
Locked Candidates Type 1 (Pointing): 2 in b4 => r8c3<>2
Hidden Rectangle: 3/7 in r6c13,r8c13 => r6c1<>7
Naked Single: r6c1=3
Discontinuous Nice Loop: 3 r1c3 -3- r8c3 -7- r8c1 -9- r2c1 -8- r5c1 =8= r5c3 =4= r1c3 => r1c3<>3
Hidden Single: r8c3=3
Hidden Single: r9c5=3
Empty Rectangle: 7 in b7 (r58c5) => r5c2<>7
Naked Single: r5c2=4
Hidden Single: r1c3=4
Locked Candidates Type 1 (Pointing): 8 in b1 => r2c9<>8
Naked Pair: 2,7 in r29c9 => r167c9<>7, r67c9<>2
Naked Single: r6c9=1
Hidden Single: r3c8=1
2-String Kite: 7 in r1c2,r9c9 (connected by r1c7,r2c9) => r9c2<>7
Turbot Fish: 7 r1c7 =7= r1c2 -7- r7c2 =7= r8c1 => r8c7<>7
Turbot Fish: 7 r6c8 =7= r5c7 -7- r5c5 =7= r8c5 => r8c8<>7
W-Wing: 7/2 in r6c8,r9c9 connected by 2 in r2c89 => r9c8<>7
Finned X-Wing: 7 c15 r58 fr4c1 => r5c3<>7
Finned Swordfish: 9 c138 r248 fr9c8 => r8c7<>9
Naked Single: r8c7=5
Naked Single: r7c9=3
Naked Single: r1c9=8
Naked Single: r3c9=5
Hidden Single: r7c6=5
Hidden Single: r9c4=8
Hidden Single: r3c6=8
Hidden Single: r3c5=4
Locked Candidates Type 1 (Pointing): 9 in b2 => r1c7<>9
X-Wing: 7 r17 c27 => r5c7<>7
Naked Single: r5c7=2
Full House: r6c8=7
Full House: r6c3=2
Naked Single: r5c3=8
Hidden Single: r2c1=8
Skyscraper: 9 in r2c3,r9c2 (connected by r29c8) => r3c2<>9
Naked Single: r3c2=3
Full House: r3c7=9
Naked Single: r1c2=7
Full House: r2c3=9
Full House: r4c3=7
Naked Single: r2c8=2
Full House: r2c9=7
Full House: r1c7=3
Full House: r7c7=7
Full House: r9c9=2
Naked Single: r4c6=1
Full House: r4c1=9
Full House: r5c1=1
Full House: r5c5=7
Full House: r8c1=7
Naked Single: r9c2=9
Full House: r7c2=2
Full House: r7c4=9
Naked Single: r8c6=4
Full House: r9c6=7
Full House: r9c8=4
Full House: r8c8=9
Naked Single: r1c4=1
Full House: r1c5=9
Full House: r8c5=1
Full House: r8c4=2
|
sudoku_normal_extremely_hard_107
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....2.6..1..5.4..2..7......6..2.8.4.......39.5..896..4.1.6..8..8.......6.5...1..
|
574192368819653427236748915967321854148576239352489671421965783783214596695837142
|
. . . . . 2 . 6 .
. 1 . . 5 . 4 . .
2 . . 7 . . . . .
. 6 . . 2 . 8 . 4
. . . . . . . 3 9
. 5 . . 8 9 6 . .
4 . 1 . 6 . . 8 .
. 8 . . . . . . .
6 . 5 . . . 1 . .
|
5 7 4 1 9 2 3 6 8
8 1 9 6 5 3 4 2 7
2 3 6 7 4 8 9 1 5
9 6 7 3 2 1 8 5 4
1 4 8 5 7 6 2 3 9
3 5 2 4 8 9 6 7 1
4 2 1 9 6 5 7 8 3
7 8 3 2 1 4 5 9 6
6 9 5 8 3 7 1 4 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3398_hard
|
574192368819653427236748915967321854148576239352489671421965783783214596695837142 #1 Extreme (21512) bf
Hidden Single: r8c9=6
Hidden Single: r1c1=5
Brute Force: r5c4=5
Hidden Single: r4c8=5
Hidden Single: r5c6=6
Hidden Single: r2c4=6
Hidden Single: r3c3=6
Locked Candidates Type 1 (Pointing): 1 in b6 => r6c14<>1
AIC: 3 3- r2c6 -8- r2c1 =8= r5c1 =1= r5c5 -1- r4c4 -3 => r1c4,r4c6<>3
Locked Candidates Type 1 (Pointing): 3 in b5 => r789c4<>3
Discontinuous Nice Loop: 3 r8c6 -3- r2c6 -8- r3c6 =8= r3c9 =5= r3c7 -5- r8c7 =5= r8c6 => r8c6<>3
Forcing Chain Contradiction in r7c6 => r3c6<>3
r3c6=3 r7c6<>3
r3c6=3 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r3c6=3 r2c6<>3 r2c6=8 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r5c5<>7 r4c6=7 r7c6<>7
Forcing Chain Contradiction in c6 => r8c4<>4
r8c4=4 r89c6<>4 r3c6=4 r3c6<>1
r8c4=4 r6c4<>4 r6c4=3 r4c4<>3 r4c4=1 r4c6<>1
r8c4=4 r89c6<>4 r3c6=4 r3c6<>8 r3c9=8 r3c9<>5 r3c7=5 r8c7<>5 r8c6=5 r8c6<>1
Forcing Chain Contradiction in r7c6 => r9c4<>4
r9c4=4 r9c4<>8 r9c6=8 r2c6<>8 r2c6=3 r7c6<>3
r9c4=4 r9c4<>8 r9c6=8 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r9c4=4 r6c4<>4 r5c5=4 r5c5<>7 r4c6=7 r7c6<>7
Forcing Chain Contradiction in r7c6 => r9c6<>3
r9c6=3 r7c6<>3
r9c6=3 r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 r3c9<>5 r7c9=5 r7c6<>5
r9c6=3 r2c6<>3 r2c6=8 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r5c5<>7 r4c6=7 r7c6<>7
Forcing Net Contradiction in c4 => r4c4=3
r4c4<>3 r4c4=1
r4c4<>3 (r4c4=1 r5c5<>1 r5c1=1 r5c1<>8 r5c3=8 r5c3<>2) (r4c4=1 r4c6<>1 r4c6=7 r5c5<>7 r5c5=4 r5c2<>4) r6c4=3 r6c1<>3 r6c1=7 r5c2<>7 r5c2=2 (r5c7<>2) r6c3<>2 r8c3=2 (r8c4<>2) r8c7<>2 r7c7=2 r7c4<>2 r7c4=9 r8c4<>9 r8c4=1
Naked Single: r6c4=4
Discontinuous Nice Loop: 9 r1c3 -9- r4c3 =9= r4c1 =1= r5c1 =8= r5c3 =4= r1c3 => r1c3<>9
Forcing Chain Contradiction in r2c3 => r8c3<>9
r8c3=9 r4c3<>9 r4c1=9 r4c1<>1 r5c1=1 r5c1<>8 r2c1=8 r2c6<>8 r2c6=3 r2c3<>3
r8c3=9 r4c3<>9 r4c3=7 r2c3<>7
r8c3=9 r4c3<>9 r4c1=9 r4c1<>1 r5c1=1 r5c1<>8 r5c3=8 r2c3<>8
r8c3=9 r2c3<>9
Forcing Net Contradiction in r7c7 => r1c2<>9
r1c2=9 (r1c5<>9 r3c5=9 r3c5<>3) (r9c2<>9) (r1c5<>9 r3c5=9 r9c5<>9) (r2c1<>9) r2c3<>9 r2c8=9 r9c8<>9 r9c4=9 r9c4<>8 r9c6=8 (r2c6<>8 r2c6=3 r7c6<>3) r3c6<>8 r3c9=8 (r3c9<>3) r3c9<>5 (r7c9=5 r7c9<>3) r3c7=5 r3c7<>3 r3c2=3 r7c2<>3 r7c7=3
r1c2=9 (r7c2<>9) (r9c2<>9) (r1c5<>9 r3c5=9 r9c5<>9) (r2c1<>9) r2c3<>9 r2c8=9 r9c8<>9 r9c4=9 r7c4<>9 r7c7=9
Forcing Net Contradiction in c7 => r1c5<>3
r1c5=3 r1c7<>3
r1c5=3 r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 r3c9<>5 r3c7=5 r3c7<>3
r1c5=3 r2c6<>3 r7c6=3 r7c7<>3
r1c5=3 (r3c5<>3) r2c6<>3 r2c6=8 r3c6<>8 r3c9=8 (r3c9<>3) r3c9<>5 r3c7=5 r3c7<>3 r3c2=3 r79c2<>3 r8c13=3 r8c7<>3
Forcing Net Contradiction in r2c1 => r2c1<>3
r2c1=3 r2c1=3
r2c1=3 (r6c1<>3 r6c3=3 r8c3<>3 r8c7=3 r1c7<>3 r1c7=9 r2c8<>9) r2c6<>3 r7c6=3 r7c6<>5 r8c6=5 r8c6<>1 r3c6=1 r4c6<>1 r4c6=7 (r4c6<>1) r4c3<>7 r4c3=9 r2c3<>9 r2c1=9
Forcing Net Contradiction in r1 => r2c1<>7
r2c1=7 (r2c1<>9) (r8c1<>7) r6c1<>7 r6c1=3 r8c1<>3 r8c1=9 (r8c4<>9) (r7c2<>9) r9c2<>9 r3c2=9 (r3c7<>9) r2c3<>9 (r2c8=9 r1c7<>9) r4c3=9 r4c1<>9 r8c1=9 (r8c4<>9) (r7c2<>9) r8c7<>9 r7c7=9 r7c4<>9 r7c4=2 r8c4<>2 r8c4=1 r1c4<>1
r2c1=7 r2c1<>8 r5c1=8 r5c1<>1 r5c5=1 r1c5<>1
r2c1=7 (r8c1<>7) r6c1<>7 r6c1=3 r8c1<>3 r8c1=9 (r7c2<>9) r9c2<>9 r3c2=9 r3c8<>9 r3c8=1 r1c9<>1
Forcing Net Verity => r2c6=3
r2c3=3 (r6c3<>3 r6c1=3 r8c1<>3 r8c7=3 r8c7<>2) (r8c3<>3) (r6c3<>3 r6c1=3 r8c1<>3) r2c6<>3 (r7c6=3 r7c2<>3 r9c2=3 r9c2<>2) (r7c6=3 r7c2<>3 r9c2=3 r9c2<>9 r7c2=9 r7c2<>2) r2c6=8 r2c1<>8 r2c1=9 r8c1<>9 r8c1=7 r8c3<>7 r8c3=2 r9c2<>2 r5c2=2 r5c7<>2 r7c7=2 r9c9<>2 r9c4=2 (r9c8<>2) r9c4<>8 r9c6=8 r2c6<>8 r2c6=3
r2c6=3 r2c6=3
r2c9=3 (r2c6<>3 r7c6=3 r9c5<>3 r9c2=3 r1c2<>3) (r2c9<>7) r2c9<>2 r2c8=2 r2c8<>7 r2c3=7 r1c2<>7 r1c2=4 (r3c2<>4) r5c2<>4 r5c3=4 r5c3<>8 r5c1=8 r2c1<>8 r2c1=9 r3c2<>9 r3c2=3 r3c5<>3 r2c6=3
Discontinuous Nice Loop: 1 r3c6 -1- r4c6 -7- r7c6 -5- r7c9 =5= r3c9 =8= r3c6 => r3c6<>1
Discontinuous Nice Loop: 2 r8c7 -2- r5c7 -7- r5c5 -1- r4c6 =1= r8c6 =5= r8c7 => r8c7<>2
Grouped Discontinuous Nice Loop: 3 r8c7 -3- r7c79 =3= r7c2 -3- r13c2 =3= r1c3 =4= r5c3 =8= r5c1 =1= r5c5 -1- r4c6 =1= r8c6 =5= r8c7 => r8c7<>3
Grouped Discontinuous Nice Loop: 9 r9c5 -9- r789c4 =9= r1c4 =1= r13c5 -1- r5c5 =1= r5c1 =8= r5c3 =4= r1c3 =3= r13c2 -3- r79c2 =3= r8c13 -3- r8c5 =3= r9c5 => r9c5<>9
Forcing Chain Contradiction in r8c4 => r5c2<>2
r5c2=2 r5c7<>2 r5c7=7 r5c5<>7 r5c5=1 r4c6<>1 r8c6=1 r8c4<>1
r5c2=2 r79c2<>2 r8c3=2 r8c4<>2
r5c2=2 r5c7<>2 r7c7=2 r7c4<>2 r7c4=9 r8c4<>9
Locked Candidates Type 1 (Pointing): 2 in b4 => r8c3<>2
Hidden Rectangle: 3/7 in r6c13,r8c13 => r6c1<>7
Naked Single: r6c1=3
Discontinuous Nice Loop: 3 r1c3 -3- r8c3 -7- r8c1 -9- r2c1 -8- r5c1 =8= r5c3 =4= r1c3 => r1c3<>3
Hidden Single: r8c3=3
Hidden Single: r9c5=3
Empty Rectangle: 7 in b7 (r58c5) => r5c2<>7
Naked Single: r5c2=4
Hidden Single: r1c3=4
Locked Candidates Type 1 (Pointing): 8 in b1 => r2c9<>8
Naked Pair: 2,7 in r29c9 => r167c9<>7, r67c9<>2
Naked Single: r6c9=1
Hidden Single: r3c8=1
2-String Kite: 7 in r1c2,r9c9 (connected by r1c7,r2c9) => r9c2<>7
Turbot Fish: 7 r1c7 =7= r1c2 -7- r7c2 =7= r8c1 => r8c7<>7
Turbot Fish: 7 r6c8 =7= r5c7 -7- r5c5 =7= r8c5 => r8c8<>7
W-Wing: 7/2 in r6c8,r9c9 connected by 2 in r2c89 => r9c8<>7
Finned X-Wing: 7 c15 r58 fr4c1 => r5c3<>7
Finned Swordfish: 9 c138 r248 fr9c8 => r8c7<>9
Naked Single: r8c7=5
Naked Single: r7c9=3
Naked Single: r1c9=8
Naked Single: r3c9=5
Hidden Single: r7c6=5
Hidden Single: r9c4=8
Hidden Single: r3c6=8
Hidden Single: r3c5=4
Locked Candidates Type 1 (Pointing): 9 in b2 => r1c7<>9
X-Wing: 7 r17 c27 => r5c7<>7
Naked Single: r5c7=2
Full House: r6c8=7
Full House: r6c3=2
Naked Single: r5c3=8
Hidden Single: r2c1=8
Skyscraper: 9 in r2c3,r9c2 (connected by r29c8) => r3c2<>9
Naked Single: r3c2=3
Full House: r3c7=9
Naked Single: r1c2=7
Full House: r2c3=9
Full House: r4c3=7
Naked Single: r2c8=2
Full House: r2c9=7
Full House: r1c7=3
Full House: r7c7=7
Full House: r9c9=2
Naked Single: r4c6=1
Full House: r4c1=9
Full House: r5c1=1
Full House: r5c5=7
Full House: r8c1=7
Naked Single: r9c2=9
Full House: r7c2=2
Full House: r7c4=9
Naked Single: r8c6=4
Full House: r9c6=7
Full House: r9c8=4
Full House: r8c8=9
Naked Single: r1c4=1
Full House: r1c5=9
Full House: r8c5=1
Full House: r8c4=2
|
sudoku_normal_hard_108
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.8.6...7..74...9...3..8...2.2..7..5..6854...1.57..6.9..423......13..5...89..1...3
|
289634175674251938135987462421879356968543721357126894542398617713465289896712543
|
. 8 . 6 . . . 7 .
. 7 4 . . . 9 . .
. 3 . . 8 . . . 2
. 2 . . 7 . . 5 .
. 6 8 5 4 . . . 1
. 5 7 . . 6 . 9 .
. 4 2 3 . . . . .
. 1 3 . . 5 . . .
8 9 . . 1 . . . 3
|
2 8 9 6 3 4 1 7 5
6 7 4 2 5 1 9 3 8
1 3 5 9 8 7 4 6 2
4 2 1 8 7 9 3 5 6
9 6 8 5 4 3 7 2 1
3 5 7 1 2 6 8 9 4
5 4 2 3 9 8 6 1 7
7 1 3 4 6 5 2 8 9
8 9 6 7 1 2 5 4 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3585_hard
|
289634175674251938135987462421879356968543721357126894542398617713465289896712543 #1 Extreme (26340) bf
Forcing Net Contradiction in r3 => r7c9<>6
r7c9=6 (r7c1<>6) (r7c5<>6 r7c5=9 r7c1<>9) (r7c5<>6 r8c5=6 r8c1<>6) r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 r3c1<>5
r7c9=6 (r7c9<>7) r7c9<>9 r8c9=9 (r8c1<>9 r8c1=7 r9c3<>7) r8c9<>7 r6c9=7 r6c3<>7 r3c3=7 r3c3<>5
r7c9=6 (r7c9<>7) r7c9<>9 r8c9=9 (r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 r5c1<>5) (r8c1<>9 r8c1=7 r5c1<>7) r8c9<>7 r6c9=7 r5c7<>7 r5c2=7 r5c2<>5 r5c4=5 r3c4<>5
r7c9=6 (r7c1<>6) (r7c5<>6 r7c5=9 r7c1<>9) (r7c5<>6 r8c5=6 r8c1<>6) r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 (r9c2<>5) r9c3<>5 r9c7=5 r3c7<>5
Brute Force: r5c4=5
Brute Force: r5c2=6
Empty Rectangle: 7 in b7 (r5c17) => r9c7<>7
Empty Rectangle: 9 in b7 (r5c16) => r9c6<>9
Forcing Net Verity => r5c7=7
r7c1=5 (r3c1<>5) (r9c2<>5) r9c3<>5 r9c7=5 r3c7<>5 r3c3=5 (r3c3<>7) r3c3<>6 r9c3=6 r9c3<>7 r6c3=7 r5c1<>7 r5c7=7
r7c1=6 (r8c1<>6) r7c5<>6 r7c5=9 r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r5c1<>7 r5c7=7
r7c1=7 r5c1<>7 r5c7=7
r7c1=9 (r3c1<>9) (r5c1<>9 r5c6=9 r3c6<>9) (r9c2<>9) r9c3<>9 r9c4=9 r3c4<>9 r3c3=9 (r3c3<>7) r3c3<>6 r9c3=6 r9c3<>7 r6c3=7 r5c1<>7 r5c7=7
Hidden Pair: 7,9 in r78c9 => r7c9<>5, r78c9<>8, r8c9<>4, r8c9<>6
Locked Candidates Type 1 (Pointing): 5 in b9 => r13c7<>5
Locked Candidates Type 2 (Claiming): 5 in r3 => r1c123,r2c12<>5
Naked Pair: 1,9 in r14c3 => r36c3<>1, r39c3<>9
2-String Kite: 9 in r1c3,r5c6 (connected by r4c3,r5c1) => r1c6<>9
Sashimi Swordfish: 9 r359 c146 fr9c2 => r78c1<>9
Hidden Single: r9c2=9
Naked Single: r4c2=2
Naked Single: r1c2=8
Naked Single: r2c2=7
Full House: r6c2=5
Naked Single: r6c3=7
Locked Candidates Type 2 (Claiming): 7 in r9 => r7c6,r8c4<>7
Discontinuous Nice Loop: 1 r1c1 -1- r6c1 =1= r6c4 -1- r2c4 -2- r2c1 =2= r1c1 => r1c1<>1
Discontinuous Nice Loop: 2 r2c5 -2- r2c4 -1- r6c4 =1= r6c1 -1- r4c3 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =5= r2c5 => r2c5<>2
Discontinuous Nice Loop: 3 r2c5 -3- r2c8 =3= r5c8 =2= r5c6 -2- r6c5 -3- r2c5 => r2c5<>3
Naked Single: r2c5=5
Hidden Single: r1c9=5
Locked Candidates Type 2 (Claiming): 4 in c9 => r46c7<>4
Discontinuous Nice Loop: 1 r4c1 -1- r4c3 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =6= r4c9 =4= r4c1 => r4c1<>1
Discontinuous Nice Loop: 9 r4c1 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =6= r4c9 =4= r4c1 => r4c1<>9
Grouped Discontinuous Nice Loop: 8 r4c9 -8- r2c9 =8= r2c8 =3= r5c8 -3- r5c1 -9- r4c3 -1- r6c1 =1= r6c4 =8= r4c46 -8- r4c9 => r4c9<>8
Grouped Discontinuous Nice Loop: 9 r7c6 -9- r5c6 =9= r5c1 -9- r3c1 =9= r1c13 -9- r1c5 =9= r78c5 -9- r7c6 => r7c6<>9
Naked Single: r7c6=8
Sue de Coq: r8c45 - {2469} (r8c19 - {679}, r9c46 - {247}) => r8c78<>6
Discontinuous Nice Loop: 9 r4c4 -9- r4c3 -1- r6c1 =1= r6c4 =8= r4c4 => r4c4<>9
Locked Candidates Type 1 (Pointing): 9 in b5 => r3c6<>9
Naked Triple: 1,2,8 in r246c4 => r3c4<>1, r89c4<>2
Turbot Fish: 2 r5c8 =2= r5c6 -2- r9c6 =2= r8c5 => r8c8<>2
Hidden Rectangle: 4/7 in r3c46,r9c46 => r3c6<>4
Discontinuous Nice Loop: 1/2/3 r1c6 =4= r9c6 =2= r8c5 =6= r8c1 =7= r7c1 =5= r3c1 =9= r3c4 =4= r1c6 => r1c6<>1, r1c6<>2, r1c6<>3
Naked Single: r1c6=4
XY-Wing: 1/7/2 in r2c4,r39c6 => r2c6<>2
X-Wing: 2 c68 r59 => r9c7<>2
Discontinuous Nice Loop: 1/6/8 r2c8 =3= r5c8 -3- r5c1 -9- r4c3 -1- r1c3 =1= r1c7 =3= r2c8 => r2c8<>1, r2c8<>6, r2c8<>8
Naked Single: r2c8=3
Naked Single: r1c7=1
Naked Single: r2c6=1
Naked Single: r5c8=2
Naked Single: r1c3=9
Naked Single: r2c4=2
Naked Single: r3c6=7
Naked Single: r1c1=2
Full House: r1c5=3
Full House: r3c4=9
Naked Single: r4c3=1
Naked Single: r2c1=6
Full House: r2c9=8
Naked Single: r9c6=2
Naked Single: r6c5=2
Naked Single: r8c4=4
Naked Single: r4c4=8
Naked Single: r3c3=5
Full House: r3c1=1
Full House: r9c3=6
Naked Single: r8c1=7
Full House: r7c1=5
Naked Single: r6c9=4
Naked Single: r8c8=8
Naked Single: r9c4=7
Full House: r6c4=1
Naked Single: r9c8=4
Full House: r9c7=5
Naked Single: r8c9=9
Naked Single: r7c7=6
Naked Single: r4c9=6
Full House: r7c9=7
Naked Single: r6c1=3
Full House: r6c7=8
Full House: r4c7=3
Naked Single: r8c7=2
Full House: r8c5=6
Full House: r3c7=4
Full House: r3c8=6
Full House: r7c5=9
Full House: r7c8=1
Naked Single: r4c1=4
Full House: r5c1=9
Full House: r4c6=9
Full House: r5c6=3
|
sudoku_normal_extremely_hard_108
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
...6...7...4...9...3..8...2....7..5...8.4...1.....6.9..423......13..5...8...1...3
|
289634175674251938135987462421879356968543721357126894542398617713465289896712543
|
. . . 6 . . . 7 .
. . 4 . . . 9 . .
. 3 . . 8 . . . 2
. . . . 7 . . 5 .
. . 8 . 4 . . . 1
. . . . . 6 . 9 .
. 4 2 3 . . . . .
. 1 3 . . 5 . . .
8 . . . 1 . . . 3
|
2 8 9 6 3 4 1 7 5
6 7 4 2 5 1 9 3 8
1 3 5 9 8 7 4 6 2
4 2 1 8 7 9 3 5 6
9 6 8 5 4 3 7 2 1
3 5 7 1 2 6 8 9 4
5 4 2 3 9 8 6 1 7
7 1 3 4 6 5 2 8 9
8 9 6 7 1 2 5 4 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3585_hard
|
289634175674251938135987462421879356968543721357126894542398617713465289896712543 #1 Extreme (26340) bf
Forcing Net Contradiction in r3 => r7c9<>6
r7c9=6 (r7c1<>6) (r7c5<>6 r7c5=9 r7c1<>9) (r7c5<>6 r8c5=6 r8c1<>6) r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 r3c1<>5
r7c9=6 (r7c9<>7) r7c9<>9 r8c9=9 (r8c1<>9 r8c1=7 r9c3<>7) r8c9<>7 r6c9=7 r6c3<>7 r3c3=7 r3c3<>5
r7c9=6 (r7c9<>7) r7c9<>9 r8c9=9 (r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 r5c1<>5) (r8c1<>9 r8c1=7 r5c1<>7) r8c9<>7 r6c9=7 r5c7<>7 r5c2=7 r5c2<>5 r5c4=5 r3c4<>5
r7c9=6 (r7c1<>6) (r7c5<>6 r7c5=9 r7c1<>9) (r7c5<>6 r8c5=6 r8c1<>6) r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r7c1<>7 r7c1=5 (r9c2<>5) r9c3<>5 r9c7=5 r3c7<>5
Brute Force: r5c4=5
Brute Force: r5c2=6
Empty Rectangle: 7 in b7 (r5c17) => r9c7<>7
Empty Rectangle: 9 in b7 (r5c16) => r9c6<>9
Forcing Net Verity => r5c7=7
r7c1=5 (r3c1<>5) (r9c2<>5) r9c3<>5 r9c7=5 r3c7<>5 r3c3=5 (r3c3<>7) r3c3<>6 r9c3=6 r9c3<>7 r6c3=7 r5c1<>7 r5c7=7
r7c1=6 (r8c1<>6) r7c5<>6 r7c5=9 r7c9<>9 r8c9=9 r8c1<>9 r8c1=7 r5c1<>7 r5c7=7
r7c1=7 r5c1<>7 r5c7=7
r7c1=9 (r3c1<>9) (r5c1<>9 r5c6=9 r3c6<>9) (r9c2<>9) r9c3<>9 r9c4=9 r3c4<>9 r3c3=9 (r3c3<>7) r3c3<>6 r9c3=6 r9c3<>7 r6c3=7 r5c1<>7 r5c7=7
Hidden Pair: 7,9 in r78c9 => r7c9<>5, r78c9<>8, r8c9<>4, r8c9<>6
Locked Candidates Type 1 (Pointing): 5 in b9 => r13c7<>5
Locked Candidates Type 2 (Claiming): 5 in r3 => r1c123,r2c12<>5
Naked Pair: 1,9 in r14c3 => r36c3<>1, r39c3<>9
2-String Kite: 9 in r1c3,r5c6 (connected by r4c3,r5c1) => r1c6<>9
Sashimi Swordfish: 9 r359 c146 fr9c2 => r78c1<>9
Hidden Single: r9c2=9
Naked Single: r4c2=2
Naked Single: r1c2=8
Naked Single: r2c2=7
Full House: r6c2=5
Naked Single: r6c3=7
Locked Candidates Type 2 (Claiming): 7 in r9 => r7c6,r8c4<>7
Discontinuous Nice Loop: 1 r1c1 -1- r6c1 =1= r6c4 -1- r2c4 -2- r2c1 =2= r1c1 => r1c1<>1
Discontinuous Nice Loop: 2 r2c5 -2- r2c4 -1- r6c4 =1= r6c1 -1- r4c3 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =5= r2c5 => r2c5<>2
Discontinuous Nice Loop: 3 r2c5 -3- r2c8 =3= r5c8 =2= r5c6 -2- r6c5 -3- r2c5 => r2c5<>3
Naked Single: r2c5=5
Hidden Single: r1c9=5
Locked Candidates Type 2 (Claiming): 4 in c9 => r46c7<>4
Discontinuous Nice Loop: 1 r4c1 -1- r4c3 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =6= r4c9 =4= r4c1 => r4c1<>1
Discontinuous Nice Loop: 9 r4c1 -9- r5c1 -3- r5c8 =3= r2c8 =8= r2c9 =6= r4c9 =4= r4c1 => r4c1<>9
Grouped Discontinuous Nice Loop: 8 r4c9 -8- r2c9 =8= r2c8 =3= r5c8 -3- r5c1 -9- r4c3 -1- r6c1 =1= r6c4 =8= r4c46 -8- r4c9 => r4c9<>8
Grouped Discontinuous Nice Loop: 9 r7c6 -9- r5c6 =9= r5c1 -9- r3c1 =9= r1c13 -9- r1c5 =9= r78c5 -9- r7c6 => r7c6<>9
Naked Single: r7c6=8
Sue de Coq: r8c45 - {2469} (r8c19 - {679}, r9c46 - {247}) => r8c78<>6
Discontinuous Nice Loop: 9 r4c4 -9- r4c3 -1- r6c1 =1= r6c4 =8= r4c4 => r4c4<>9
Locked Candidates Type 1 (Pointing): 9 in b5 => r3c6<>9
Naked Triple: 1,2,8 in r246c4 => r3c4<>1, r89c4<>2
Turbot Fish: 2 r5c8 =2= r5c6 -2- r9c6 =2= r8c5 => r8c8<>2
Hidden Rectangle: 4/7 in r3c46,r9c46 => r3c6<>4
Discontinuous Nice Loop: 1/2/3 r1c6 =4= r9c6 =2= r8c5 =6= r8c1 =7= r7c1 =5= r3c1 =9= r3c4 =4= r1c6 => r1c6<>1, r1c6<>2, r1c6<>3
Naked Single: r1c6=4
XY-Wing: 1/7/2 in r2c4,r39c6 => r2c6<>2
X-Wing: 2 c68 r59 => r9c7<>2
Discontinuous Nice Loop: 1/6/8 r2c8 =3= r5c8 -3- r5c1 -9- r4c3 -1- r1c3 =1= r1c7 =3= r2c8 => r2c8<>1, r2c8<>6, r2c8<>8
Naked Single: r2c8=3
Naked Single: r1c7=1
Naked Single: r2c6=1
Naked Single: r5c8=2
Naked Single: r1c3=9
Naked Single: r2c4=2
Naked Single: r3c6=7
Naked Single: r1c1=2
Full House: r1c5=3
Full House: r3c4=9
Naked Single: r4c3=1
Naked Single: r2c1=6
Full House: r2c9=8
Naked Single: r9c6=2
Naked Single: r6c5=2
Naked Single: r8c4=4
Naked Single: r4c4=8
Naked Single: r3c3=5
Full House: r3c1=1
Full House: r9c3=6
Naked Single: r8c1=7
Full House: r7c1=5
Naked Single: r6c9=4
Naked Single: r8c8=8
Naked Single: r9c4=7
Full House: r6c4=1
Naked Single: r9c8=4
Full House: r9c7=5
Naked Single: r8c9=9
Naked Single: r7c7=6
Naked Single: r4c9=6
Full House: r7c9=7
Naked Single: r6c1=3
Full House: r6c7=8
Full House: r4c7=3
Naked Single: r8c7=2
Full House: r8c5=6
Full House: r3c7=4
Full House: r3c8=6
Full House: r7c5=9
Full House: r7c8=1
Naked Single: r4c1=4
Full House: r5c1=9
Full House: r4c6=9
Full House: r5c6=3
|
sudoku_normal_hard_109
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8.5..1.4..13...2.1...63...4.......2..34..7...79....8.....36....4.9..235..7..1.9
|
368254917475139862912876354843567291291348576657921438729413685184695723536782149
|
. . 8 . 5 . . 1 .
4 . . 1 3 . . . 2
. 1 . . . 6 3 . .
. 4 . . . . . . .
2 . . 3 4 . . 7 .
. . 7 9 . . . . 8
. . . . . 3 6 . .
. . 4 . 9 . . 2 3
5 . . 7 . . 1 . 9
|
3 6 8 2 5 4 9 1 7
4 7 5 1 3 9 8 6 2
9 1 2 8 7 6 3 5 4
8 4 3 5 6 7 2 9 1
2 9 1 3 4 8 5 7 6
6 5 7 9 2 1 4 3 8
7 2 9 4 1 3 6 8 5
1 8 4 6 9 5 7 2 3
5 3 6 7 8 2 1 4 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7547_hard
|
368254917475139862912876354843567291291348576657921438729413685184695723536782149 #1 Extreme (20530) bf
Brute Force: r5c4=3
Hidden Single: r2c5=3
Skyscraper: 3 in r8c9,r9c3 (connected by r4c39) => r8c12,r9c8<>3
Hidden Single: r8c9=3
Grouped AIC: 8/9 9- r2c6 =9= r1c6 =4= r9c6 -4- r9c8 -8- r89c7 =8= r2c7 -8 => r2c6<>8, r2c7<>9
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c8<>8
Grouped Discontinuous Nice Loop: 5 r2c7 -5- r2c23 =5= r3c3 =2= r1c2 -2- r1c4 -4- r1c6 =4= r9c6 -4- r9c8 -8- r2c8 =8= r2c7 => r2c7<>5
Almost Locked Set XY-Wing: A=r6c12568 {123456}, B=r137c4 {2458}, C=r79c8 {458}, X,Y=4,5, Z=2 => r4c4<>2
Almost Locked Set XY-Wing: A=r124569c7 {1245789}, B=r34679c8 {345689}, C=r45c9 {156}, X,Y=5,6, Z=8 => r8c7<>8
Forcing Chain Contradiction in c8 => r4c5<>2
r4c5=2 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r2c8<>9
r4c5=2 r4c5<>7 r3c5=7 r3c1<>7 r3c1=9 r3c8<>9
r4c5=2 r4c7<>2 r6c7=2 r6c7<>4 r6c8=4 r6c8<>3 r4c8=3 r4c8<>9
Almost Locked Set XY-Wing: A=r4c1345689 {12356789}, B=r9c78 {148}, C=r5689c6 {12458}, X,Y=2,4, Z=1 => r4c7<>1
Forcing Chain Contradiction in c1 => r4c8<>6
r4c8=6 r2c8<>6 r1c9=6 r1c1<>6
r4c8=6 r4c1<>6
r4c8=6 r5c9<>6 r5c23=6 r6c1<>6
r4c8=6 r4c4<>6 r8c4=6 r8c1<>6
Forcing Chain Contradiction in r1c7 => r2c7=8
r2c7<>8 r2c7=7 r8c7<>7 r7c9=7 r7c9<>4 r13c9=4 r1c7<>4
r2c7<>8 r2c7=7 r1c7<>7
r2c7<>8 r2c8=8 r2c8<>6 r6c8=6 r6c8<>3 r4c8=3 r4c8<>9 r45c7=9 r1c7<>9
AIC: 9 9- r1c6 =9= r2c6 =7= r2c2 -7- r3c1 -9 => r1c12<>9
Discontinuous Nice Loop: 1 r8c7 -1- r9c7 -4- r9c6 =4= r1c6 =9= r1c7 =7= r8c7 => r8c7<>1
Discontinuous Nice Loop: 1 r9c3 -1- r9c7 -4- r6c7 =4= r6c8 =3= r4c8 -3- r4c3 =3= r9c3 => r9c3<>1
Grouped AIC: 1/4 4- r6c7 =4= r6c8 =3= r4c8 =9= r45c7 -9- r1c7 =9= r1c6 =4= r9c6 -4- r9c7 -1 => r6c7<>1, r9c7<>4
Naked Single: r9c7=1
Finned X-Wing: 1 r68 c16 fr6c5 => r45c6<>1
Discontinuous Nice Loop: 8 r4c5 -8- r5c6 -5- r5c7 -9- r1c7 =9= r1c6 -9- r2c6 -7- r4c6 =7= r4c5 => r4c5<>8
Discontinuous Nice Loop: 8 r9c6 -8- r5c6 -5- r5c7 -9- r1c7 =9= r1c6 =4= r9c6 => r9c6<>8
Forcing Chain Contradiction in r6c1 => r2c8<>5
r2c8=5 r2c8<>6 r6c8=6 r6c8<>3 r4c8=3 r4c8<>9 r45c7=9 r1c7<>9 r1c6=9 r2c6<>9 r2c6=7 r4c6<>7 r4c5=7 r4c5<>1 r6c56=1 r6c1<>1
r2c8=5 r2c23<>5 r3c3=5 r3c3<>2 r1c2=2 r1c2<>3 r1c1=3 r6c1<>3
r2c8=5 r2c8<>6 r6c8=6 r6c1<>6
Locked Candidates Type 1 (Pointing): 5 in b3 => r3c3<>5
Forcing Chain Contradiction in r1c7 => r3c5<>2
r3c5=2 r1c4<>2 r1c4=4 r1c7<>4
r3c5=2 r13c4<>2 r7c4=2 r7c4<>5 r7c89=5 r8c7<>5 r8c7=7 r1c7<>7
r3c5=2 r3c3<>2 r3c3=9 r3c1<>9 r3c1=7 r2c2<>7 r2c6=7 r2c6<>9 r1c6=9 r1c7<>9
Forcing Chain Contradiction in r4 => r4c5<>1
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c2=7 r2c2<>5 r2c3=5 r4c3<>5
r4c5=1 r7c5<>1 r8c6=1 r8c6<>5 r78c4=5 r4c4<>5
r4c5=1 r4c5<>7 r4c6=7 r4c6<>5
r4c5=1 r4c5<>7 r4c6=7 r4c6<>2 r4c7=2 r4c7<>5
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r1c6<>9 r1c7=9 r5c7<>9 r5c7=5 r4c8<>5
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r1c6<>9 r1c7=9 r5c7<>9 r5c7=5 r4c9<>5
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c1<>1
Sue de Coq: r45c3 - {13569} (r37c3 - {129}, r6c12 - {356}) => r4c1<>3, r4c1,r5c2<>6, r5c2<>5, r2c3<>9, r9c3<>2
Naked Triple: 5,8,9 in r5c267 => r5c39<>5, r5c3<>9
2-String Kite: 6 in r2c8,r5c3 (connected by r5c9,r6c8) => r2c3<>6
Naked Single: r2c3=5
Hidden Single: r6c2=5
Grouped Discontinuous Nice Loop: 2 r1c6 -2- r13c4 =2= r7c4 -2- r7c23 =2= r9c2 =3= r9c3 -3- r4c3 =3= r4c8 =9= r45c7 -9- r1c7 =9= r1c6 => r1c6<>2
Locked Candidates Type 1 (Pointing): 2 in b2 => r7c4<>2
Grouped Discontinuous Nice Loop: 8 r9c2 -8- r9c8 -4- r9c6 =4= r1c6 =9= r1c7 -9- r45c7 =9= r4c8 =3= r4c3 -3- r9c3 =3= r9c2 => r9c2<>8
Almost Locked Set XZ-Rule: A=r9c2356 {23468}, B=r12c6,r3c5 {4789}, X=4,8, Z=8 => r7c5<>8
Almost Locked Set XY-Wing: A=r5c2 {89}, B=r7c489 {4578}, C=r58c7 {579}, X,Y=7,9, Z=8 => r7c2<>8
Almost Locked Set Chain: 27- r1c4679 {24679} -6- r5c2679 {15689} -1- r5c3 {16} -6- r6c1 {36} -3- r13c1,r2c2,r3c3 {23679} -27 => r1c2,r3c4<>2, r1c2<>7
Hidden Single: r1c4=2
Hidden Single: r3c3=2
2-String Kite: 4 in r3c4,r9c8 (connected by r7c4,r9c6) => r3c8<>4
Grouped Discontinuous Nice Loop: 7 r8c1 -7- r8c7 =7= r1c7 =9= r1c6 -9- r2c6 -7- r2c2 =7= r13c1 -7- r8c1 => r8c1<>7
Almost Locked Set XY-Wing: A=r1456c7 {24579}, B=r137c9 {4567}, C=r1c12 {367}, X,Y=6,7, Z=5 => r4c9<>5
Locked Pair: 1,6 in r45c9 => r1c9,r6c8<>6
Hidden Single: r2c8=6
Naked Pair: 7,9 in r2c2,r3c1 => r1c1<>7
Naked Pair: 3,6 in r16c1 => r8c1<>6
Swordfish: 9 r125 c267 => r4c7,r7c2<>9
Uniqueness Test 1: 1/6 in r4c39,r5c39 => r4c3<>1, r4c3<>6
2-String Kite: 6 in r6c5,r9c3 (connected by r5c3,r6c1) => r9c5<>6
Hidden Single: r8c4=6
Naked Pair: 5,8 in r4c4,r5c6 => r4c6<>5, r4c6<>8
Naked Triple: 2,4,8 in r9c568 => r9c2<>2
Hidden Single: r7c2=2
Naked Single: r7c5=1
Naked Single: r7c3=9
Naked Single: r4c3=3
Naked Single: r6c1=6
Naked Single: r9c3=6
Full House: r5c3=1
Naked Single: r1c1=3
Naked Single: r6c5=2
Naked Single: r9c2=3
Naked Single: r5c9=6
Naked Single: r1c2=6
Naked Single: r4c6=7
Naked Single: r6c6=1
Naked Single: r6c7=4
Full House: r6c8=3
Naked Single: r9c5=8
Naked Single: r4c9=1
Naked Single: r2c6=9
Full House: r2c2=7
Full House: r3c1=9
Naked Single: r4c5=6
Full House: r3c5=7
Naked Single: r8c6=5
Naked Single: r9c8=4
Full House: r9c6=2
Full House: r7c4=4
Naked Single: r1c6=4
Full House: r5c6=8
Full House: r3c4=8
Full House: r4c4=5
Naked Single: r8c2=8
Full House: r5c2=9
Full House: r4c1=8
Full House: r5c7=5
Naked Single: r3c8=5
Full House: r3c9=4
Naked Single: r8c7=7
Full House: r8c1=1
Full House: r7c1=7
Naked Single: r1c9=7
Full House: r1c7=9
Full House: r4c7=2
Full House: r4c8=9
Full House: r7c8=8
Full House: r7c9=5
|
sudoku_normal_extremely_hard_109
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8.5..1.4..1....2.1...63...4.......2...4..7...79....8.....36....4.9..2.5..7....9
|
368254917475139862912876354843567291291348576657921438729413685184695723536782149
|
. . 8 . 5 . . 1 .
4 . . 1 . . . . 2
. 1 . . . 6 3 . .
. 4 . . . . . . .
2 . . . 4 . . 7 .
. . 7 9 . . . . 8
. . . . . 3 6 . .
. . 4 . 9 . . 2 .
5 . . 7 . . . . 9
|
3 6 8 2 5 4 9 1 7
4 7 5 1 3 9 8 6 2
9 1 2 8 7 6 3 5 4
8 4 3 5 6 7 2 9 1
2 9 1 3 4 8 5 7 6
6 5 7 9 2 1 4 3 8
7 2 9 4 1 3 6 8 5
1 8 4 6 9 5 7 2 3
5 3 6 7 8 2 1 4 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7547_hard
|
368254917475139862912876354843567291291348576657921438729413685184695723536782149 #1 Extreme (20530) bf
Brute Force: r5c4=3
Hidden Single: r2c5=3
Skyscraper: 3 in r8c9,r9c3 (connected by r4c39) => r8c12,r9c8<>3
Hidden Single: r8c9=3
Grouped AIC: 8/9 9- r2c6 =9= r1c6 =4= r9c6 -4- r9c8 -8- r89c7 =8= r2c7 -8 => r2c6<>8, r2c7<>9
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c8<>8
Grouped Discontinuous Nice Loop: 5 r2c7 -5- r2c23 =5= r3c3 =2= r1c2 -2- r1c4 -4- r1c6 =4= r9c6 -4- r9c8 -8- r2c8 =8= r2c7 => r2c7<>5
Almost Locked Set XY-Wing: A=r6c12568 {123456}, B=r137c4 {2458}, C=r79c8 {458}, X,Y=4,5, Z=2 => r4c4<>2
Almost Locked Set XY-Wing: A=r124569c7 {1245789}, B=r34679c8 {345689}, C=r45c9 {156}, X,Y=5,6, Z=8 => r8c7<>8
Forcing Chain Contradiction in c8 => r4c5<>2
r4c5=2 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r2c8<>9
r4c5=2 r4c5<>7 r3c5=7 r3c1<>7 r3c1=9 r3c8<>9
r4c5=2 r4c7<>2 r6c7=2 r6c7<>4 r6c8=4 r6c8<>3 r4c8=3 r4c8<>9
Almost Locked Set XY-Wing: A=r4c1345689 {12356789}, B=r9c78 {148}, C=r5689c6 {12458}, X,Y=2,4, Z=1 => r4c7<>1
Forcing Chain Contradiction in c1 => r4c8<>6
r4c8=6 r2c8<>6 r1c9=6 r1c1<>6
r4c8=6 r4c1<>6
r4c8=6 r5c9<>6 r5c23=6 r6c1<>6
r4c8=6 r4c4<>6 r8c4=6 r8c1<>6
Forcing Chain Contradiction in r1c7 => r2c7=8
r2c7<>8 r2c7=7 r8c7<>7 r7c9=7 r7c9<>4 r13c9=4 r1c7<>4
r2c7<>8 r2c7=7 r1c7<>7
r2c7<>8 r2c8=8 r2c8<>6 r6c8=6 r6c8<>3 r4c8=3 r4c8<>9 r45c7=9 r1c7<>9
AIC: 9 9- r1c6 =9= r2c6 =7= r2c2 -7- r3c1 -9 => r1c12<>9
Discontinuous Nice Loop: 1 r8c7 -1- r9c7 -4- r9c6 =4= r1c6 =9= r1c7 =7= r8c7 => r8c7<>1
Discontinuous Nice Loop: 1 r9c3 -1- r9c7 -4- r6c7 =4= r6c8 =3= r4c8 -3- r4c3 =3= r9c3 => r9c3<>1
Grouped AIC: 1/4 4- r6c7 =4= r6c8 =3= r4c8 =9= r45c7 -9- r1c7 =9= r1c6 =4= r9c6 -4- r9c7 -1 => r6c7<>1, r9c7<>4
Naked Single: r9c7=1
Finned X-Wing: 1 r68 c16 fr6c5 => r45c6<>1
Discontinuous Nice Loop: 8 r4c5 -8- r5c6 -5- r5c7 -9- r1c7 =9= r1c6 -9- r2c6 -7- r4c6 =7= r4c5 => r4c5<>8
Discontinuous Nice Loop: 8 r9c6 -8- r5c6 -5- r5c7 -9- r1c7 =9= r1c6 =4= r9c6 => r9c6<>8
Forcing Chain Contradiction in r6c1 => r2c8<>5
r2c8=5 r2c8<>6 r6c8=6 r6c8<>3 r4c8=3 r4c8<>9 r45c7=9 r1c7<>9 r1c6=9 r2c6<>9 r2c6=7 r4c6<>7 r4c5=7 r4c5<>1 r6c56=1 r6c1<>1
r2c8=5 r2c23<>5 r3c3=5 r3c3<>2 r1c2=2 r1c2<>3 r1c1=3 r6c1<>3
r2c8=5 r2c8<>6 r6c8=6 r6c1<>6
Locked Candidates Type 1 (Pointing): 5 in b3 => r3c3<>5
Forcing Chain Contradiction in r1c7 => r3c5<>2
r3c5=2 r1c4<>2 r1c4=4 r1c7<>4
r3c5=2 r13c4<>2 r7c4=2 r7c4<>5 r7c89=5 r8c7<>5 r8c7=7 r1c7<>7
r3c5=2 r3c3<>2 r3c3=9 r3c1<>9 r3c1=7 r2c2<>7 r2c6=7 r2c6<>9 r1c6=9 r1c7<>9
Forcing Chain Contradiction in r4 => r4c5<>1
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c2=7 r2c2<>5 r2c3=5 r4c3<>5
r4c5=1 r7c5<>1 r8c6=1 r8c6<>5 r78c4=5 r4c4<>5
r4c5=1 r4c5<>7 r4c6=7 r4c6<>5
r4c5=1 r4c5<>7 r4c6=7 r4c6<>2 r4c7=2 r4c7<>5
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r1c6<>9 r1c7=9 r5c7<>9 r5c7=5 r4c8<>5
r4c5=1 r4c5<>7 r4c6=7 r2c6<>7 r2c6=9 r1c6<>9 r1c7=9 r5c7<>9 r5c7=5 r4c9<>5
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c1<>1
Sue de Coq: r45c3 - {13569} (r37c3 - {129}, r6c12 - {356}) => r4c1<>3, r4c1,r5c2<>6, r5c2<>5, r2c3<>9, r9c3<>2
Naked Triple: 5,8,9 in r5c267 => r5c39<>5, r5c3<>9
2-String Kite: 6 in r2c8,r5c3 (connected by r5c9,r6c8) => r2c3<>6
Naked Single: r2c3=5
Hidden Single: r6c2=5
Grouped Discontinuous Nice Loop: 2 r1c6 -2- r13c4 =2= r7c4 -2- r7c23 =2= r9c2 =3= r9c3 -3- r4c3 =3= r4c8 =9= r45c7 -9- r1c7 =9= r1c6 => r1c6<>2
Locked Candidates Type 1 (Pointing): 2 in b2 => r7c4<>2
Grouped Discontinuous Nice Loop: 8 r9c2 -8- r9c8 -4- r9c6 =4= r1c6 =9= r1c7 -9- r45c7 =9= r4c8 =3= r4c3 -3- r9c3 =3= r9c2 => r9c2<>8
Almost Locked Set XZ-Rule: A=r9c2356 {23468}, B=r12c6,r3c5 {4789}, X=4,8, Z=8 => r7c5<>8
Almost Locked Set XY-Wing: A=r5c2 {89}, B=r7c489 {4578}, C=r58c7 {579}, X,Y=7,9, Z=8 => r7c2<>8
Almost Locked Set Chain: 27- r1c4679 {24679} -6- r5c2679 {15689} -1- r5c3 {16} -6- r6c1 {36} -3- r13c1,r2c2,r3c3 {23679} -27 => r1c2,r3c4<>2, r1c2<>7
Hidden Single: r1c4=2
Hidden Single: r3c3=2
2-String Kite: 4 in r3c4,r9c8 (connected by r7c4,r9c6) => r3c8<>4
Grouped Discontinuous Nice Loop: 7 r8c1 -7- r8c7 =7= r1c7 =9= r1c6 -9- r2c6 -7- r2c2 =7= r13c1 -7- r8c1 => r8c1<>7
Almost Locked Set XY-Wing: A=r1456c7 {24579}, B=r137c9 {4567}, C=r1c12 {367}, X,Y=6,7, Z=5 => r4c9<>5
Locked Pair: 1,6 in r45c9 => r1c9,r6c8<>6
Hidden Single: r2c8=6
Naked Pair: 7,9 in r2c2,r3c1 => r1c1<>7
Naked Pair: 3,6 in r16c1 => r8c1<>6
Swordfish: 9 r125 c267 => r4c7,r7c2<>9
Uniqueness Test 1: 1/6 in r4c39,r5c39 => r4c3<>1, r4c3<>6
2-String Kite: 6 in r6c5,r9c3 (connected by r5c3,r6c1) => r9c5<>6
Hidden Single: r8c4=6
Naked Pair: 5,8 in r4c4,r5c6 => r4c6<>5, r4c6<>8
Naked Triple: 2,4,8 in r9c568 => r9c2<>2
Hidden Single: r7c2=2
Naked Single: r7c5=1
Naked Single: r7c3=9
Naked Single: r4c3=3
Naked Single: r6c1=6
Naked Single: r9c3=6
Full House: r5c3=1
Naked Single: r1c1=3
Naked Single: r6c5=2
Naked Single: r9c2=3
Naked Single: r5c9=6
Naked Single: r1c2=6
Naked Single: r4c6=7
Naked Single: r6c6=1
Naked Single: r6c7=4
Full House: r6c8=3
Naked Single: r9c5=8
Naked Single: r4c9=1
Naked Single: r2c6=9
Full House: r2c2=7
Full House: r3c1=9
Naked Single: r4c5=6
Full House: r3c5=7
Naked Single: r8c6=5
Naked Single: r9c8=4
Full House: r9c6=2
Full House: r7c4=4
Naked Single: r1c6=4
Full House: r5c6=8
Full House: r3c4=8
Full House: r4c4=5
Naked Single: r8c2=8
Full House: r5c2=9
Full House: r4c1=8
Full House: r5c7=5
Naked Single: r3c8=5
Full House: r3c9=4
Naked Single: r8c7=7
Full House: r8c1=1
Full House: r7c1=7
Naked Single: r1c9=7
Full House: r1c7=9
Full House: r4c7=2
Full House: r4c8=9
Full House: r7c8=8
Full House: r7c9=5
|
sudoku_normal_hard_110
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
71.92.6.4....14..22.46.7.9..2.4....5.46172..3..7...42.67.24......27.1.464.1.692.7
|
718925634963814572254637198129483765546172983837596421675248319392751846481369257
|
7 1 . 9 2 . 6 . 4
. . . . 1 4 . . 2
2 . 4 6 . 7 . 9 .
. 2 . 4 . . . . 5
. 4 6 1 7 2 . . 3
. . 7 . . . 4 2 .
6 7 . 2 4 . . . .
. . 2 7 . 1 . 4 6
4 . 1 . 6 9 2 . 7
|
7 1 8 9 2 5 6 3 4
9 6 3 8 1 4 5 7 2
2 5 4 6 3 7 1 9 8
1 2 9 4 8 3 7 6 5
5 4 6 1 7 2 9 8 3
8 3 7 5 9 6 4 2 1
6 7 5 2 4 8 3 1 9
3 9 2 7 5 1 8 4 6
4 8 1 3 6 9 2 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9917_hard
|
718925634963814572254637198129483765546172983837596421675248319392751846481369257 #1 Extreme (21124) bf
Hidden Single: r1c5=2
Hidden Single: r6c8=2
Hidden Single: r2c6=4
Hidden Single: r1c9=4
Hidden Single: r5c2=4
Hidden Single: r8c3=2
Hidden Single: r9c5=6
Hidden Single: r7c2=7
Hidden Single: r7c5=4
Hidden Single: r9c7=2
Hidden Single: r3c6=7
Brute Force: r5c4=1
Locked Candidates Type 1 (Pointing): 5 in b5 => r6c12<>5
Brute Force: r5c3=6
Naked Single: r5c8=8
Naked Single: r5c7=9
Full House: r5c1=5
Naked Single: r6c9=1
Naked Single: r3c9=8
Full House: r7c9=9
Naked Single: r4c7=7
Full House: r4c8=6
Hidden Single: r2c2=6
Hidden Single: r6c6=6
Hidden Single: r3c7=1
Hidden Single: r4c1=1
Hidden Single: r7c8=1
Hidden Single: r2c8=7
Skyscraper: 5 in r7c6,r9c8 (connected by r1c68) => r7c7,r9c4<>5
W-Wing: 3/5 in r1c8,r3c2 connected by 5 in r9c28 => r1c3<>3
W-Wing: 5/3 in r2c7,r3c5 connected by 3 in r1c68 => r2c4<>5
Hidden Single: r6c4=5
Skyscraper: 3 in r1c8,r2c4 (connected by r9c48) => r1c6,r2c7<>3
Naked Single: r2c7=5
Full House: r1c8=3
Full House: r9c8=5
Skyscraper: 3 in r3c5,r9c4 (connected by r39c2) => r2c4,r8c5<>3
Naked Single: r2c4=8
Full House: r9c4=3
Full House: r9c2=8
Naked Single: r1c6=5
Full House: r1c3=8
Full House: r3c5=3
Full House: r3c2=5
Naked Single: r7c6=8
Full House: r4c6=3
Full House: r8c5=5
Naked Single: r7c7=3
Full House: r7c3=5
Full House: r8c7=8
Naked Single: r4c3=9
Full House: r2c3=3
Full House: r4c5=8
Full House: r2c1=9
Full House: r6c5=9
Naked Single: r6c2=3
Full House: r6c1=8
Full House: r8c1=3
Full House: r8c2=9
|
sudoku_normal_extremely_hard_110
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
71.9..6......1...22.46...9..2.4....5....72..3..7...4..6..2........7.1.464.1..9..7
|
718925634963814572254637198129483765546172983837596421675248319392751846481369257
|
7 1 . 9 . . 6 . .
. . . . 1 . . . 2
2 . 4 6 . . . 9 .
. 2 . 4 . . . . 5
. . . . 7 2 . . 3
. . 7 . . . 4 . .
6 . . 2 . . . . .
. . . 7 . 1 . 4 6
4 . 1 . . 9 . . 7
|
7 1 8 9 2 5 6 3 4
9 6 3 8 1 4 5 7 2
2 5 4 6 3 7 1 9 8
1 2 9 4 8 3 7 6 5
5 4 6 1 7 2 9 8 3
8 3 7 5 9 6 4 2 1
6 7 5 2 4 8 3 1 9
3 9 2 7 5 1 8 4 6
4 8 1 3 6 9 2 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9917_hard
|
718925634963814572254637198129483765546172983837596421675248319392751846481369257 #1 Extreme (21124) bf
Hidden Single: r1c5=2
Hidden Single: r6c8=2
Hidden Single: r2c6=4
Hidden Single: r1c9=4
Hidden Single: r5c2=4
Hidden Single: r8c3=2
Hidden Single: r9c5=6
Hidden Single: r7c2=7
Hidden Single: r7c5=4
Hidden Single: r9c7=2
Hidden Single: r3c6=7
Brute Force: r5c4=1
Locked Candidates Type 1 (Pointing): 5 in b5 => r6c12<>5
Brute Force: r5c3=6
Naked Single: r5c8=8
Naked Single: r5c7=9
Full House: r5c1=5
Naked Single: r6c9=1
Naked Single: r3c9=8
Full House: r7c9=9
Naked Single: r4c7=7
Full House: r4c8=6
Hidden Single: r2c2=6
Hidden Single: r6c6=6
Hidden Single: r3c7=1
Hidden Single: r4c1=1
Hidden Single: r7c8=1
Hidden Single: r2c8=7
Skyscraper: 5 in r7c6,r9c8 (connected by r1c68) => r7c7,r9c4<>5
W-Wing: 3/5 in r1c8,r3c2 connected by 5 in r9c28 => r1c3<>3
W-Wing: 5/3 in r2c7,r3c5 connected by 3 in r1c68 => r2c4<>5
Hidden Single: r6c4=5
Skyscraper: 3 in r1c8,r2c4 (connected by r9c48) => r1c6,r2c7<>3
Naked Single: r2c7=5
Full House: r1c8=3
Full House: r9c8=5
Skyscraper: 3 in r3c5,r9c4 (connected by r39c2) => r2c4,r8c5<>3
Naked Single: r2c4=8
Full House: r9c4=3
Full House: r9c2=8
Naked Single: r1c6=5
Full House: r1c3=8
Full House: r3c5=3
Full House: r3c2=5
Naked Single: r7c6=8
Full House: r4c6=3
Full House: r8c5=5
Naked Single: r7c7=3
Full House: r7c3=5
Full House: r8c7=8
Naked Single: r4c3=9
Full House: r2c3=3
Full House: r4c5=8
Full House: r2c1=9
Full House: r6c5=9
Naked Single: r6c2=3
Full House: r6c1=8
Full House: r8c1=3
Full House: r8c2=9
|
sudoku_normal_hard_111
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7....9..69.5..2..441..3.....5.......3478916252....5..7.2...476...49....26.....4..
|
783549216965182374412637598856723941347891625291465837128354769534976182679218453
|
7 . . . . 9 . . 6
9 . 5 . . 2 . . 4
4 1 . . 3 . . . .
. 5 . . . . . . .
3 4 7 8 9 1 6 2 5
2 . . . . 5 . . 7
. 2 . . . 4 7 6 .
. . 4 9 . . . . 2
6 . . . . . 4 . .
|
7 8 3 5 4 9 2 1 6
9 6 5 1 8 2 3 7 4
4 1 2 6 3 7 5 9 8
8 5 6 7 2 3 9 4 1
3 4 7 8 9 1 6 2 5
2 9 1 4 6 5 8 3 7
1 2 8 3 5 4 7 6 9
5 3 4 9 7 6 1 8 2
6 7 9 2 1 8 4 5 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4615_hard
|
783549216965182374412637598856723941347891625291465837128354769534976182679218453 #1 Extreme (45378) bf
Brute Force: r5c5=9
Locked Candidates Type 2 (Claiming): 4 in r5 => r4c1,r6c2<>4
Brute Force: r5c2=4
Hidden Single: r3c1=4
Forcing Net Contradiction in r3c6 => r2c5<>6
r2c5=6 r3c6<>6
r2c5=6 (r2c4<>6) (r3c4<>6) r2c2<>6 r6c2=6 r6c4<>6 r4c4=6 (r4c4<>7) r4c4<>2 r4c5=2 r4c5<>7 r4c6=7 r3c6<>7
r2c5=6 (r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9) r8c5<>6 r8c6=6 r5c6<>6 r5c7=6 r5c7<>5 r5c9=5 r3c9<>5 r3c9=8 r3c6<>8
Brute Force: r5c6=1
Naked Single: r5c1=3
Naked Single: r5c9=5
Full House: r5c7=6
Forcing Chain Contradiction in r7 => r4c9<>9
r4c9=9 r79c9<>9 r9c8=9 r9c8<>5 r8c78=5 r8c1<>5 r7c1=5 r7c1<>8
r4c9=9 r7c9<>9 r7c3=9 r7c3<>8
r4c9=9 r3c9<>9 r3c9=8 r3c6<>8 r12c5=8 r7c5<>8
r4c9=9 r3c9<>9 r3c9=8 r7c9<>8
Forcing Chain Contradiction in r9 => r9c5<>8
r9c5=8 r9c5<>2 r9c4=2 r9c4<>5
r9c5=8 r9c5<>5
r9c5=8 r12c5<>8 r3c6=8 r3c9<>8 r3c9=9 r79c9<>9 r9c8=9 r9c8<>5
Forcing Net Contradiction in c4 => r1c4<>1
r1c4=1 r2c4=6
r1c4=1 r1c4<>4 r1c5=4 r6c5<>4 r6c5=6 (r4c6<>6 r4c3=6 r3c3<>6) r8c5<>6 r8c6=6 r3c6<>6 r3c4=6
Forcing Net Contradiction in r7c5 => r1c7<>3
r1c7=3 (r2c7<>3) r2c8<>3 r2c2=3 r2c2<>6 r2c4=6 r2c4<>1 r79c4=1 r7c5<>1
r1c7=3 (r1c7<>5) r1c7<>2 r1c3=2 r3c3<>2 r3c7=2 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c5<>5
r1c7=3 (r1c2<>3 r1c2=8 r9c2<>8) (r1c2<>3 r1c2=8 r8c2<>8) (r2c7<>3) r2c8<>3 r2c2=3 (r9c2<>3) r8c2<>3 r8c2=7 r9c2<>7 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r3c6<>8 r12c5=8 r7c5<>8
Forcing Net Verity => r3c3<>8
r7c1=8 r7c1<>5 r8c1=5 (r8c7<>5) r8c8<>5 r9c8=5 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c3<>8
r7c3=8 r3c3<>8
r7c5=8 (r8c6<>8) r9c6<>8 r3c6=8 r3c3<>8
r7c9=8 (r7c9<>3) (r7c9<>3) r7c9<>9 r7c3=9 r7c3<>3 r7c4=3 (r8c6<>3) (r8c6<>3) r9c6<>3 r4c6=3 r4c9<>3 r9c9=3 (r8c7<>3) r8c8<>3 r8c2=3 r1c2<>3 r1c2=8 r3c3<>8
Discontinuous Nice Loop: 8 r1c7 -8- r3c9 -9- r7c9 =9= r7c3 -9- r9c2 =9= r6c2 =6= r2c2 -6- r3c3 -2- r3c7 =2= r1c7 => r1c7<>8
Grouped Discontinuous Nice Loop: 8 r1c8 -8- r3c9 -9- r7c9 =9= r7c3 -9- r9c2 =9= r6c2 =6= r2c2 =8= r1c23 -8- r1c8 => r1c8<>8
Forcing Net Contradiction in b7 => r1c5<>8
r1c5=8 (r1c5<>4 r1c4=4 r1c4<>5 r3c4=5 r7c4<>5) (r1c5<>4 r1c4=4 r6c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r6c4<>6 r6c4=3 r7c4<>3 r7c4=1 r7c1<>1
r1c5=8 (r1c5<>4 r1c4=4 r1c4<>5 r3c4=5 r7c4<>5) (r1c5<>4 r1c4=4 r6c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r6c4<>6 r6c4=3 r7c4<>3 r7c4=1 r7c3<>1
r1c5=8 (r7c5<>8) (r1c5<>1) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r2c4<>1 r2c5=1 r7c5<>1 r7c5=5 r7c1<>5 r8c1=5 r8c1<>1
r1c5=8 (r1c5<>4 r1c4=4 r4c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 (r2c4=6 r2c4<>1 r2c5=1 r2c7<>1 r2c7=3 r4c7<>3) r6c2=6 r6c5<>6 r6c5=4 r4c5<>4 r4c8=4 r4c8<>3 r4c9=3 (r4c9<>1) r6c8<>3 r6c4=3 (r6c7<>3) (r4c4<>3) (r4c6<>3) r7c4<>3 r7c3=3 r7c3<>9 r7c9=9 (r7c9<>3) r7c9<>1 r9c9=1 r9c3<>1
Locked Candidates Type 2 (Claiming): 8 in r1 => r2c2<>8
Forcing Chain Contradiction in r2c7 => r1c7<>1
r1c7=1 r2c7<>1
r1c7=1 r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r2c2=3 r2c7<>3
r1c7=1 r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r2c7<>8
Forcing Chain Contradiction in r7c5 => r9c8<>1
r9c8=1 r1c8<>1 r1c5=1 r7c5<>1
r9c8=1 r9c8<>5 r9c45=5 r7c5<>5
r9c8=1 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
Forcing Net Contradiction in r8 => r1c7=2
r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 (r2c4=6 r6c4<>6 r6c4=3 r7c4<>3) r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r7c9<>3 r7c3=3 (r7c3<>8) r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 (r7c9<>8) (r2c7<>8) r2c8<>8 r2c5=8 r7c5<>8 r7c1=8 r4c1<>8 r4c1=1 r8c1<>1
r1c7<>2 r1c7=5 (r1c5<>5) r1c4<>5 r1c4=4 r1c5<>4 r1c5=1 r8c5<>1
r1c7<>2 (r1c7=5 r1c4<>5 r1c4=4 r1c5<>4 r1c5=1 r1c8<>1 r1c8=3 r2c7<>3) r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r2c7<>8 r2c7=1 r8c7<>1
r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 (r2c4=6 r6c4<>6 r6c4=3 r7c4<>3) r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r7c9<>3 r7c3=3 (r7c3<>8) r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 (r7c9<>8) (r2c7<>8) r2c8<>8 r2c5=8 r7c5<>8 r7c1=8 r4c1<>8 r4c1=1 r4c9<>1 r79c9=1 r8c8<>1
Hidden Single: r3c3=2
Hidden Single: r2c2=6
Locked Candidates Type 1 (Pointing): 3 in b1 => r1c8<>3
Grouped Discontinuous Nice Loop: 1 r4c8 -1- r1c8 -5- r1c45 =5= r3c4 =6= r46c4 -6- r6c5 -4- r6c8 =4= r4c8 => r4c8<>1
Forcing Chain Contradiction in r7c5 => r1c8=1
r1c8<>1 r1c5=1 r7c5<>1
r1c8<>1 r1c8=5 r9c8<>5 r9c45=5 r7c5<>5
r1c8<>1 r1c8=5 r1c45<>5 r3c4=5 r3c4<>6 r3c6=6 r3c6<>8 r2c5=8 r7c5<>8
Locked Candidates Type 1 (Pointing): 5 in b3 => r3c4<>5
Discontinuous Nice Loop: 9 r6c7 -9- r6c2 -8- r4c1 -1- r6c3 =1= r6c7 => r6c7<>9
Discontinuous Nice Loop: 3 r4c7 -3- r2c7 -8- r3c9 -9- r3c7 =9= r4c7 => r4c7<>3
Forcing Chain Contradiction in r7 => r4c3<>9
r4c3=9 r4c7<>9 r3c7=9 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c1<>8
r4c3=9 r6c2<>9 r6c2=8 r1c2<>8 r1c3=8 r7c3<>8
r4c3=9 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
r4c3=9 r7c3<>9 r7c9=9 r7c9<>8
Locked Candidates Type 1 (Pointing): 9 in b4 => r6c8<>9
Forcing Chain Contradiction in r7 => r4c7<>8
r4c7=8 r4c7<>9 r3c7=9 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c1<>8
r4c7=8 r4c1<>8 r78c1=8 r7c3<>8
r4c7=8 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
r4c7=8 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r7c9<>8
Forcing Chain Contradiction in r7 => r8c7<>3
r8c7=3 r2c7<>3 r2c7=8 r3c9<>8 r3c9=9 r7c9<>9 r7c3=9 r7c3<>3
r8c7=3 r79c9<>3 r4c9=3 r4c6<>3 r46c4=3 r7c4<>3
r8c7=3 r7c9<>3
Forcing Chain Contradiction in r9 => r9c4<>1
r9c4=1 r9c4<>5
r9c4=1 r9c4<>2 r9c5=2 r9c5<>5
r9c4=1 r2c4<>1 r2c5=1 r2c5<>8 r3c6=8 r3c9<>8 r3c9=9 r79c9<>9 r9c8=9 r9c8<>5
Forcing Chain Contradiction in r7c4 => r9c8<>3
r9c8=3 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r2c5<>1 r2c4=1 r7c4<>1
r9c8=3 r79c9<>3 r4c9=3 r4c6<>3 r46c4=3 r7c4<>3
r9c8=3 r9c8<>5 r9c45=5 r7c4<>5
Forcing Net Verity => r2c4=1
r4c9=1 (r9c9<>1) r6c7<>1 r6c3=1 r9c3<>1 r9c5=1 r2c5<>1 r2c4=1
r4c9=3 (r6c7<>3 r2c7=3 r2c7<>8) (r7c9<>3) (r6c7<>3) r6c8<>3 r6c4=3 r7c4<>3 r7c3=3 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r2c8<>8 r2c5=8 r2c5<>1 r2c4=1
r4c9=8 r4c1<>8 r4c1=1 (r8c1<>1) r6c3<>1 r6c7=1 r8c7<>1 r8c5=1 r2c5<>1 r2c4=1
Almost Locked Set XZ-Rule: A=r6c45 {346}, B=r17c4 {345}, X=3, Z=4 => r4c4<>4
Forcing Chain Contradiction in r4c9 => r4c7=9
r4c7<>9 r4c7=1 r4c9<>1
r4c7<>9 r3c7=9 r3c7<>5 r3c8=5 r9c8<>5 r9c45=5 r7c4<>5 r7c4=3 r6c4<>3 r4c46=3 r4c9<>3
r4c7<>9 r4c7=1 r4c1<>1 r4c1=8 r4c9<>8
Almost Locked Set XY-Wing: A=r2c5 {78}, B=r8c178 {1358}, C=r246c8 {3478}, X,Y=3,7, Z=8 => r8c5<>8
Forcing Chain Contradiction in r8c1 => r2c7=3
r2c7<>3 r6c7=3 r6c7<>1 r8c7=1 r8c1<>1
r2c7<>3 r2c7=8 r3c9<>8 r3c9=9 r3c8<>9 r9c8=9 r9c8<>5 r8c78=5 r8c1<>5
r2c7<>3 r6c7=3 r6c7<>1 r6c3=1 r4c1<>1 r4c1=8 r8c1<>8
Almost Locked Set XY-Wing: A=r8c178 {1358}, B=r34679c4 {234567}, C=r6c23578 {134689}, X,Y=3,4, Z=5 => r8c5<>5
Forcing Chain Contradiction in r8 => r4c6<>6
r4c6=6 r4c6<>3 r46c4=3 r7c4<>3 r7c4=5 r7c1<>5 r8c1=5 r8c1<>1
r4c6=6 r8c6<>6 r8c5=6 r8c5<>1
r4c6=6 r4c3<>6 r6c3=6 r6c3<>1 r6c7=1 r8c7<>1
Forcing Chain Contradiction in r3 => r4c8=4
r4c8<>4 r4c5=4 r6c5<>4 r6c5=6 r46c4<>6 r3c4=6 r3c4<>7
r4c8<>4 r6c8=4 r6c8<>3 r6c4=3 r4c6<>3 r4c6=7 r3c6<>7
r4c8<>4 r6c8=4 r6c8<>3 r6c4=3 r7c4<>3 r7c4=5 r9c45<>5 r9c8=5 r9c8<>9 r3c8=9 r3c8<>7
Grouped AIC: 9 9- r6c2 -8- r4c13 =8= r4c9 -8- r3c9 -9- r7c9 =9= r7c3 -9 => r6c3,r9c2<>9
Hidden Single: r6c2=9
Avoidable Rectangle Type 1: 4/9 in r5c25,r6c25 => r6c5<>4
Naked Single: r6c5=6
Hidden Single: r6c4=4
Naked Single: r1c4=5
Naked Single: r1c5=4
Naked Single: r7c4=3
Hidden Single: r4c3=6
Hidden Single: r3c4=6
Hidden Single: r8c6=6
Hidden Single: r6c8=3
Hidden Single: r4c6=3
Hidden Single: r9c9=3
Hidden Single: r8c2=3
Naked Single: r1c2=8
Full House: r1c3=3
Full House: r9c2=7
Naked Single: r9c4=2
Full House: r4c4=7
Full House: r4c5=2
Naked Single: r9c6=8
Full House: r3c6=7
Full House: r2c5=8
Full House: r2c8=7
Hidden Single: r8c5=7
Skyscraper: 1 in r4c9,r8c7 (connected by r48c1) => r6c7,r7c9<>1
Naked Single: r6c7=8
Full House: r4c9=1
Full House: r6c3=1
Full House: r4c1=8
Naked Single: r3c7=5
Full House: r8c7=1
Naked Single: r9c3=9
Full House: r7c3=8
Naked Single: r8c1=5
Full House: r7c1=1
Full House: r8c8=8
Naked Single: r9c8=5
Full House: r7c9=9
Full House: r7c5=5
Full House: r3c8=9
Full House: r9c5=1
Full House: r3c9=8
|
sudoku_normal_extremely_hard_111
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7....9..69.5..2..4.1..3.....5.........78...2.2....5..7.2...476...49....26.....4..
|
783549216965182374412637598856723941347891625291465837128354769534976182679218453
|
7 . . . . 9 . . 6
9 . 5 . . 2 . . 4
. 1 . . 3 . . . .
. 5 . . . . . . .
. . 7 8 . . . 2 .
2 . . . . 5 . . 7
. 2 . . . 4 7 6 .
. . 4 9 . . . . 2
6 . . . . . 4 . .
|
7 8 3 5 4 9 2 1 6
9 6 5 1 8 2 3 7 4
4 1 2 6 3 7 5 9 8
8 5 6 7 2 3 9 4 1
3 4 7 8 9 1 6 2 5
2 9 1 4 6 5 8 3 7
1 2 8 3 5 4 7 6 9
5 3 4 9 7 6 1 8 2
6 7 9 2 1 8 4 5 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4615_hard
|
783549216965182374412637598856723941347891625291465837128354769534976182679218453 #1 Extreme (45378) bf
Brute Force: r5c5=9
Locked Candidates Type 2 (Claiming): 4 in r5 => r4c1,r6c2<>4
Brute Force: r5c2=4
Hidden Single: r3c1=4
Forcing Net Contradiction in r3c6 => r2c5<>6
r2c5=6 r3c6<>6
r2c5=6 (r2c4<>6) (r3c4<>6) r2c2<>6 r6c2=6 r6c4<>6 r4c4=6 (r4c4<>7) r4c4<>2 r4c5=2 r4c5<>7 r4c6=7 r3c6<>7
r2c5=6 (r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9) r8c5<>6 r8c6=6 r5c6<>6 r5c7=6 r5c7<>5 r5c9=5 r3c9<>5 r3c9=8 r3c6<>8
Brute Force: r5c6=1
Naked Single: r5c1=3
Naked Single: r5c9=5
Full House: r5c7=6
Forcing Chain Contradiction in r7 => r4c9<>9
r4c9=9 r79c9<>9 r9c8=9 r9c8<>5 r8c78=5 r8c1<>5 r7c1=5 r7c1<>8
r4c9=9 r7c9<>9 r7c3=9 r7c3<>8
r4c9=9 r3c9<>9 r3c9=8 r3c6<>8 r12c5=8 r7c5<>8
r4c9=9 r3c9<>9 r3c9=8 r7c9<>8
Forcing Chain Contradiction in r9 => r9c5<>8
r9c5=8 r9c5<>2 r9c4=2 r9c4<>5
r9c5=8 r9c5<>5
r9c5=8 r12c5<>8 r3c6=8 r3c9<>8 r3c9=9 r79c9<>9 r9c8=9 r9c8<>5
Forcing Net Contradiction in c4 => r1c4<>1
r1c4=1 r2c4=6
r1c4=1 r1c4<>4 r1c5=4 r6c5<>4 r6c5=6 (r4c6<>6 r4c3=6 r3c3<>6) r8c5<>6 r8c6=6 r3c6<>6 r3c4=6
Forcing Net Contradiction in r7c5 => r1c7<>3
r1c7=3 (r2c7<>3) r2c8<>3 r2c2=3 r2c2<>6 r2c4=6 r2c4<>1 r79c4=1 r7c5<>1
r1c7=3 (r1c7<>5) r1c7<>2 r1c3=2 r3c3<>2 r3c7=2 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c5<>5
r1c7=3 (r1c2<>3 r1c2=8 r9c2<>8) (r1c2<>3 r1c2=8 r8c2<>8) (r2c7<>3) r2c8<>3 r2c2=3 (r9c2<>3) r8c2<>3 r8c2=7 r9c2<>7 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r3c6<>8 r12c5=8 r7c5<>8
Forcing Net Verity => r3c3<>8
r7c1=8 r7c1<>5 r8c1=5 (r8c7<>5) r8c8<>5 r9c8=5 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c3<>8
r7c3=8 r3c3<>8
r7c5=8 (r8c6<>8) r9c6<>8 r3c6=8 r3c3<>8
r7c9=8 (r7c9<>3) (r7c9<>3) r7c9<>9 r7c3=9 r7c3<>3 r7c4=3 (r8c6<>3) (r8c6<>3) r9c6<>3 r4c6=3 r4c9<>3 r9c9=3 (r8c7<>3) r8c8<>3 r8c2=3 r1c2<>3 r1c2=8 r3c3<>8
Discontinuous Nice Loop: 8 r1c7 -8- r3c9 -9- r7c9 =9= r7c3 -9- r9c2 =9= r6c2 =6= r2c2 -6- r3c3 -2- r3c7 =2= r1c7 => r1c7<>8
Grouped Discontinuous Nice Loop: 8 r1c8 -8- r3c9 -9- r7c9 =9= r7c3 -9- r9c2 =9= r6c2 =6= r2c2 =8= r1c23 -8- r1c8 => r1c8<>8
Forcing Net Contradiction in b7 => r1c5<>8
r1c5=8 (r1c5<>4 r1c4=4 r1c4<>5 r3c4=5 r7c4<>5) (r1c5<>4 r1c4=4 r6c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r6c4<>6 r6c4=3 r7c4<>3 r7c4=1 r7c1<>1
r1c5=8 (r1c5<>4 r1c4=4 r1c4<>5 r3c4=5 r7c4<>5) (r1c5<>4 r1c4=4 r6c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r6c4<>6 r6c4=3 r7c4<>3 r7c4=1 r7c3<>1
r1c5=8 (r7c5<>8) (r1c5<>1) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 r2c4=6 r2c4<>1 r2c5=1 r7c5<>1 r7c5=5 r7c1<>5 r8c1=5 r8c1<>1
r1c5=8 (r1c5<>4 r1c4=4 r4c4<>4) (r1c2<>8) r1c3<>8 r2c2=8 r2c2<>6 (r2c4=6 r2c4<>1 r2c5=1 r2c7<>1 r2c7=3 r4c7<>3) r6c2=6 r6c5<>6 r6c5=4 r4c5<>4 r4c8=4 r4c8<>3 r4c9=3 (r4c9<>1) r6c8<>3 r6c4=3 (r6c7<>3) (r4c4<>3) (r4c6<>3) r7c4<>3 r7c3=3 r7c3<>9 r7c9=9 (r7c9<>3) r7c9<>1 r9c9=1 r9c3<>1
Locked Candidates Type 2 (Claiming): 8 in r1 => r2c2<>8
Forcing Chain Contradiction in r2c7 => r1c7<>1
r1c7=1 r2c7<>1
r1c7=1 r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r2c2=3 r2c7<>3
r1c7=1 r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r2c7<>8
Forcing Chain Contradiction in r7c5 => r9c8<>1
r9c8=1 r1c8<>1 r1c5=1 r7c5<>1
r9c8=1 r9c8<>5 r9c45=5 r7c5<>5
r9c8=1 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
Forcing Net Contradiction in r8 => r1c7=2
r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 (r2c4=6 r6c4<>6 r6c4=3 r7c4<>3) r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r7c9<>3 r7c3=3 (r7c3<>8) r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 (r7c9<>8) (r2c7<>8) r2c8<>8 r2c5=8 r7c5<>8 r7c1=8 r4c1<>8 r4c1=1 r8c1<>1
r1c7<>2 r1c7=5 (r1c5<>5) r1c4<>5 r1c4=4 r1c5<>4 r1c5=1 r8c5<>1
r1c7<>2 (r1c7=5 r1c4<>5 r1c4=4 r1c5<>4 r1c5=1 r1c8<>1 r1c8=3 r2c7<>3) r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r2c7<>8 r2c7=1 r8c7<>1
r1c7<>2 r1c3=2 r3c3<>2 r3c3=6 r2c2<>6 (r2c4=6 r6c4<>6 r6c4=3 r7c4<>3) r6c2=6 r6c2<>9 r9c2=9 r7c3<>9 r7c9=9 r7c9<>3 r7c3=3 (r7c3<>8) r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 (r7c9<>8) (r2c7<>8) r2c8<>8 r2c5=8 r7c5<>8 r7c1=8 r4c1<>8 r4c1=1 r4c9<>1 r79c9=1 r8c8<>1
Hidden Single: r3c3=2
Hidden Single: r2c2=6
Locked Candidates Type 1 (Pointing): 3 in b1 => r1c8<>3
Grouped Discontinuous Nice Loop: 1 r4c8 -1- r1c8 -5- r1c45 =5= r3c4 =6= r46c4 -6- r6c5 -4- r6c8 =4= r4c8 => r4c8<>1
Forcing Chain Contradiction in r7c5 => r1c8=1
r1c8<>1 r1c5=1 r7c5<>1
r1c8<>1 r1c8=5 r9c8<>5 r9c45=5 r7c5<>5
r1c8<>1 r1c8=5 r1c45<>5 r3c4=5 r3c4<>6 r3c6=6 r3c6<>8 r2c5=8 r7c5<>8
Locked Candidates Type 1 (Pointing): 5 in b3 => r3c4<>5
Discontinuous Nice Loop: 9 r6c7 -9- r6c2 -8- r4c1 -1- r6c3 =1= r6c7 => r6c7<>9
Discontinuous Nice Loop: 3 r4c7 -3- r2c7 -8- r3c9 -9- r3c7 =9= r4c7 => r4c7<>3
Forcing Chain Contradiction in r7 => r4c3<>9
r4c3=9 r4c7<>9 r3c7=9 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c1<>8
r4c3=9 r6c2<>9 r6c2=8 r1c2<>8 r1c3=8 r7c3<>8
r4c3=9 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
r4c3=9 r7c3<>9 r7c9=9 r7c9<>8
Locked Candidates Type 1 (Pointing): 9 in b4 => r6c8<>9
Forcing Chain Contradiction in r7 => r4c7<>8
r4c7=8 r4c7<>9 r3c7=9 r3c7<>5 r8c7=5 r8c1<>5 r7c1=5 r7c1<>8
r4c7=8 r4c1<>8 r78c1=8 r7c3<>8
r4c7=8 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r7c5<>8
r4c7=8 r4c7<>9 r3c7=9 r3c9<>9 r3c9=8 r7c9<>8
Forcing Chain Contradiction in r7 => r8c7<>3
r8c7=3 r2c7<>3 r2c7=8 r3c9<>8 r3c9=9 r7c9<>9 r7c3=9 r7c3<>3
r8c7=3 r79c9<>3 r4c9=3 r4c6<>3 r46c4=3 r7c4<>3
r8c7=3 r7c9<>3
Forcing Chain Contradiction in r9 => r9c4<>1
r9c4=1 r9c4<>5
r9c4=1 r9c4<>2 r9c5=2 r9c5<>5
r9c4=1 r2c4<>1 r2c5=1 r2c5<>8 r3c6=8 r3c9<>8 r3c9=9 r79c9<>9 r9c8=9 r9c8<>5
Forcing Chain Contradiction in r7c4 => r9c8<>3
r9c8=3 r9c8<>9 r79c9=9 r3c9<>9 r3c9=8 r3c6<>8 r2c5=8 r2c5<>1 r2c4=1 r7c4<>1
r9c8=3 r79c9<>3 r4c9=3 r4c6<>3 r46c4=3 r7c4<>3
r9c8=3 r9c8<>5 r9c45=5 r7c4<>5
Forcing Net Verity => r2c4=1
r4c9=1 (r9c9<>1) r6c7<>1 r6c3=1 r9c3<>1 r9c5=1 r2c5<>1 r2c4=1
r4c9=3 (r6c7<>3 r2c7=3 r2c7<>8) (r7c9<>3) (r6c7<>3) r6c8<>3 r6c4=3 r7c4<>3 r7c3=3 r7c3<>9 r7c9=9 r3c9<>9 r3c9=8 r2c8<>8 r2c5=8 r2c5<>1 r2c4=1
r4c9=8 r4c1<>8 r4c1=1 (r8c1<>1) r6c3<>1 r6c7=1 r8c7<>1 r8c5=1 r2c5<>1 r2c4=1
Almost Locked Set XZ-Rule: A=r6c45 {346}, B=r17c4 {345}, X=3, Z=4 => r4c4<>4
Forcing Chain Contradiction in r4c9 => r4c7=9
r4c7<>9 r4c7=1 r4c9<>1
r4c7<>9 r3c7=9 r3c7<>5 r3c8=5 r9c8<>5 r9c45=5 r7c4<>5 r7c4=3 r6c4<>3 r4c46=3 r4c9<>3
r4c7<>9 r4c7=1 r4c1<>1 r4c1=8 r4c9<>8
Almost Locked Set XY-Wing: A=r2c5 {78}, B=r8c178 {1358}, C=r246c8 {3478}, X,Y=3,7, Z=8 => r8c5<>8
Forcing Chain Contradiction in r8c1 => r2c7=3
r2c7<>3 r6c7=3 r6c7<>1 r8c7=1 r8c1<>1
r2c7<>3 r2c7=8 r3c9<>8 r3c9=9 r3c8<>9 r9c8=9 r9c8<>5 r8c78=5 r8c1<>5
r2c7<>3 r6c7=3 r6c7<>1 r6c3=1 r4c1<>1 r4c1=8 r8c1<>8
Almost Locked Set XY-Wing: A=r8c178 {1358}, B=r34679c4 {234567}, C=r6c23578 {134689}, X,Y=3,4, Z=5 => r8c5<>5
Forcing Chain Contradiction in r8 => r4c6<>6
r4c6=6 r4c6<>3 r46c4=3 r7c4<>3 r7c4=5 r7c1<>5 r8c1=5 r8c1<>1
r4c6=6 r8c6<>6 r8c5=6 r8c5<>1
r4c6=6 r4c3<>6 r6c3=6 r6c3<>1 r6c7=1 r8c7<>1
Forcing Chain Contradiction in r3 => r4c8=4
r4c8<>4 r4c5=4 r6c5<>4 r6c5=6 r46c4<>6 r3c4=6 r3c4<>7
r4c8<>4 r6c8=4 r6c8<>3 r6c4=3 r4c6<>3 r4c6=7 r3c6<>7
r4c8<>4 r6c8=4 r6c8<>3 r6c4=3 r7c4<>3 r7c4=5 r9c45<>5 r9c8=5 r9c8<>9 r3c8=9 r3c8<>7
Grouped AIC: 9 9- r6c2 -8- r4c13 =8= r4c9 -8- r3c9 -9- r7c9 =9= r7c3 -9 => r6c3,r9c2<>9
Hidden Single: r6c2=9
Avoidable Rectangle Type 1: 4/9 in r5c25,r6c25 => r6c5<>4
Naked Single: r6c5=6
Hidden Single: r6c4=4
Naked Single: r1c4=5
Naked Single: r1c5=4
Naked Single: r7c4=3
Hidden Single: r4c3=6
Hidden Single: r3c4=6
Hidden Single: r8c6=6
Hidden Single: r6c8=3
Hidden Single: r4c6=3
Hidden Single: r9c9=3
Hidden Single: r8c2=3
Naked Single: r1c2=8
Full House: r1c3=3
Full House: r9c2=7
Naked Single: r9c4=2
Full House: r4c4=7
Full House: r4c5=2
Naked Single: r9c6=8
Full House: r3c6=7
Full House: r2c5=8
Full House: r2c8=7
Hidden Single: r8c5=7
Skyscraper: 1 in r4c9,r8c7 (connected by r48c1) => r6c7,r7c9<>1
Naked Single: r6c7=8
Full House: r4c9=1
Full House: r6c3=1
Full House: r4c1=8
Naked Single: r3c7=5
Full House: r8c7=1
Naked Single: r9c3=9
Full House: r7c3=8
Naked Single: r8c1=5
Full House: r7c1=1
Full House: r8c8=8
Naked Single: r9c8=5
Full House: r7c9=9
Full House: r7c5=5
Full House: r3c8=9
Full House: r9c5=1
Full House: r3c9=8
|
sudoku_normal_hard_112
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2......8..4.2..9.5..1..2.....5...12.52.816..1...62.8..9.273.6.6.....92.2..6..8.7
|
721936458364825791589147236876594312952381674143762589498273165617458923235619847
|
. 2 . . . . . . 8
. . 4 . 2 . . 9 .
5 . . 1 . . 2 . .
. . . 5 . . . 1 2
. 5 2 . 8 1 6 . .
1 . . . 6 2 . 8 .
. 9 . 2 7 3 . 6 .
6 . . . . . 9 2 .
2 . . 6 . . 8 . 7
|
7 2 1 9 3 6 4 5 8
3 6 4 8 2 5 7 9 1
5 8 9 1 4 7 2 3 6
8 7 6 5 9 4 3 1 2
9 5 2 3 8 1 6 7 4
1 4 3 7 6 2 5 8 9
4 9 8 2 7 3 1 6 5
6 1 7 4 5 8 9 2 3
2 3 5 6 1 9 8 4 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7885_hard
|
721936458364825791589147236876594312952381674143762589498273165617458923235619847 #1 Extreme (33984) bf
Brute Force: r4c9=2
Hidden Single: r8c8=2
Hidden Single: r7c4=2
Hidden Single: r2c5=2
Locked Candidates Type 1 (Pointing): 8 in b8 => r8c23<>8
Finned Swordfish: 1 r147 c378 fr7c9 => r9c8<>1
Finned Swordfish: 9 r349 c356 fr4c1 => r6c3<>9
Forcing Net Contradiction in b5 => r4c8<>4
r4c8=4 r4c5<>4
r4c8=4 r4c6<>4
r4c8=4 (r4c1<>4) (r4c8<>1 r4c7=1 r7c7<>1) (r4c8<>1 r1c8=1 r1c8<>5) r4c8<>8 r6c8=8 r6c8<>5 r9c8=5 r7c7<>5 r7c7=4 r7c1<>4 r5c1=4 r5c4<>4
r4c8=4 (r5c9<>4) (r4c8<>1 r1c8=1 r1c8<>5) r4c8<>8 r6c8=8 r6c8<>5 r9c8=5 r9c8<>3 r8c9=3 r5c9<>3 r5c9=9 r6c9<>9 r6c4=9 r6c4<>4
Forcing Net Contradiction in b1 => r8c9<>4
r8c9=4 (r8c9<>3 r9c8=3 r9c8<>5) (r8c6<>4) r8c4<>4 r8c4=8 r8c6<>8 r8c6=5 (r8c5<>5) r9c5<>5 r1c5=5 r1c8<>5 r6c8=5 r6c8<>8 r4c8=8 r4c8<>1 r1c8=1 r1c3<>1
r8c9=4 (r7c9<>4 r7c1=4 r9c2<>4) r8c9<>3 r9c8=3 r9c2<>3 r9c2=1 r2c2<>1
Brute Force: r4c8=1
Hidden Single: r6c8=8
Empty Rectangle: 5 in b2 (r19c8) => r9c6<>5
Forcing Chain Contradiction in r6c2 => r6c9<>3
r6c9=3 r6c2<>3
r6c9=3 r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r45c1=4 r6c2<>4
r6c9=3 r6c3<>3 r6c3=7 r6c2<>7
Forcing Net Contradiction in c8 => r1c6<>9
r1c6=9 (r3c6<>9 r3c3=9 r3c3<>7) (r9c6<>9 r9c6=4 r4c6<>4 r4c6=7 r3c6<>7) r1c6<>6 r1c3=6 (r4c3<>6 r4c2=6 r4c2<>8) r1c3<>1 r1c7=1 (r2c7<>1) r2c9<>1 r2c2=1 r2c2<>8 r3c2=8 r3c2<>7 r3c8=7
r1c6=9 (r3c6<>9 r3c3=9 r4c3<>9) (r4c6<>9) r9c6<>9 (r9c6=4 r4c6<>4 r4c6=7 r5c4<>7) (r9c6=4 r8c6<>4 r8c2=4 r7c1<>4) r9c5=9 r4c5<>9 r4c1=9 r4c1<>4 r5c1=4 r5c1<>7 r5c8=7
Forcing Net Contradiction in c3 => r1c7<>5
r1c7=5 (r1c7<>1 r1c3=1 r8c3<>1) (r1c7<>1 r1c3=1 r9c3<>1 r9c3=3 r8c3<>3) (r7c7<>5) r1c8<>5 r9c8=5 r7c9<>5 r7c3=5 r8c3<>5 r8c3=7 r6c3<>7 r6c3=3
r1c7=5 (r1c8<>5 r9c8=5 r9c3<>5) r1c7<>1 r1c3=1 r9c3<>1 r9c3=3
Forcing Net Contradiction in r7 => r2c9<>3
r2c9=3 r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r7c1=8
r2c9=3 (r2c9<>6) (r2c9<>5) r8c9<>3 r9c8=3 r9c8<>5 r1c8=5 r2c7<>5 r2c6=5 r2c6<>6 r2c2=6 (r4c2<>6 r4c3=6 r4c3<>8) (r4c2<>6 r4c3=6 r4c3<>9) r2c2<>1 r1c3=1 r1c3<>9 r3c3=9 r3c3<>8 r7c3=8
Forcing Net Contradiction in c6 => r4c1<>7
r4c1=7 (r4c1<>8) (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 r7c1<>8 r2c1=8 (r2c2<>8) r3c2<>8 r4c2=8 r4c2<>6 r4c3=6 r1c3<>6 r1c6=6 r1c6<>7
r4c1=7 (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r9c8<>5 r1c8=5 (r2c7<>5) r2c9<>5 r2c6=5 r2c6<>7
r4c1=7 (r4c1<>8) (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 r7c1<>8 r2c1=8 (r3c2<>8) r3c3<>8 r3c6=8 r3c6<>7
r4c1=7 r4c6<>7
Forcing Net Contradiction in r4c5 => r1c3<>7
r1c3=7 (r6c3<>7 r6c3=3 r3c3<>3) (r2c1<>7 r5c1=7 r5c8<>7 r3c8=7 r3c8<>3) (r6c3<>7 r6c3=3 r9c3<>3) (r6c3<>7 r6c3=3 r8c3<>3) r8c3<>7 r8c2=7 r8c2<>3 r8c9=3 (r3c9<>3) r9c8<>3 r9c2=3 r3c2<>3 r3c5=3 r4c5<>3
r1c3=7 (r1c3<>1 r1c7=1 r1c7<>4) (r6c3<>7 r6c3=3 r6c2<>3) (r1c1<>7) r2c1<>7 r5c1=7 (r5c1<>4) r6c2<>7 r6c2=4 (r6c7<>4) r4c1<>4 r7c1=4 r7c7<>4 r4c7=4 r4c5<>4
r1c3=7 (r1c1<>7) r2c1<>7 r5c1=7 r5c1<>9 r4c13=9 r4c5<>9
Forcing Net Contradiction in b3 => r1c7<>7
r1c7=7 r1c7<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r1c8<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r3c8<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c4<>9 r6c9=9 r6c9<>5 r6c7=5 r7c7<>5) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 r7c7<>4 r7c7=1 (r2c7<>1) r1c7<>1 r1c3=1 r2c2<>1 r2c9=1 r2c9<>6 r3c9=6 r3c9<>4
Forcing Net Contradiction in r9c8 => r2c4<>7
r2c4=7 (r2c7<>7) (r1c6<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c7<>7 r6c7=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4
r2c4=7 (r1c4<>7) (r1c6<>7) (r5c4<>7) (r2c7<>7) (r1c6<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c7<>7 r6c7=7 r5c8<>7 r5c1=7 r1c1<>7 r1c8=7 r1c8<>5 r9c8=5
Forcing Net Contradiction in c7 => r9c6=9
r9c6<>9 r9c6=4 (r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r2c1<>3) (r8c4<>4) (r8c5<>4) r8c6<>4 r8c2=4 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 (r4c1<>3) r5c1<>3 r1c1=3 r1c7<>3
r9c6<>9 r9c6=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r2c7<>3
r9c6<>9 r9c6=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 (r1c5<>3) r3c5<>3 r4c5=3 r4c7<>3
r9c6<>9 r9c6=4 (r8c4<>4) (r8c5<>4) r8c6<>4 r8c2=4 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r6c7<>3
Forcing Chain Contradiction in r4c7 => r4c1<>4
r4c1=4 r4c56<>4 r56c4=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r56c4<>3 r4c5=3 r4c7<>3
r4c1=4 r4c7<>4
r4c1=4 r4c6<>4 r4c6=7 r4c7<>7
Empty Rectangle: 4 in b9 (r57c1) => r5c8<>4
Forcing Chain Contradiction in r3c8 => r3c2<>7
r3c2=7 r12c1<>7 r5c1=7 r5c8<>7 r5c8=3 r3c8<>3
r3c2=7 r12c1<>7 r5c1=7 r5c1<>4 r7c1=4 r7c79<>4 r9c8=4 r3c8<>4
r3c2=7 r3c8<>7
Forcing Chain Contradiction in r3c8 => r3c3<>7
r3c3=7 r12c1<>7 r5c1=7 r5c8<>7 r5c8=3 r3c8<>3
r3c3=7 r12c1<>7 r5c1=7 r5c1<>4 r7c1=4 r7c79<>4 r9c8=4 r3c8<>4
r3c3=7 r3c8<>7
Forcing Chain Contradiction in r5 => r1c6<>4
r1c6=4 r1c6<>6 r1c3=6 r1c3<>1 r2c2=1 r2c2<>7 r12c1=7 r5c1<>7
r1c6=4 r4c6<>4 r4c6=7 r5c4<>7
r1c6=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7
Forcing Chain Contradiction in r4c7 => r4c2<>4
r4c2=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r4c2=4 r4c7<>4
r4c2=4 r4c6<>4 r4c6=7 r4c7<>7
Forcing Chain Contradiction in r4c7 => r4c5<>4
r4c5=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r4c5=4 r4c7<>4
r4c5=4 r4c6<>4 r4c6=7 r4c7<>7
Forcing Chain Contradiction in r4c7 => r8c9=3
r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r4c7<>3
r8c9<>3 r9c8=3 r5c8<>3 r5c8=7 r3c8<>7 r3c6=7 r4c6<>7 r4c6=4 r4c7<>4
r8c9<>3 r9c8=3 r5c8<>3 r5c8=7 r4c7<>7
Locked Candidates Type 1 (Pointing): 1 in b9 => r7c3<>1
Discontinuous Nice Loop: 4 r6c4 -4- r6c2 =4= r5c1 -4- r5c9 -9- r6c9 =9= r6c4 => r6c4<>4
Forcing Chain Contradiction in r5 => r1c8<>3
r1c8=3 r1c8<>5 r9c8=5 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>3
r1c8=3 r1c8<>5 r9c8=5 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r5c4<>3
r1c8=3 r5c8<>3
Forcing Chain Contradiction in r3 => r2c2<>7
r2c2=7 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r9c3<>3 r9c2=3 r3c2<>3
r2c2=7 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r3c3<>3
r2c2=7 r12c1<>7 r5c1=7 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r3c5<>3
r2c2=7 r2c7<>7 r46c7=7 r5c8<>7 r5c8=3 r3c8<>3
Locked Candidates Type 1 (Pointing): 7 in b1 => r5c1<>7
Skyscraper: 7 in r3c6,r5c4 (connected by r35c8) => r1c4,r4c6<>7
Naked Single: r4c6=4
Naked Pair: 3,7 in r4c7,r5c8 => r6c7<>3, r6c7<>7
W-Wing: 3/7 in r5c8,r6c3 connected by 7 in r56c4 => r5c1<>3
Naked Pair: 4,9 in r5c19 => r5c4<>9
Finned Swordfish: 3 c147 r124 fr5c4 fr6c4 => r4c5<>3
Naked Single: r4c5=9
Hidden Single: r3c3=9
Hidden Single: r1c4=9
Hidden Single: r5c1=9
Naked Single: r5c9=4
Naked Single: r3c9=6
Naked Single: r6c7=5
Naked Single: r6c9=9
Hidden Single: r8c4=4
Hidden Single: r7c1=4
Naked Single: r7c7=1
Naked Single: r7c9=5
Full House: r2c9=1
Full House: r7c3=8
Full House: r9c8=4
Hidden Single: r6c2=4
Hidden Single: r8c6=8
Naked Single: r3c6=7
Naked Single: r3c8=3
Naked Single: r1c7=4
Naked Single: r2c7=7
Full House: r1c8=5
Full House: r5c8=7
Full House: r4c7=3
Full House: r5c4=3
Full House: r6c4=7
Full House: r2c4=8
Full House: r6c3=3
Naked Single: r3c2=8
Full House: r3c5=4
Naked Single: r1c5=3
Naked Single: r1c6=6
Full House: r2c6=5
Naked Single: r4c1=8
Naked Single: r2c1=3
Full House: r1c1=7
Full House: r1c3=1
Full House: r2c2=6
Naked Single: r9c3=5
Naked Single: r4c2=7
Full House: r4c3=6
Full House: r8c3=7
Naked Single: r9c5=1
Full House: r8c5=5
Full House: r8c2=1
Full House: r9c2=3
|
sudoku_normal_extremely_hard_112
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2......8..4....9.5..1..2.....5......52.816..1...62....9..73.6.6.....9..2..6..8.7
|
721936458364825791589147236876594312952381674143762589498273165617458923235619847
|
. 2 . . . . . . 8
. . 4 . . . . 9 .
5 . . 1 . . 2 . .
. . . 5 . . . . .
. 5 2 . 8 1 6 . .
1 . . . 6 2 . . .
. 9 . . 7 3 . 6 .
6 . . . . . 9 . .
2 . . 6 . . 8 . 7
|
7 2 1 9 3 6 4 5 8
3 6 4 8 2 5 7 9 1
5 8 9 1 4 7 2 3 6
8 7 6 5 9 4 3 1 2
9 5 2 3 8 1 6 7 4
1 4 3 7 6 2 5 8 9
4 9 8 2 7 3 1 6 5
6 1 7 4 5 8 9 2 3
2 3 5 6 1 9 8 4 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7885_hard
|
721936458364825791589147236876594312952381674143762589498273165617458923235619847 #1 Extreme (33984) bf
Brute Force: r4c9=2
Hidden Single: r8c8=2
Hidden Single: r7c4=2
Hidden Single: r2c5=2
Locked Candidates Type 1 (Pointing): 8 in b8 => r8c23<>8
Finned Swordfish: 1 r147 c378 fr7c9 => r9c8<>1
Finned Swordfish: 9 r349 c356 fr4c1 => r6c3<>9
Forcing Net Contradiction in b5 => r4c8<>4
r4c8=4 r4c5<>4
r4c8=4 r4c6<>4
r4c8=4 (r4c1<>4) (r4c8<>1 r4c7=1 r7c7<>1) (r4c8<>1 r1c8=1 r1c8<>5) r4c8<>8 r6c8=8 r6c8<>5 r9c8=5 r7c7<>5 r7c7=4 r7c1<>4 r5c1=4 r5c4<>4
r4c8=4 (r5c9<>4) (r4c8<>1 r1c8=1 r1c8<>5) r4c8<>8 r6c8=8 r6c8<>5 r9c8=5 r9c8<>3 r8c9=3 r5c9<>3 r5c9=9 r6c9<>9 r6c4=9 r6c4<>4
Forcing Net Contradiction in b1 => r8c9<>4
r8c9=4 (r8c9<>3 r9c8=3 r9c8<>5) (r8c6<>4) r8c4<>4 r8c4=8 r8c6<>8 r8c6=5 (r8c5<>5) r9c5<>5 r1c5=5 r1c8<>5 r6c8=5 r6c8<>8 r4c8=8 r4c8<>1 r1c8=1 r1c3<>1
r8c9=4 (r7c9<>4 r7c1=4 r9c2<>4) r8c9<>3 r9c8=3 r9c2<>3 r9c2=1 r2c2<>1
Brute Force: r4c8=1
Hidden Single: r6c8=8
Empty Rectangle: 5 in b2 (r19c8) => r9c6<>5
Forcing Chain Contradiction in r6c2 => r6c9<>3
r6c9=3 r6c2<>3
r6c9=3 r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r45c1=4 r6c2<>4
r6c9=3 r6c3<>3 r6c3=7 r6c2<>7
Forcing Net Contradiction in c8 => r1c6<>9
r1c6=9 (r3c6<>9 r3c3=9 r3c3<>7) (r9c6<>9 r9c6=4 r4c6<>4 r4c6=7 r3c6<>7) r1c6<>6 r1c3=6 (r4c3<>6 r4c2=6 r4c2<>8) r1c3<>1 r1c7=1 (r2c7<>1) r2c9<>1 r2c2=1 r2c2<>8 r3c2=8 r3c2<>7 r3c8=7
r1c6=9 (r3c6<>9 r3c3=9 r4c3<>9) (r4c6<>9) r9c6<>9 (r9c6=4 r4c6<>4 r4c6=7 r5c4<>7) (r9c6=4 r8c6<>4 r8c2=4 r7c1<>4) r9c5=9 r4c5<>9 r4c1=9 r4c1<>4 r5c1=4 r5c1<>7 r5c8=7
Forcing Net Contradiction in c3 => r1c7<>5
r1c7=5 (r1c7<>1 r1c3=1 r8c3<>1) (r1c7<>1 r1c3=1 r9c3<>1 r9c3=3 r8c3<>3) (r7c7<>5) r1c8<>5 r9c8=5 r7c9<>5 r7c3=5 r8c3<>5 r8c3=7 r6c3<>7 r6c3=3
r1c7=5 (r1c8<>5 r9c8=5 r9c3<>5) r1c7<>1 r1c3=1 r9c3<>1 r9c3=3
Forcing Net Contradiction in r7 => r2c9<>3
r2c9=3 r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r7c1=8
r2c9=3 (r2c9<>6) (r2c9<>5) r8c9<>3 r9c8=3 r9c8<>5 r1c8=5 r2c7<>5 r2c6=5 r2c6<>6 r2c2=6 (r4c2<>6 r4c3=6 r4c3<>8) (r4c2<>6 r4c3=6 r4c3<>9) r2c2<>1 r1c3=1 r1c3<>9 r3c3=9 r3c3<>8 r7c3=8
Forcing Net Contradiction in c6 => r4c1<>7
r4c1=7 (r4c1<>8) (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 r7c1<>8 r2c1=8 (r2c2<>8) r3c2<>8 r4c2=8 r4c2<>6 r4c3=6 r1c3<>6 r1c6=6 r1c6<>7
r4c1=7 (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r9c8<>5 r1c8=5 (r2c7<>5) r2c9<>5 r2c6=5 r2c6<>7
r4c1=7 (r4c1<>8) (r4c1<>4) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 r5c1<>4 r7c1=4 r7c1<>8 r2c1=8 (r3c2<>8) r3c3<>8 r3c6=8 r3c6<>7
r4c1=7 r4c6<>7
Forcing Net Contradiction in r4c5 => r1c3<>7
r1c3=7 (r6c3<>7 r6c3=3 r3c3<>3) (r2c1<>7 r5c1=7 r5c8<>7 r3c8=7 r3c8<>3) (r6c3<>7 r6c3=3 r9c3<>3) (r6c3<>7 r6c3=3 r8c3<>3) r8c3<>7 r8c2=7 r8c2<>3 r8c9=3 (r3c9<>3) r9c8<>3 r9c2=3 r3c2<>3 r3c5=3 r4c5<>3
r1c3=7 (r1c3<>1 r1c7=1 r1c7<>4) (r6c3<>7 r6c3=3 r6c2<>3) (r1c1<>7) r2c1<>7 r5c1=7 (r5c1<>4) r6c2<>7 r6c2=4 (r6c7<>4) r4c1<>4 r7c1=4 r7c7<>4 r4c7=4 r4c5<>4
r1c3=7 (r1c1<>7) r2c1<>7 r5c1=7 r5c1<>9 r4c13=9 r4c5<>9
Forcing Net Contradiction in b3 => r1c7<>7
r1c7=7 r1c7<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r1c8<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4 r3c8<>4
r1c7=7 (r1c4<>7) (r1c1<>7) (r1c8<>7) r3c8<>7 r5c8=7 (r5c4<>7) r5c1<>7 r2c1=7 r2c4<>7 r6c4=7 (r6c4<>9 r6c9=9 r6c9<>5 r6c7=5 r7c7<>5) (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 r7c7<>4 r7c7=1 (r2c7<>1) r1c7<>1 r1c3=1 r2c2<>1 r2c9=1 r2c9<>6 r3c9=6 r3c9<>4
Forcing Net Contradiction in r9c8 => r2c4<>7
r2c4=7 (r2c7<>7) (r1c6<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c7<>7 r6c7=7 (r6c2<>7) r6c3<>7 r6c3=3 r6c2<>3 r6c2=4 (r4c1<>4) r5c1<>4 r7c1=4 (r7c7<>4) r7c9<>4 r9c8=4
r2c4=7 (r1c4<>7) (r1c6<>7) (r5c4<>7) (r2c7<>7) (r1c6<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c7<>7 r6c7=7 r5c8<>7 r5c1=7 r1c1<>7 r1c8=7 r1c8<>5 r9c8=5
Forcing Net Contradiction in c7 => r9c6=9
r9c6<>9 r9c6=4 (r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r2c1<>3) (r8c4<>4) (r8c5<>4) r8c6<>4 r8c2=4 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 (r4c1<>3) r5c1<>3 r1c1=3 r1c7<>3
r9c6<>9 r9c6=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r2c7<>3
r9c6<>9 r9c6=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 (r1c5<>3) r3c5<>3 r4c5=3 r4c7<>3
r9c6<>9 r9c6=4 (r8c4<>4) (r8c5<>4) r8c6<>4 r8c2=4 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r6c7<>3
Forcing Chain Contradiction in r4c7 => r4c1<>4
r4c1=4 r4c56<>4 r56c4=4 r8c4<>4 r8c4=8 r2c4<>8 r2c4=3 r56c4<>3 r4c5=3 r4c7<>3
r4c1=4 r4c7<>4
r4c1=4 r4c6<>4 r4c6=7 r4c7<>7
Empty Rectangle: 4 in b9 (r57c1) => r5c8<>4
Forcing Chain Contradiction in r3c8 => r3c2<>7
r3c2=7 r12c1<>7 r5c1=7 r5c8<>7 r5c8=3 r3c8<>3
r3c2=7 r12c1<>7 r5c1=7 r5c1<>4 r7c1=4 r7c79<>4 r9c8=4 r3c8<>4
r3c2=7 r3c8<>7
Forcing Chain Contradiction in r3c8 => r3c3<>7
r3c3=7 r12c1<>7 r5c1=7 r5c8<>7 r5c8=3 r3c8<>3
r3c3=7 r12c1<>7 r5c1=7 r5c1<>4 r7c1=4 r7c79<>4 r9c8=4 r3c8<>4
r3c3=7 r3c8<>7
Forcing Chain Contradiction in r5 => r1c6<>4
r1c6=4 r1c6<>6 r1c3=6 r1c3<>1 r2c2=1 r2c2<>7 r12c1=7 r5c1<>7
r1c6=4 r4c6<>4 r4c6=7 r5c4<>7
r1c6=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7
Forcing Chain Contradiction in r4c7 => r4c2<>4
r4c2=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r4c2=4 r4c7<>4
r4c2=4 r4c6<>4 r4c6=7 r4c7<>7
Forcing Chain Contradiction in r4c7 => r4c5<>4
r4c5=4 r4c6<>4 r4c6=7 r3c6<>7 r3c8=7 r5c8<>7 r5c8=3 r4c7<>3
r4c5=4 r4c7<>4
r4c5=4 r4c6<>4 r4c6=7 r4c7<>7
Forcing Chain Contradiction in r4c7 => r8c9=3
r8c9<>3 r9c8=3 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r4c7<>3
r8c9<>3 r9c8=3 r5c8<>3 r5c8=7 r3c8<>7 r3c6=7 r4c6<>7 r4c6=4 r4c7<>4
r8c9<>3 r9c8=3 r5c8<>3 r5c8=7 r4c7<>7
Locked Candidates Type 1 (Pointing): 1 in b9 => r7c3<>1
Discontinuous Nice Loop: 4 r6c4 -4- r6c2 =4= r5c1 -4- r5c9 -9- r6c9 =9= r6c4 => r6c4<>4
Forcing Chain Contradiction in r5 => r1c8<>3
r1c8=3 r1c8<>5 r9c8=5 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>3
r1c8=3 r1c8<>5 r9c8=5 r9c8<>4 r7c79=4 r7c1<>4 r5c1=4 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r5c4<>3
r1c8=3 r5c8<>3
Forcing Chain Contradiction in r3 => r2c2<>7
r2c2=7 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r9c3<>3 r9c2=3 r3c2<>3
r2c2=7 r8c2<>7 r8c3=7 r6c3<>7 r6c3=3 r3c3<>3
r2c2=7 r12c1<>7 r5c1=7 r5c1<>9 r4c13=9 r4c5<>9 r4c5=3 r3c5<>3
r2c2=7 r2c7<>7 r46c7=7 r5c8<>7 r5c8=3 r3c8<>3
Locked Candidates Type 1 (Pointing): 7 in b1 => r5c1<>7
Skyscraper: 7 in r3c6,r5c4 (connected by r35c8) => r1c4,r4c6<>7
Naked Single: r4c6=4
Naked Pair: 3,7 in r4c7,r5c8 => r6c7<>3, r6c7<>7
W-Wing: 3/7 in r5c8,r6c3 connected by 7 in r56c4 => r5c1<>3
Naked Pair: 4,9 in r5c19 => r5c4<>9
Finned Swordfish: 3 c147 r124 fr5c4 fr6c4 => r4c5<>3
Naked Single: r4c5=9
Hidden Single: r3c3=9
Hidden Single: r1c4=9
Hidden Single: r5c1=9
Naked Single: r5c9=4
Naked Single: r3c9=6
Naked Single: r6c7=5
Naked Single: r6c9=9
Hidden Single: r8c4=4
Hidden Single: r7c1=4
Naked Single: r7c7=1
Naked Single: r7c9=5
Full House: r2c9=1
Full House: r7c3=8
Full House: r9c8=4
Hidden Single: r6c2=4
Hidden Single: r8c6=8
Naked Single: r3c6=7
Naked Single: r3c8=3
Naked Single: r1c7=4
Naked Single: r2c7=7
Full House: r1c8=5
Full House: r5c8=7
Full House: r4c7=3
Full House: r5c4=3
Full House: r6c4=7
Full House: r2c4=8
Full House: r6c3=3
Naked Single: r3c2=8
Full House: r3c5=4
Naked Single: r1c5=3
Naked Single: r1c6=6
Full House: r2c6=5
Naked Single: r4c1=8
Naked Single: r2c1=3
Full House: r1c1=7
Full House: r1c3=1
Full House: r2c2=6
Naked Single: r9c3=5
Naked Single: r4c2=7
Full House: r4c3=6
Full House: r8c3=7
Naked Single: r9c5=1
Full House: r8c5=5
Full House: r8c2=1
Full House: r9c2=3
|
sudoku_normal_hard_113
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.4...63....893...4...41..5..3.6..9..8....327...2...5.32.........9..6.1..7....9.35
|
149756382658932714327418659531627948864593271972184563285371496493865127716249835
|
. 4 . . . 6 3 . .
. . 8 9 3 . . . 4
. . . 4 1 . . 5 .
. 3 . 6 . . 9 . .
8 . . . . 3 2 7 .
. . 2 . . . 5 . 3
2 . . . . . . . .
. 9 . . 6 . 1 . .
7 . . . . 9 . 3 5
|
1 4 9 7 5 6 3 8 2
6 5 8 9 3 2 7 1 4
3 2 7 4 1 8 6 5 9
5 3 1 6 2 7 9 4 8
8 6 4 5 9 3 2 7 1
9 7 2 1 8 4 5 6 3
2 8 5 3 7 1 4 9 6
4 9 3 8 6 5 1 2 7
7 1 6 2 4 9 8 3 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3441_hard
|
149756382658932714327418659531627948864593271972184563285371496493865127716249835 #1 Extreme (24726) bf
Hidden Single: r2c5=3
Hidden Single: r6c9=3
Brute Force: r5c7=2
Hidden Single: r6c7=5
Locked Candidates Type 1 (Pointing): 4 in b6 => r78c8<>4
Locked Candidates Type 1 (Pointing): 2 in b9 => r8c46<>2
Naked Triple: 1,5,6 in r5c249 => r5c3<>1, r5c35<>5, r5c3<>6
Forcing Net Contradiction in r4c3 => r4c5<>8
r4c5=8 (r4c5<>2 r4c6=2 r2c6<>2) (r6c4<>8) (r6c5<>8) r6c6<>8 r6c8=8 r8c8<>8 r8c8=2 r2c8<>2 r2c2=2 r2c2<>5 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 r5c4=5 (r5c2<>5) r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c5=8 (r4c5<>7) r4c5<>2 r4c6=2 r4c6<>7 r4c3=7
Forcing Net Contradiction in r2 => r7c2<>1
r7c2=1 (r7c2<>5) (r9c2<>1) r9c3<>1 r9c4=1 r5c4<>1 r5c4=5 r5c2<>5 r2c2=5
r7c2=1 (r7c2<>5) (r9c2<>1) r9c3<>1 r9c4=1 (r9c4<>2 r1c4=2 r2c6<>2) (r9c4<>2 r1c4=2 r3c6<>2) (r9c4<>2 r1c4=2 r2c6<>2) r5c4<>1 r5c4=5 r5c2<>5 r2c2=5 r2c2<>2 r2c8=2 r8c8<>2 r8c8=8 (r7c7<>8) r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r2c6<>7 r2c6=5
Forcing Net Contradiction in b3 => r7c2<>6
r7c2=6 (r7c2<>8 r9c2=8 r9c5<>8) (r6c2<>6) r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4 r9c5=2 r9c4<>2 r1c4=2 r1c8<>2
r7c2=6 (r7c2<>8 r9c2=8 r9c5<>8) (r6c2<>6) r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4 r9c5=2 r9c4<>2 r1c4=2 r1c9<>2
r7c2=6 (r2c2<>6) (r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r2c1<>6) (r9c2<>6) r9c3<>6 r9c7=6 r2c7<>6 r2c8=6 r2c8<>2
r7c2=6 (r3c2<>6) (r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r3c1<>6) (r5c2<>6 r5c9=6 r3c9<>6) (r9c2<>6) r9c3<>6 r9c7=6 r3c7<>6 r3c3=6 (r3c3<>9) r3c3<>3 r3c1=3 r3c1<>9 r3c9=9 r3c9<>2
Almost Locked Set XZ-Rule: A=r15689c4 {123578}, B=r7c2,r8c13 {3458}, X=3, Z=8 => r7c4<>8
Forcing Net Contradiction in r4c3 => r4c5<>4
r4c5=4 (r4c8<>4 r6c8=4 r6c8<>6) r5c5<>4 r5c5=9 r6c5<>9 r6c1=9 r6c1<>6 r6c2=6 r9c2<>6 r9c2=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 (r5c2=1 r9c2<>1) r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c5=4 (r4c5<>7) r4c5<>2 r4c6=2 r4c6<>7 r4c3=7
Forcing Net Contradiction in r4c3 => r4c6<>4
r4c6=4 (r4c8<>4 r6c8=4 r6c8<>6) r5c5<>4 r5c5=9 r6c5<>9 r6c1=9 r6c1<>6 r6c2=6 r9c2<>6 r9c2=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 (r5c2=1 r9c2<>1) r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c6=4 (r4c6<>7) r4c6<>2 r4c5=2 r4c5<>7 r4c3=7
Forcing Net Verity => r1c9<>8
r1c5=8 r1c9<>8
r6c5=8 (r4c6<>8) r6c5<>9 r6c1=9 r5c3<>9 r5c3=4 (r4c1<>4) r4c3<>4 r4c8=4 r4c8<>8 r4c9=8 r1c9<>8
r7c5=8 (r7c7<>8) r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r1c9<>8
r9c5=8 (r9c7<>8) r9c2<>8 r7c2=8 r7c7<>8 r3c7=8 r1c9<>8
Forcing Net Contradiction in c8 => r7c4<>7
r7c4=7 (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r3c6<>8 r1c45=8 r1c8<>8
r7c4=7 (r7c4<>3 r7c3=3 r7c3<>1 r7c6=1 r7c6<>4) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r8c6<>4 r6c6=4 r6c8<>4 r4c8=4 r4c8<>8
r7c4=7 (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r4c6<>8 r4c89=8 r6c8<>8
r7c4=7 (r7c4<>5) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>5) (r7c4<>3 r7c3=3 r7c3<>1 r7c6=1 r7c6<>5) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r8c6<>5 r7c5=5 r7c2<>5 r7c2=8 r7c8<>8
r7c4=7 (r8c4<>7) r8c6<>7 r8c9=7 r8c9<>2 r8c8=2 r8c8<>8
Forcing Net Contradiction in r6c4 => r7c6<>8
r7c6=8 r7c6<>1 r79c4=1 r6c4<>1
r7c6=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5 r4c3<>7 r6c2=7 r6c4<>7
r7c6=8 r7c2<>8 (r9c2=8 r9c7<>8 r3c7=8 r1c8<>8) r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r1c5<>8 r1c4=8 r6c4<>8
Forcing Net Contradiction in r6c6 => r7c7<>8
r7c7=8 (r7c2<>8 r9c2=8 r9c5<>8) r7c7<>4 r9c7=4 r9c5<>4 r9c5=2 (r9c4<>2 r9c4=1 r7c6<>1) r4c5<>2 r4c6=2 r4c6<>1 r6c6=1
r7c7=8 (r7c5<>8) (r7c7<>4 r9c7=4 r9c5<>4 r9c5=2 r4c5<>2) r7c2<>8 r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r4c5=7 r7c5<>7 r7c5=4 (r7c6<>4) r8c6<>4 r6c6=4
Forcing Net Contradiction in r9 => r2c2<>6
r2c2=6 (r9c2<>6) (r2c8<>6) (r2c1<>6) r3c1<>6 r6c1=6 r6c8<>6 r7c8=6 r9c7<>6 r9c3=6 r9c3<>4
r2c2=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4
r2c2=6 (r2c7<>6 r2c7=7 r7c7<>7) (r2c8<>6) (r2c1<>6) r3c1<>6 r6c1=6 r6c8<>6 r7c8=6 r7c7<>6 r7c7=4 r9c7<>4
Forcing Net Contradiction in r7c8 => r7c8<>8
r7c8=8 (r1c8<>8) r7c2<>8 (r9c2=8 r9c4<>8) (r9c2=8 r9c5<>8) r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 (r8c4<>5 r8c6=5 r8c6<>8) r4c5<>5 r1c5=5 r1c5<>8 r1c4=8 r8c4<>8 r7c5=8 r7c8<>8
Forcing Net Verity => r7c5<>4
r3c1=6 r3c1<>3 r8c1=3 r8c1<>4 r46c1=4 r5c3<>4 r5c3=9 r5c5<>9 r5c5=4 r7c5<>4
r3c2=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r7c5<>4
r3c3=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r7c5<>4
r3c7=6 (r7c7<>6) r2c7<>6 r2c7=7 r7c7<>7 r7c7=4 r7c5<>4
r3c9=6 (r2c7<>6 r2c7=7 r3c7<>7 r3c7=8 r3c6<>8) (r2c7<>6 r2c7=7 r3c7<>7 r3c7=8 r1c8<>8) r5c9<>6 (r5c2=6 r6c2<>6 r6c8=6 r6c8<>8) r5c9=1 r4c9<>1 r4c9=8 (r4c6<>8) r4c8<>8 r8c8=8 r8c6<>8 r6c6=8 r6c6<>4 r56c5=4 r7c5<>4
Forcing Net Verity => r3c9<>6
r2c2=5 (r2c2<>2 r3c2=2 r3c2<>7) (r7c2<>5 r7c2=8 r7c5<>8) (r1c1<>5) (r1c3<>5) r5c2<>5 r5c4=5 r1c4<>5 r1c5=5 r7c5<>5 r7c5=7 r4c5<>7 r4c6=7 (r3c6<>7) (r2c6<>7) r6c6<>7 r6c2=7 (r6c4<>7) (r6c5<>7) (r4c3<>7) r2c2<>7 r2c7=7 (r3c7<>7) r3c9<>7 r3c3=7 (r3c3<>9) r3c3<>3 r3c1=3 r3c1<>9 r3c9=9 r3c9<>6
r5c2=5 r5c2<>6 r5c9=6 r3c9<>6
r7c2=5 (r2c2<>5) (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r2c6<>5 r2c1=5 r2c1<>6 r2c78=6 r3c9<>6
Forcing Net Contradiction in c1 => r6c5<>4
r6c5=4 (r9c5<>4) r5c5<>4 r5c3=4 r9c3<>4 r9c7=4 r9c7<>8 r3c7=8 r3c7<>6 r2c78=6 r2c1<>6
r6c5=4 (r6c1<>4) r5c5<>4 r5c3=4 r4c1<>4 r8c1=4 r8c1<>3 r3c1=3 r3c1<>6
r6c5=4 r6c5<>9 r6c1=9 r6c1<>6
Forcing Net Contradiction in r6 => r2c8<>2
r2c8=2 (r2c8<>6) r8c8<>2 r8c8=8 r9c7<>8 r3c7=8 (r3c6<>8 r3c6=7 r2c6<>7) r3c7<>6 r2c7=6 r2c7<>7 r2c2=7 r6c2<>7
r2c8=2 (r2c2<>2 r3c2=2 r3c6<>2) r8c8<>2 (r8c9=2 r8c9<>7) r8c8=8 r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r8c6<>7 r8c4=7 r6c4<>7
r2c8=2 (r2c8<>6) r8c8<>2 r8c8=8 (r9c7<>8) r9c7<>8 r3c7=8 r3c7<>6 r2c7=6 r9c7<>6 r9c7=4 r9c5<>4 r5c5=4 r5c3<>4 r5c3=9 r6c1<>9 r6c5=9 r6c5<>7
r2c8=2 (r2c2<>2 r3c2=2 r3c6<>2) r8c8<>2 r8c8=8 r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r6c6<>7
Forcing Net Verity => r9c4=2
r4c5=2 r9c5<>2 r9c4=2
r4c5=5 (r4c5<>7) r4c5<>2 r4c6=2 (r4c6<>8 r4c89=8 r6c8<>8) (r2c6<>2 r2c2=2 r3c2<>2 r3c9=2 r8c9<>2 r8c8=2 r8c8<>8) (r3c6<>2) (r2c6<>2 r2c2=2 r2c2<>7) r4c6<>7 r4c3=7 r6c2<>7 r3c2=7 r3c6<>7 r3c6=8 (r6c6<>8) (r8c6<>8) r3c7<>8 r9c7=8 r8c9<>8 r8c4=8 r6c4<>8 r6c5=8 r6c5<>9 r6c1=9 r5c3<>9 r5c5=9 r5c5<>4 r9c5=4 r9c5<>2 r9c4=2
r4c5=7 (r7c5<>7) (r4c5<>5) r4c5<>2 r4c6=2 (r2c6<>2 r2c2=2 r2c2<>5) r4c6<>5 r5c4=5 r5c2<>5 r7c2=5 r7c5<>5 r7c5=8 (r1c5<>8) r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r1c8<>8 r1c4=8 r1c4<>2 r9c4=2
Locked Candidates Type 1 (Pointing): 1 in b8 => r7c3<>1
Forcing Chain Contradiction in c1 => r7c2=8
r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r3c7<>6 r2c78=6 r2c1<>6
r7c2<>8 r9c2=8 r9c5<>8 r9c5=4 r5c5<>4 r5c3=4 r46c1<>4 r8c1=4 r8c1<>3 r3c1=3 r3c1<>6
r7c2<>8 r9c2=8 r9c5<>8 r9c5=4 r5c5<>4 r5c5=9 r5c3<>9 r6c1=9 r6c1<>6
Almost Locked Set XZ-Rule: A=r4c1389 {14578}, B=r569c2 {1567}, X=5,7 => r2c2,r4c6<>1, r4c6,r6c8<>8, r3c2<>6
Discontinuous Nice Loop: 8 r3c9 -8- r3c7 =8= r9c7 -8- r9c5 -4- r5c5 =4= r6c6 -4- r6c8 =4= r4c8 =8= r4c9 -8- r3c9 => r3c9<>8
Skyscraper: 8 in r3c6,r9c5 (connected by r39c7) => r1c5,r8c6<>8
Naked Triple: 2,5,7 in r147c5 => r6c5<>7
Swordfish: 8 r148 c489 => r6c4<>8
Hidden Triple: 4,8,9 in r56c5,r6c6 => r6c6<>1, r6c6<>7
Hidden Single: r7c6=1
Swordfish: 4 r579 c357 => r48c3<>4
Hidden Rectangle: 3/5 in r7c34,r8c34 => r7c4<>5
Naked Single: r7c4=3
Discontinuous Nice Loop: 7 r4c5 -7- r4c3 =7= r6c2 -7- r3c2 -2- r2c2 =2= r2c6 -2- r4c6 =2= r4c5 => r4c5<>7
Empty Rectangle: 7 in b2 (r4c36) => r1c3<>7
Empty Rectangle: 7 in b9 (r17c5) => r1c9<>7
Locked Candidates Type 2 (Claiming): 7 in r1 => r23c6<>7
AIC: 4 4- r5c3 =4= r5c5 -4- r6c6 -8- r3c6 -2- r3c2 -7- r3c3 =7= r4c3 -7- r4c6 =7= r8c6 =4= r8c1 -4 => r46c1,r79c3<>4
Hidden Single: r4c8=4
Hidden Single: r8c1=4
Hidden Single: r5c3=4
Naked Single: r5c5=9
Naked Single: r6c5=8
Naked Single: r6c6=4
Naked Single: r9c5=4
Hidden Single: r7c7=4
Hidden Single: r4c9=8
Hidden Single: r8c3=3
Hidden Single: r3c1=3
Hidden Single: r6c1=9
Hidden Single: r3c6=8
Hidden Single: r9c7=8
Naked Single: r8c8=2
Naked Single: r8c9=7
Naked Single: r8c6=5
Full House: r8c4=8
Full House: r7c5=7
Naked Single: r2c6=2
Full House: r4c6=7
Naked Single: r1c5=5
Full House: r1c4=7
Full House: r4c5=2
Naked Single: r6c4=1
Full House: r5c4=5
Naked Single: r1c1=1
Naked Single: r6c8=6
Full House: r5c9=1
Full House: r6c2=7
Full House: r5c2=6
Naked Single: r1c3=9
Naked Single: r4c1=5
Full House: r2c1=6
Full House: r4c3=1
Naked Single: r2c8=1
Naked Single: r7c8=9
Full House: r1c8=8
Full House: r1c9=2
Full House: r7c9=6
Full House: r3c9=9
Full House: r7c3=5
Naked Single: r2c2=5
Full House: r2c7=7
Full House: r3c7=6
Naked Single: r3c2=2
Full House: r9c2=1
Full House: r3c3=7
Full House: r9c3=6
|
sudoku_normal_extremely_hard_113
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.4...63....89....4...41..5..3.6..9..8....3.7...2......2.........9..6.1..7....9.35
|
149756382658932714327418659531627948864593271972184563285371496493865127716249835
|
. 4 . . . 6 3 . .
. . 8 9 . . . . 4
. . . 4 1 . . 5 .
. 3 . 6 . . 9 . .
8 . . . . 3 . 7 .
. . 2 . . . . . .
2 . . . . . . . .
. 9 . . 6 . 1 . .
7 . . . . 9 . 3 5
|
1 4 9 7 5 6 3 8 2
6 5 8 9 3 2 7 1 4
3 2 7 4 1 8 6 5 9
5 3 1 6 2 7 9 4 8
8 6 4 5 9 3 2 7 1
9 7 2 1 8 4 5 6 3
2 8 5 3 7 1 4 9 6
4 9 3 8 6 5 1 2 7
7 1 6 2 4 9 8 3 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3441_hard
|
149756382658932714327418659531627948864593271972184563285371496493865127716249835 #1 Extreme (24726) bf
Hidden Single: r2c5=3
Hidden Single: r6c9=3
Brute Force: r5c7=2
Hidden Single: r6c7=5
Locked Candidates Type 1 (Pointing): 4 in b6 => r78c8<>4
Locked Candidates Type 1 (Pointing): 2 in b9 => r8c46<>2
Naked Triple: 1,5,6 in r5c249 => r5c3<>1, r5c35<>5, r5c3<>6
Forcing Net Contradiction in r4c3 => r4c5<>8
r4c5=8 (r4c5<>2 r4c6=2 r2c6<>2) (r6c4<>8) (r6c5<>8) r6c6<>8 r6c8=8 r8c8<>8 r8c8=2 r2c8<>2 r2c2=2 r2c2<>5 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 r5c4=5 (r5c2<>5) r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c5=8 (r4c5<>7) r4c5<>2 r4c6=2 r4c6<>7 r4c3=7
Forcing Net Contradiction in r2 => r7c2<>1
r7c2=1 (r7c2<>5) (r9c2<>1) r9c3<>1 r9c4=1 r5c4<>1 r5c4=5 r5c2<>5 r2c2=5
r7c2=1 (r7c2<>5) (r9c2<>1) r9c3<>1 r9c4=1 (r9c4<>2 r1c4=2 r2c6<>2) (r9c4<>2 r1c4=2 r3c6<>2) (r9c4<>2 r1c4=2 r2c6<>2) r5c4<>1 r5c4=5 r5c2<>5 r2c2=5 r2c2<>2 r2c8=2 r8c8<>2 r8c8=8 (r7c7<>8) r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r2c6<>7 r2c6=5
Forcing Net Contradiction in b3 => r7c2<>6
r7c2=6 (r7c2<>8 r9c2=8 r9c5<>8) (r6c2<>6) r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4 r9c5=2 r9c4<>2 r1c4=2 r1c8<>2
r7c2=6 (r7c2<>8 r9c2=8 r9c5<>8) (r6c2<>6) r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4 r9c5=2 r9c4<>2 r1c4=2 r1c9<>2
r7c2=6 (r2c2<>6) (r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r2c1<>6) (r9c2<>6) r9c3<>6 r9c7=6 r2c7<>6 r2c8=6 r2c8<>2
r7c2=6 (r3c2<>6) (r5c2<>6 r5c9=6 r6c8<>6 r6c1=6 r3c1<>6) (r5c2<>6 r5c9=6 r3c9<>6) (r9c2<>6) r9c3<>6 r9c7=6 r3c7<>6 r3c3=6 (r3c3<>9) r3c3<>3 r3c1=3 r3c1<>9 r3c9=9 r3c9<>2
Almost Locked Set XZ-Rule: A=r15689c4 {123578}, B=r7c2,r8c13 {3458}, X=3, Z=8 => r7c4<>8
Forcing Net Contradiction in r4c3 => r4c5<>4
r4c5=4 (r4c8<>4 r6c8=4 r6c8<>6) r5c5<>4 r5c5=9 r6c5<>9 r6c1=9 r6c1<>6 r6c2=6 r9c2<>6 r9c2=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 (r5c2=1 r9c2<>1) r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c5=4 (r4c5<>7) r4c5<>2 r4c6=2 r4c6<>7 r4c3=7
Forcing Net Contradiction in r4c3 => r4c6<>4
r4c6=4 (r4c8<>4 r6c8=4 r6c8<>6) r5c5<>4 r5c5=9 r6c5<>9 r6c1=9 r6c1<>6 r6c2=6 r9c2<>6 r9c2=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 (r5c2=1 r9c2<>1) r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5
r4c6=4 (r4c6<>7) r4c6<>2 r4c5=2 r4c5<>7 r4c3=7
Forcing Net Verity => r1c9<>8
r1c5=8 r1c9<>8
r6c5=8 (r4c6<>8) r6c5<>9 r6c1=9 r5c3<>9 r5c3=4 (r4c1<>4) r4c3<>4 r4c8=4 r4c8<>8 r4c9=8 r1c9<>8
r7c5=8 (r7c7<>8) r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r1c9<>8
r9c5=8 (r9c7<>8) r9c2<>8 r7c2=8 r7c7<>8 r3c7=8 r1c9<>8
Forcing Net Contradiction in c8 => r7c4<>7
r7c4=7 (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r3c6<>8 r1c45=8 r1c8<>8
r7c4=7 (r7c4<>3 r7c3=3 r7c3<>1 r7c6=1 r7c6<>4) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r8c6<>4 r6c6=4 r6c8<>4 r4c8=4 r4c8<>8
r7c4=7 (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r4c6<>8 r4c89=8 r6c8<>8
r7c4=7 (r7c4<>5) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>5) (r7c4<>3 r7c3=3 r7c3<>1 r7c6=1 r7c6<>5) (r7c4<>3 r7c3=3 r8c3<>3 r8c4=3 r8c4<>8) (r8c4<>7) r8c6<>7 r8c9=7 (r8c9<>8) r8c9<>2 r8c8=2 r8c8<>8 r8c6=8 r8c6<>5 r7c5=5 r7c2<>5 r7c2=8 r7c8<>8
r7c4=7 (r8c4<>7) r8c6<>7 r8c9=7 r8c9<>2 r8c8=2 r8c8<>8
Forcing Net Contradiction in r6c4 => r7c6<>8
r7c6=8 r7c6<>1 r79c4=1 r6c4<>1
r7c6=8 r7c2<>8 r7c2=5 (r7c3<>5) (r8c3<>5) (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r1c3<>5 r4c3=5 r4c3<>7 r6c2=7 r6c4<>7
r7c6=8 r7c2<>8 (r9c2=8 r9c7<>8 r3c7=8 r1c8<>8) r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r1c5<>8 r1c4=8 r6c4<>8
Forcing Net Contradiction in r6c6 => r7c7<>8
r7c7=8 (r7c2<>8 r9c2=8 r9c5<>8) r7c7<>4 r9c7=4 r9c5<>4 r9c5=2 (r9c4<>2 r9c4=1 r7c6<>1) r4c5<>2 r4c6=2 r4c6<>1 r6c6=1
r7c7=8 (r7c5<>8) (r7c7<>4 r9c7=4 r9c5<>4 r9c5=2 r4c5<>2) r7c2<>8 r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r4c5=7 r7c5<>7 r7c5=4 (r7c6<>4) r8c6<>4 r6c6=4
Forcing Net Contradiction in r9 => r2c2<>6
r2c2=6 (r9c2<>6) (r2c8<>6) (r2c1<>6) r3c1<>6 r6c1=6 r6c8<>6 r7c8=6 r9c7<>6 r9c3=6 r9c3<>4
r2c2=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r9c5<>4
r2c2=6 (r2c7<>6 r2c7=7 r7c7<>7) (r2c8<>6) (r2c1<>6) r3c1<>6 r6c1=6 r6c8<>6 r7c8=6 r7c7<>6 r7c7=4 r9c7<>4
Forcing Net Contradiction in r7c8 => r7c8<>8
r7c8=8 (r1c8<>8) r7c2<>8 (r9c2=8 r9c4<>8) (r9c2=8 r9c5<>8) r7c2=5 (r7c5<>5) r5c2<>5 r5c4=5 (r8c4<>5 r8c6=5 r8c6<>8) r4c5<>5 r1c5=5 r1c5<>8 r1c4=8 r8c4<>8 r7c5=8 r7c8<>8
Forcing Net Verity => r7c5<>4
r3c1=6 r3c1<>3 r8c1=3 r8c1<>4 r46c1=4 r5c3<>4 r5c3=9 r5c5<>9 r5c5=4 r7c5<>4
r3c2=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r7c5<>4
r3c3=6 (r2c1<>6) r3c1<>6 r6c1=6 r6c1<>9 r6c5=9 r5c5<>9 r5c5=4 r7c5<>4
r3c7=6 (r7c7<>6) r2c7<>6 r2c7=7 r7c7<>7 r7c7=4 r7c5<>4
r3c9=6 (r2c7<>6 r2c7=7 r3c7<>7 r3c7=8 r3c6<>8) (r2c7<>6 r2c7=7 r3c7<>7 r3c7=8 r1c8<>8) r5c9<>6 (r5c2=6 r6c2<>6 r6c8=6 r6c8<>8) r5c9=1 r4c9<>1 r4c9=8 (r4c6<>8) r4c8<>8 r8c8=8 r8c6<>8 r6c6=8 r6c6<>4 r56c5=4 r7c5<>4
Forcing Net Verity => r3c9<>6
r2c2=5 (r2c2<>2 r3c2=2 r3c2<>7) (r7c2<>5 r7c2=8 r7c5<>8) (r1c1<>5) (r1c3<>5) r5c2<>5 r5c4=5 r1c4<>5 r1c5=5 r7c5<>5 r7c5=7 r4c5<>7 r4c6=7 (r3c6<>7) (r2c6<>7) r6c6<>7 r6c2=7 (r6c4<>7) (r6c5<>7) (r4c3<>7) r2c2<>7 r2c7=7 (r3c7<>7) r3c9<>7 r3c3=7 (r3c3<>9) r3c3<>3 r3c1=3 r3c1<>9 r3c9=9 r3c9<>6
r5c2=5 r5c2<>6 r5c9=6 r3c9<>6
r7c2=5 (r2c2<>5) (r7c5<>5) r5c2<>5 r5c4=5 r4c5<>5 r1c5=5 r2c6<>5 r2c1=5 r2c1<>6 r2c78=6 r3c9<>6
Forcing Net Contradiction in c1 => r6c5<>4
r6c5=4 (r9c5<>4) r5c5<>4 r5c3=4 r9c3<>4 r9c7=4 r9c7<>8 r3c7=8 r3c7<>6 r2c78=6 r2c1<>6
r6c5=4 (r6c1<>4) r5c5<>4 r5c3=4 r4c1<>4 r8c1=4 r8c1<>3 r3c1=3 r3c1<>6
r6c5=4 r6c5<>9 r6c1=9 r6c1<>6
Forcing Net Contradiction in r6 => r2c8<>2
r2c8=2 (r2c8<>6) r8c8<>2 r8c8=8 r9c7<>8 r3c7=8 (r3c6<>8 r3c6=7 r2c6<>7) r3c7<>6 r2c7=6 r2c7<>7 r2c2=7 r6c2<>7
r2c8=2 (r2c2<>2 r3c2=2 r3c6<>2) r8c8<>2 (r8c9=2 r8c9<>7) r8c8=8 r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r8c6<>7 r8c4=7 r6c4<>7
r2c8=2 (r2c8<>6) r8c8<>2 r8c8=8 (r9c7<>8) r9c7<>8 r3c7=8 r3c7<>6 r2c7=6 r9c7<>6 r9c7=4 r9c5<>4 r5c5=4 r5c3<>4 r5c3=9 r6c1<>9 r6c5=9 r6c5<>7
r2c8=2 (r2c2<>2 r3c2=2 r3c6<>2) r8c8<>2 r8c8=8 r9c7<>8 r3c7=8 r3c6<>8 r3c6=7 r6c6<>7
Forcing Net Verity => r9c4=2
r4c5=2 r9c5<>2 r9c4=2
r4c5=5 (r4c5<>7) r4c5<>2 r4c6=2 (r4c6<>8 r4c89=8 r6c8<>8) (r2c6<>2 r2c2=2 r3c2<>2 r3c9=2 r8c9<>2 r8c8=2 r8c8<>8) (r3c6<>2) (r2c6<>2 r2c2=2 r2c2<>7) r4c6<>7 r4c3=7 r6c2<>7 r3c2=7 r3c6<>7 r3c6=8 (r6c6<>8) (r8c6<>8) r3c7<>8 r9c7=8 r8c9<>8 r8c4=8 r6c4<>8 r6c5=8 r6c5<>9 r6c1=9 r5c3<>9 r5c5=9 r5c5<>4 r9c5=4 r9c5<>2 r9c4=2
r4c5=7 (r7c5<>7) (r4c5<>5) r4c5<>2 r4c6=2 (r2c6<>2 r2c2=2 r2c2<>5) r4c6<>5 r5c4=5 r5c2<>5 r7c2=5 r7c5<>5 r7c5=8 (r1c5<>8) r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r1c8<>8 r1c4=8 r1c4<>2 r9c4=2
Locked Candidates Type 1 (Pointing): 1 in b8 => r7c3<>1
Forcing Chain Contradiction in c1 => r7c2=8
r7c2<>8 r9c2=8 r9c7<>8 r3c7=8 r3c7<>6 r2c78=6 r2c1<>6
r7c2<>8 r9c2=8 r9c5<>8 r9c5=4 r5c5<>4 r5c3=4 r46c1<>4 r8c1=4 r8c1<>3 r3c1=3 r3c1<>6
r7c2<>8 r9c2=8 r9c5<>8 r9c5=4 r5c5<>4 r5c5=9 r5c3<>9 r6c1=9 r6c1<>6
Almost Locked Set XZ-Rule: A=r4c1389 {14578}, B=r569c2 {1567}, X=5,7 => r2c2,r4c6<>1, r4c6,r6c8<>8, r3c2<>6
Discontinuous Nice Loop: 8 r3c9 -8- r3c7 =8= r9c7 -8- r9c5 -4- r5c5 =4= r6c6 -4- r6c8 =4= r4c8 =8= r4c9 -8- r3c9 => r3c9<>8
Skyscraper: 8 in r3c6,r9c5 (connected by r39c7) => r1c5,r8c6<>8
Naked Triple: 2,5,7 in r147c5 => r6c5<>7
Swordfish: 8 r148 c489 => r6c4<>8
Hidden Triple: 4,8,9 in r56c5,r6c6 => r6c6<>1, r6c6<>7
Hidden Single: r7c6=1
Swordfish: 4 r579 c357 => r48c3<>4
Hidden Rectangle: 3/5 in r7c34,r8c34 => r7c4<>5
Naked Single: r7c4=3
Discontinuous Nice Loop: 7 r4c5 -7- r4c3 =7= r6c2 -7- r3c2 -2- r2c2 =2= r2c6 -2- r4c6 =2= r4c5 => r4c5<>7
Empty Rectangle: 7 in b2 (r4c36) => r1c3<>7
Empty Rectangle: 7 in b9 (r17c5) => r1c9<>7
Locked Candidates Type 2 (Claiming): 7 in r1 => r23c6<>7
AIC: 4 4- r5c3 =4= r5c5 -4- r6c6 -8- r3c6 -2- r3c2 -7- r3c3 =7= r4c3 -7- r4c6 =7= r8c6 =4= r8c1 -4 => r46c1,r79c3<>4
Hidden Single: r4c8=4
Hidden Single: r8c1=4
Hidden Single: r5c3=4
Naked Single: r5c5=9
Naked Single: r6c5=8
Naked Single: r6c6=4
Naked Single: r9c5=4
Hidden Single: r7c7=4
Hidden Single: r4c9=8
Hidden Single: r8c3=3
Hidden Single: r3c1=3
Hidden Single: r6c1=9
Hidden Single: r3c6=8
Hidden Single: r9c7=8
Naked Single: r8c8=2
Naked Single: r8c9=7
Naked Single: r8c6=5
Full House: r8c4=8
Full House: r7c5=7
Naked Single: r2c6=2
Full House: r4c6=7
Naked Single: r1c5=5
Full House: r1c4=7
Full House: r4c5=2
Naked Single: r6c4=1
Full House: r5c4=5
Naked Single: r1c1=1
Naked Single: r6c8=6
Full House: r5c9=1
Full House: r6c2=7
Full House: r5c2=6
Naked Single: r1c3=9
Naked Single: r4c1=5
Full House: r2c1=6
Full House: r4c3=1
Naked Single: r2c8=1
Naked Single: r7c8=9
Full House: r1c8=8
Full House: r1c9=2
Full House: r7c9=6
Full House: r3c9=9
Full House: r7c3=5
Naked Single: r2c2=5
Full House: r2c7=7
Full House: r3c7=6
Naked Single: r3c2=2
Full House: r9c2=1
Full House: r3c3=7
Full House: r9c3=6
|
sudoku_normal_hard_114
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8...7..3..1...6..9......54...3..2....27.......6.43.7..534.8...49.1...36....2.4.
|
168495732354127968792863415476938521583271694921654387215349876849716253637582149
|
. . 8 . . . 7 . .
3 . . 1 . . . 6 .
. 9 . . . . . . 5
4 . . . 3 . . 2 .
. . . 2 7 . . . .
. . . 6 . 4 3 . 7
. . 5 3 4 . 8 . .
. 4 9 . 1 . . . 3
6 . . . . 2 . 4 .
|
1 6 8 4 9 5 7 3 2
3 5 4 1 2 7 9 6 8
7 9 2 8 6 3 4 1 5
4 7 6 9 3 8 5 2 1
5 8 3 2 7 1 6 9 4
9 2 1 6 5 4 3 8 7
2 1 5 3 4 9 8 7 6
8 4 9 7 1 6 2 5 3
6 3 7 5 8 2 1 4 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7097_hard
|
168495732354127968792863415476938521583271694921654387215349876849716253637582149 #1 Extreme (19284) bf
Locked Candidates Type 1 (Pointing): 4 in b7 => r12c2<>4
Brute Force: r5c5=7
Finned Swordfish: 7 r249 c234 fr2c6 => r3c4<>7
Locked Candidates Type 1 (Pointing): 7 in b2 => r78c6<>7
Discontinuous Nice Loop: 4 r2c9 -4- r2c3 =4= r3c3 -4- r3c4 -8- r3c8 =8= r2c9 => r2c9<>4
Discontinuous Nice Loop: 8 r2c6 -8- r2c9 =8= r3c8 =3= r3c6 =7= r2c6 => r2c6<>8
Forcing Net Contradiction in r8 => r6c5<>8
r6c5=8 (r6c1<>8) (r6c8<>8) r2c5<>8 r2c9=8 r3c8<>8 r5c8=8 r5c1<>8 r8c1=8 r8c1<>2
r6c5=8 (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 r8c2<>2
r6c5=8 (r3c5<>8) (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 (r2c9<>2) (r3c8<>8) r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c6=8 (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 (r1c5<>4 r1c9=4 r1c9<>2) r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2 r7c9=2 r8c7<>2
r6c5=8 (r3c5<>8) (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 (r3c8<>8) r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c6=8 (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2
Forcing Net Contradiction in b9 => r3c6<>8
r3c6=8 (r2c5<>8 r2c9=8 r2c9<>2) (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 (r1c5<>4 r1c9=4 r1c9<>2) r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2 r7c9=2
r3c6=8 (r3c5<>8 r9c5=8 r8c4<>8) (r8c6<>8) r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 (r8c2<>2) (r8c2<>3 r8c9=3 r8c9<>2) r8c2<>8 r8c1=8 r8c1<>2 r8c7=2
Forcing Net Contradiction in b1 => r4c6<>5
r4c6=5 (r1c6<>5) (r2c6<>5) (r6c5<>5 r6c5=9 r9c5<>9) (r4c6<>8) r4c6<>1 r5c6=1 r5c6<>8 r8c6=8 r9c5<>8 r9c5=5 (r1c5<>5) r2c5<>5 r2c2=5 r1c2<>5 r1c1=5
r4c6=5 (r2c6<>5) (r6c5<>5 r6c5=9 r9c5<>9) (r4c6<>8) r4c6<>1 r5c6=1 r5c6<>8 r8c6=8 r9c5<>8 r9c5=5 r2c5<>5 r2c2=5
Forcing Net Contradiction in r7c8 => r1c4<>5
r1c4=5 (r1c5<>5) (r1c6<>5) (r2c6<>5) (r1c6<>5) (r2c6<>5) (r4c4<>5) (r2c5<>5) r2c6<>5 r2c2=5 r4c2<>5 r4c7=5 (r5c8<>5) r6c8<>5 r8c8=5 r8c6<>5 r5c6=5 (r5c6<>8) r5c6<>1 r4c6=1 r4c6<>8 r8c6=8 r9c5<>8 r9c5=5 (r9c5<>9) r2c5<>5 r2c2=5 r1c2<>5 r1c1=5 r1c4<>5
Almost Locked Set XY-Wing: A=r6c5 {59}, B=r78c6,r89c4,r9c5 {456789}, C=r134c4 {4589}, X,Y=4,5, Z=9 => r7c5<>9
Forcing Chain Verity => r2c6<>9
r7c6=9 r2c6<>9
r9c4=9 r9c4<>7 r9c23=7 r78c1<>7 r3c1=7 r3c6<>7 r2c6=7 r2c6<>9
r9c5=9 r9c5<>8 r23c5=8 r3c4<>8 r3c4=4 r1c4<>4 r1c4=9 r2c6<>9
Forcing Net Verity => r6c5=5
r1c8=9 (r2c7<>9) r2c9<>9 r2c5=9 r6c5<>9 r6c5=5
r5c8=9 r5c1<>9 r6c1=9 r6c5<>9 r6c5=5
r6c8=9 r6c5<>9 r6c5=5
r7c8=9 (r9c7<>9) (r9c9<>9) r7c8<>7 r8c8=7 r8c4<>7 r9c4=7 r9c4<>9 r9c5=9 r6c5<>9 r6c5=5
Locked Candidates Type 1 (Pointing): 5 in b2 => r8c6<>5
Naked Triple: 6,8,9 in r78c6,r9c5 => r7c5<>6, r89c4<>8, r9c4<>9
Naked Single: r7c5=4
Hidden Single: r8c2=4
Locked Candidates Type 1 (Pointing): 3 in b7 => r9c9<>3
Locked Candidates Type 1 (Pointing): 6 in b8 => r13c6<>6
Hidden Triple: 3,5,7 in r123c6 => r1c6<>9
2-String Kite: 8 in r2c9,r4c4 (connected by r2c5,r3c4) => r4c9<>8
AIC: 3 3- r3c8 =3= r3c6 -3- r1c6 -5- r1c1 =5= r5c1 -5- r5c8 =5= r8c8 =3= r8c9 -3 => r1c9,r8c8<>3
Hidden Single: r8c9=3
Naked Pair: 5,7 in r8c48 => r8c1<>7, r8c7<>5
Hidden Pair: 2,6 in r7c9,r8c7 => r7c9<>1, r7c9<>9
Discontinuous Nice Loop: 2/9 r2c9 =8= r2c5 -8- r9c5 -9- r7c6 =9= r7c8 =7= r8c8 =5= r5c8 -5- r5c1 =5= r1c1 -5- r1c6 -3- r1c8 =3= r3c8 =8= r2c9 => r2c9<>2, r2c9<>9
Naked Single: r2c9=8
2-String Kite: 2 in r1c9,r8c1 (connected by r7c9,r8c7) => r1c1<>2
2-String Kite: 9 in r2c7,r4c4 (connected by r1c4,r2c5) => r4c7<>9
XY-Chain: 2 2- r2c5 -9- r9c5 -8- r8c6 -6- r8c7 -2 => r2c7<>2
Discontinuous Nice Loop: 1/2/8 r6c1 =9= r6c8 =8= r5c8 =5= r8c8 =7= r7c8 -7- r7c1 =7= r3c1 -7- r3c6 -3- r1c6 -5- r1c1 =5= r5c1 =9= r6c1 => r6c1<>1, r6c1<>2, r6c1<>8
Naked Single: r6c1=9
Continuous Nice Loop: 1/9 4= r1c9 =2= r7c9 =6= r7c6 =9= r9c5 =8= r3c5 -8- r3c4 -4- r1c4 =4= r1c9 =2 => r1c9<>1, r1c9<>9
XY-Wing: 4/9/2 in r1c49,r2c5 => r1c5<>2
Finned Swordfish: 1 r167 c128 fr6c3 => r45c2,r5c1<>1
Continuous Nice Loop: 1/5 9= r7c8 =7= r8c8 =5= r5c8 -5- r5c1 -8- r8c1 =8= r8c6 =6= r7c6 =9= r7c8 =7 => r7c8<>1, r5c27<>5
Locked Candidates Type 1 (Pointing): 1 in b9 => r9c23<>1
AIC: 2/5 2- r1c2 =2= r1c9 -2- r7c9 -6- r7c6 -9- r7c8 -7- r7c1 =7= r3c1 -7- r3c6 =7= r2c6 =5= r2c2 -5 => r2c2<>2, r1c2<>5
Naked Pair: 5,7 in r2c26 => r2c3<>7
AIC: 9 9- r1c5 -6- r1c2 =6= r3c3 =4= r2c3 -4- r2c7 -9 => r1c8,r2c5<>9
Naked Single: r2c5=2
Naked Single: r2c3=4
Naked Single: r2c7=9
Locked Pair: 1,3 in r13c8 => r3c7,r56c8<>1
Naked Single: r6c8=8
Locked Candidates Type 2 (Claiming): 1 in r6 => r45c3<>1
Naked Triple: 1,3,5 in r1c168 => r1c2<>1
Naked Triple: 3,6,7 in r459c3 => r3c3<>6, r3c3<>7
Hidden Single: r3c5=6
Naked Single: r1c5=9
Full House: r9c5=8
Naked Single: r1c4=4
Naked Single: r8c6=6
Naked Single: r1c9=2
Naked Single: r3c4=8
Naked Single: r7c6=9
Naked Single: r8c7=2
Naked Single: r1c2=6
Naked Single: r3c7=4
Naked Single: r7c9=6
Naked Single: r4c4=9
Naked Single: r7c8=7
Naked Single: r8c1=8
Naked Single: r4c9=1
Naked Single: r8c8=5
Full House: r8c4=7
Full House: r9c4=5
Naked Single: r5c1=5
Naked Single: r4c6=8
Full House: r5c6=1
Naked Single: r5c7=6
Naked Single: r9c9=9
Full House: r9c7=1
Full House: r4c7=5
Full House: r5c9=4
Full House: r5c8=9
Naked Single: r1c1=1
Naked Single: r4c2=7
Full House: r4c3=6
Naked Single: r5c3=3
Full House: r5c2=8
Naked Single: r1c8=3
Full House: r1c6=5
Full House: r3c8=1
Naked Single: r3c3=2
Naked Single: r7c1=2
Full House: r3c1=7
Full House: r2c2=5
Full House: r2c6=7
Full House: r7c2=1
Full House: r3c6=3
Naked Single: r9c2=3
Full House: r9c3=7
Full House: r6c3=1
Full House: r6c2=2
|
sudoku_normal_extremely_hard_114
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8...7..3..1...6..9......54...3..2....2........6.43.7..53..8....9.1....6....2.4.
|
168495732354127968792863415476938521583271694921654387215349876849716253637582149
|
. . 8 . . . 7 . .
3 . . 1 . . . 6 .
. 9 . . . . . . 5
4 . . . 3 . . 2 .
. . . 2 . . . . .
. . . 6 . 4 3 . 7
. . 5 3 . . 8 . .
. . 9 . 1 . . . .
6 . . . . 2 . 4 .
|
1 6 8 4 9 5 7 3 2
3 5 4 1 2 7 9 6 8
7 9 2 8 6 3 4 1 5
4 7 6 9 3 8 5 2 1
5 8 3 2 7 1 6 9 4
9 2 1 6 5 4 3 8 7
2 1 5 3 4 9 8 7 6
8 4 9 7 1 6 2 5 3
6 3 7 5 8 2 1 4 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7097_hard
|
168495732354127968792863415476938521583271694921654387215349876849716253637582149 #1 Extreme (19284) bf
Locked Candidates Type 1 (Pointing): 4 in b7 => r12c2<>4
Brute Force: r5c5=7
Finned Swordfish: 7 r249 c234 fr2c6 => r3c4<>7
Locked Candidates Type 1 (Pointing): 7 in b2 => r78c6<>7
Discontinuous Nice Loop: 4 r2c9 -4- r2c3 =4= r3c3 -4- r3c4 -8- r3c8 =8= r2c9 => r2c9<>4
Discontinuous Nice Loop: 8 r2c6 -8- r2c9 =8= r3c8 =3= r3c6 =7= r2c6 => r2c6<>8
Forcing Net Contradiction in r8 => r6c5<>8
r6c5=8 (r6c1<>8) (r6c8<>8) r2c5<>8 r2c9=8 r3c8<>8 r5c8=8 r5c1<>8 r8c1=8 r8c1<>2
r6c5=8 (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 r8c2<>2
r6c5=8 (r3c5<>8) (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 (r2c9<>2) (r3c8<>8) r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c6=8 (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 (r1c5<>4 r1c9=4 r1c9<>2) r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2 r7c9=2 r8c7<>2
r6c5=8 (r3c5<>8) (r9c5<>8) (r4c4<>8) (r4c6<>8) r2c5<>8 r2c9=8 (r3c8<>8) r4c9<>8 r4c2=8 r9c2<>8 r9c4=8 r3c4<>8 r3c6=8 (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2
Forcing Net Contradiction in b9 => r3c6<>8
r3c6=8 (r2c5<>8 r2c9=8 r2c9<>2) (r3c6<>3 r3c8=3 r8c8<>3) r3c4<>8 r3c4=4 (r1c5<>4 r1c9=4 r1c9<>2) r8c4<>4 r8c2=4 r8c2<>3 r8c9=3 r8c9<>2 r7c9=2
r3c6=8 (r3c5<>8 r9c5=8 r8c4<>8) (r8c6<>8) r3c4<>8 r3c4=4 r8c4<>4 r8c2=4 (r8c2<>2) (r8c2<>3 r8c9=3 r8c9<>2) r8c2<>8 r8c1=8 r8c1<>2 r8c7=2
Forcing Net Contradiction in b1 => r4c6<>5
r4c6=5 (r1c6<>5) (r2c6<>5) (r6c5<>5 r6c5=9 r9c5<>9) (r4c6<>8) r4c6<>1 r5c6=1 r5c6<>8 r8c6=8 r9c5<>8 r9c5=5 (r1c5<>5) r2c5<>5 r2c2=5 r1c2<>5 r1c1=5
r4c6=5 (r2c6<>5) (r6c5<>5 r6c5=9 r9c5<>9) (r4c6<>8) r4c6<>1 r5c6=1 r5c6<>8 r8c6=8 r9c5<>8 r9c5=5 r2c5<>5 r2c2=5
Forcing Net Contradiction in r7c8 => r1c4<>5
r1c4=5 (r1c5<>5) (r1c6<>5) (r2c6<>5) (r1c6<>5) (r2c6<>5) (r4c4<>5) (r2c5<>5) r2c6<>5 r2c2=5 r4c2<>5 r4c7=5 (r5c8<>5) r6c8<>5 r8c8=5 r8c6<>5 r5c6=5 (r5c6<>8) r5c6<>1 r4c6=1 r4c6<>8 r8c6=8 r9c5<>8 r9c5=5 (r9c5<>9) r2c5<>5 r2c2=5 r1c2<>5 r1c1=5 r1c4<>5
Almost Locked Set XY-Wing: A=r6c5 {59}, B=r78c6,r89c4,r9c5 {456789}, C=r134c4 {4589}, X,Y=4,5, Z=9 => r7c5<>9
Forcing Chain Verity => r2c6<>9
r7c6=9 r2c6<>9
r9c4=9 r9c4<>7 r9c23=7 r78c1<>7 r3c1=7 r3c6<>7 r2c6=7 r2c6<>9
r9c5=9 r9c5<>8 r23c5=8 r3c4<>8 r3c4=4 r1c4<>4 r1c4=9 r2c6<>9
Forcing Net Verity => r6c5=5
r1c8=9 (r2c7<>9) r2c9<>9 r2c5=9 r6c5<>9 r6c5=5
r5c8=9 r5c1<>9 r6c1=9 r6c5<>9 r6c5=5
r6c8=9 r6c5<>9 r6c5=5
r7c8=9 (r9c7<>9) (r9c9<>9) r7c8<>7 r8c8=7 r8c4<>7 r9c4=7 r9c4<>9 r9c5=9 r6c5<>9 r6c5=5
Locked Candidates Type 1 (Pointing): 5 in b2 => r8c6<>5
Naked Triple: 6,8,9 in r78c6,r9c5 => r7c5<>6, r89c4<>8, r9c4<>9
Naked Single: r7c5=4
Hidden Single: r8c2=4
Locked Candidates Type 1 (Pointing): 3 in b7 => r9c9<>3
Locked Candidates Type 1 (Pointing): 6 in b8 => r13c6<>6
Hidden Triple: 3,5,7 in r123c6 => r1c6<>9
2-String Kite: 8 in r2c9,r4c4 (connected by r2c5,r3c4) => r4c9<>8
AIC: 3 3- r3c8 =3= r3c6 -3- r1c6 -5- r1c1 =5= r5c1 -5- r5c8 =5= r8c8 =3= r8c9 -3 => r1c9,r8c8<>3
Hidden Single: r8c9=3
Naked Pair: 5,7 in r8c48 => r8c1<>7, r8c7<>5
Hidden Pair: 2,6 in r7c9,r8c7 => r7c9<>1, r7c9<>9
Discontinuous Nice Loop: 2/9 r2c9 =8= r2c5 -8- r9c5 -9- r7c6 =9= r7c8 =7= r8c8 =5= r5c8 -5- r5c1 =5= r1c1 -5- r1c6 -3- r1c8 =3= r3c8 =8= r2c9 => r2c9<>2, r2c9<>9
Naked Single: r2c9=8
2-String Kite: 2 in r1c9,r8c1 (connected by r7c9,r8c7) => r1c1<>2
2-String Kite: 9 in r2c7,r4c4 (connected by r1c4,r2c5) => r4c7<>9
XY-Chain: 2 2- r2c5 -9- r9c5 -8- r8c6 -6- r8c7 -2 => r2c7<>2
Discontinuous Nice Loop: 1/2/8 r6c1 =9= r6c8 =8= r5c8 =5= r8c8 =7= r7c8 -7- r7c1 =7= r3c1 -7- r3c6 -3- r1c6 -5- r1c1 =5= r5c1 =9= r6c1 => r6c1<>1, r6c1<>2, r6c1<>8
Naked Single: r6c1=9
Continuous Nice Loop: 1/9 4= r1c9 =2= r7c9 =6= r7c6 =9= r9c5 =8= r3c5 -8- r3c4 -4- r1c4 =4= r1c9 =2 => r1c9<>1, r1c9<>9
XY-Wing: 4/9/2 in r1c49,r2c5 => r1c5<>2
Finned Swordfish: 1 r167 c128 fr6c3 => r45c2,r5c1<>1
Continuous Nice Loop: 1/5 9= r7c8 =7= r8c8 =5= r5c8 -5- r5c1 -8- r8c1 =8= r8c6 =6= r7c6 =9= r7c8 =7 => r7c8<>1, r5c27<>5
Locked Candidates Type 1 (Pointing): 1 in b9 => r9c23<>1
AIC: 2/5 2- r1c2 =2= r1c9 -2- r7c9 -6- r7c6 -9- r7c8 -7- r7c1 =7= r3c1 -7- r3c6 =7= r2c6 =5= r2c2 -5 => r2c2<>2, r1c2<>5
Naked Pair: 5,7 in r2c26 => r2c3<>7
AIC: 9 9- r1c5 -6- r1c2 =6= r3c3 =4= r2c3 -4- r2c7 -9 => r1c8,r2c5<>9
Naked Single: r2c5=2
Naked Single: r2c3=4
Naked Single: r2c7=9
Locked Pair: 1,3 in r13c8 => r3c7,r56c8<>1
Naked Single: r6c8=8
Locked Candidates Type 2 (Claiming): 1 in r6 => r45c3<>1
Naked Triple: 1,3,5 in r1c168 => r1c2<>1
Naked Triple: 3,6,7 in r459c3 => r3c3<>6, r3c3<>7
Hidden Single: r3c5=6
Naked Single: r1c5=9
Full House: r9c5=8
Naked Single: r1c4=4
Naked Single: r8c6=6
Naked Single: r1c9=2
Naked Single: r3c4=8
Naked Single: r7c6=9
Naked Single: r8c7=2
Naked Single: r1c2=6
Naked Single: r3c7=4
Naked Single: r7c9=6
Naked Single: r4c4=9
Naked Single: r7c8=7
Naked Single: r8c1=8
Naked Single: r4c9=1
Naked Single: r8c8=5
Full House: r8c4=7
Full House: r9c4=5
Naked Single: r5c1=5
Naked Single: r4c6=8
Full House: r5c6=1
Naked Single: r5c7=6
Naked Single: r9c9=9
Full House: r9c7=1
Full House: r4c7=5
Full House: r5c9=4
Full House: r5c8=9
Naked Single: r1c1=1
Naked Single: r4c2=7
Full House: r4c3=6
Naked Single: r5c3=3
Full House: r5c2=8
Naked Single: r1c8=3
Full House: r1c6=5
Full House: r3c8=1
Naked Single: r3c3=2
Naked Single: r7c1=2
Full House: r3c1=7
Full House: r2c2=5
Full House: r2c6=7
Full House: r7c2=1
Full House: r3c6=3
Naked Single: r9c2=3
Full House: r9c3=7
Full House: r6c3=1
Full House: r6c2=2
|
sudoku_normal_hard_115
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
....82.6.26.95..1.9...1.2....6.2...141.8396...29.6..84..429..3..3..7....69.3451..
|
541782963263954817978613245386427591415839672729561384154298736832176459697345128
|
. . . . 8 2 . 6 .
2 6 . 9 5 . . 1 .
9 . . . 1 . 2 . .
. . 6 . 2 . . . 1
4 1 . 8 3 9 6 . .
. 2 9 . 6 . . 8 4
. . 4 2 9 . . 3 .
. 3 . . 7 . . . .
6 9 . 3 4 5 1 . .
|
5 4 1 7 8 2 9 6 3
2 6 3 9 5 4 8 1 7
9 7 8 6 1 3 2 4 5
3 8 6 4 2 7 5 9 1
4 1 5 8 3 9 6 7 2
7 2 9 5 6 1 3 8 4
1 5 4 2 9 8 7 3 6
8 3 2 1 7 6 4 5 9
6 9 7 3 4 5 1 2 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4242_hard
|
541782963263954817978613245386427591415839672729561384154298736832176459697345128 #1 Extreme (23992) bf
Hidden Single: r7c5=9
Hidden Single: r4c9=1
Locked Candidates Type 2 (Claiming): 6 in c5 => r4c46,r6c46<>6
Hidden Pair: 6,9 in r46c3 => r46c3<>3, r46c3<>5, r46c3<>7, r4c3<>8
Brute Force: r5c4=8
Forcing Chain Contradiction in r1 => r4c8<>5
r4c8=5 r5c89<>5 r5c3=5 r5c3<>3 r46c1=3 r1c1<>3
r4c8=5 r4c4<>5 r6c4=5 r6c4<>1 r8c4=1 r8c3<>1 r1c3=1 r1c3<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r9c5<>3 r9c4=3 r1c4<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r1c5<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r5c9<>3 r46c7=3 r1c7<>3
r4c8=5 r4c8<>9 r8c8=9 r8c9<>9 r1c9=9 r1c9<>3
Forcing Net Contradiction in b6 => r6c4<>3
r6c4=3 (r9c4<>3 r9c4=4 r9c8<>4) r5c5<>3 r5c5=2 (r5c8<>2) r4c5<>2 r4c8=2 r9c8<>2 r9c8=7 r5c8<>7 r5c8=5
r6c4=3 (r6c7<>3) (r6c5<>3 r6c5=6 r6c3<>6 r6c3=9 r6c7<>9) (r6c4<>1 r6c6=1 r7c6<>1 r7c1=1 r7c1<>7) (r6c4<>1 r6c6=1 r6c6<>7) (r1c4<>3) r9c4<>3 r9c4=4 r1c4<>4 r1c4=7 (r1c1<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c1<>7 r6c1=7 r6c7<>7 r6c7=5
Brute Force: r5c5=3
Naked Single: r6c5=6
Naked Single: r6c3=9
Naked Single: r4c3=6
Hidden Single: r9c4=3
Hidden Single: r4c5=2
Locked Candidates Type 1 (Pointing): 3 in b4 => r1c1<>3
Locked Candidates Type 1 (Pointing): 3 in b6 => r12c7<>3
Avoidable Rectangle Type 1: 8/3 in r5c45,r9c45 => r9c5<>8
Naked Single: r9c5=4
Full House: r1c5=8
Empty Rectangle: 8 in b1 (r9c39) => r3c9<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r2c3<>8
AIC: 7 7- r1c4 -4- r1c2 =4= r3c2 =8= r3c3 -8- r9c3 =8= r9c9 -8- r2c9 =8= r2c7 =4= r2c6 -4- r4c6 -7 => r23c6,r46c4<>7
XY-Wing: 3/4/7 in r1c4,r2c36 => r1c123<>7
Finned Swordfish: 7 r259 c389 fr2c7 => r13c9,r3c8<>7
XY-Chain: 5 5- r5c3 -7- r2c3 -3- r2c6 -4- r4c6 -7- r6c6 -1- r6c4 -5 => r6c1<>5
Hidden Rectangle: 3/7 in r4c17,r6c17 => r4c7<>7
Continuous Nice Loop: 1/3/4/5 3= r1c3 =1= r1c1 -1- r7c1 =1= r7c6 -1- r6c6 -7- r4c6 -4- r2c6 =4= r2c7 -4- r3c8 -5- r3c9 -3- r1c9 =3= r1c3 =1 => r8c16<>1, r2c9<>3, r1c7,r3c6<>4, r1c37,r3c23<>5
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c9<>5
Empty Rectangle: 5 in b6 (r58c3) => r8c7<>5
XYZ-Wing: 2/7/8 in r29c9,r9c8 => r7c9<>7
Hidden Rectangle: 6/8 in r7c69,r8c69 => r7c9<>8
XY-Wing: 3/5/6 in r3c69,r7c9 => r7c6<>6
Hidden Single: r7c9=6
Swordfish: 5 c389 r358 => r8c1<>5
Naked Single: r8c1=8
Naked Single: r8c6=6
Naked Single: r3c6=3
Naked Single: r8c4=1
Full House: r7c6=8
Naked Single: r2c6=4
Naked Single: r3c9=5
Naked Single: r6c4=5
Naked Single: r1c4=7
Full House: r3c4=6
Full House: r4c4=4
Naked Single: r4c6=7
Full House: r6c6=1
Naked Single: r3c8=4
Naked Single: r1c7=9
Naked Single: r4c8=9
Naked Single: r1c9=3
Naked Single: r8c7=4
Naked Single: r1c3=1
Naked Single: r1c1=5
Full House: r1c2=4
Naked Single: r4c1=3
Naked Single: r4c7=5
Full House: r4c2=8
Naked Single: r6c1=7
Full House: r5c3=5
Full House: r6c7=3
Full House: r7c1=1
Naked Single: r7c7=7
Full House: r2c7=8
Full House: r7c2=5
Full House: r3c2=7
Full House: r2c9=7
Full House: r2c3=3
Full House: r3c3=8
Naked Single: r8c3=2
Full House: r9c3=7
Naked Single: r9c8=2
Full House: r9c9=8
Naked Single: r5c9=2
Full House: r8c9=9
Full House: r8c8=5
Full House: r5c8=7
|
sudoku_normal_extremely_hard_115
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....2.6.26.95..1.9...1.2...........41...96...2.....84..42...3..3..7....69...51..
|
541782963263954817978613245386427591415839672729561384154298736832176459697345128
|
. . . . . 2 . 6 .
2 6 . 9 5 . . 1 .
9 . . . 1 . 2 . .
. . . . . . . . .
4 1 . . . 9 6 . .
. 2 . . . . . 8 4
. . 4 2 . . . 3 .
. 3 . . 7 . . . .
6 9 . . . 5 1 . .
|
5 4 1 7 8 2 9 6 3
2 6 3 9 5 4 8 1 7
9 7 8 6 1 3 2 4 5
3 8 6 4 2 7 5 9 1
4 1 5 8 3 9 6 7 2
7 2 9 5 6 1 3 8 4
1 5 4 2 9 8 7 3 6
8 3 2 1 7 6 4 5 9
6 9 7 3 4 5 1 2 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4242_hard
|
541782963263954817978613245386427591415839672729561384154298736832176459697345128 #1 Extreme (23992) bf
Hidden Single: r7c5=9
Hidden Single: r4c9=1
Locked Candidates Type 2 (Claiming): 6 in c5 => r4c46,r6c46<>6
Hidden Pair: 6,9 in r46c3 => r46c3<>3, r46c3<>5, r46c3<>7, r4c3<>8
Brute Force: r5c4=8
Forcing Chain Contradiction in r1 => r4c8<>5
r4c8=5 r5c89<>5 r5c3=5 r5c3<>3 r46c1=3 r1c1<>3
r4c8=5 r4c4<>5 r6c4=5 r6c4<>1 r8c4=1 r8c3<>1 r1c3=1 r1c3<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r9c5<>3 r9c4=3 r1c4<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r1c5<>3
r4c8=5 r4c8<>2 r4c5=2 r5c5<>2 r5c5=3 r5c9<>3 r46c7=3 r1c7<>3
r4c8=5 r4c8<>9 r8c8=9 r8c9<>9 r1c9=9 r1c9<>3
Forcing Net Contradiction in b6 => r6c4<>3
r6c4=3 (r9c4<>3 r9c4=4 r9c8<>4) r5c5<>3 r5c5=2 (r5c8<>2) r4c5<>2 r4c8=2 r9c8<>2 r9c8=7 r5c8<>7 r5c8=5
r6c4=3 (r6c7<>3) (r6c5<>3 r6c5=6 r6c3<>6 r6c3=9 r6c7<>9) (r6c4<>1 r6c6=1 r7c6<>1 r7c1=1 r7c1<>7) (r6c4<>1 r6c6=1 r6c6<>7) (r1c4<>3) r9c4<>3 r9c4=4 r1c4<>4 r1c4=7 (r1c1<>7) (r2c6<>7) r3c6<>7 r4c6=7 r4c1<>7 r6c1=7 r6c7<>7 r6c7=5
Brute Force: r5c5=3
Naked Single: r6c5=6
Naked Single: r6c3=9
Naked Single: r4c3=6
Hidden Single: r9c4=3
Hidden Single: r4c5=2
Locked Candidates Type 1 (Pointing): 3 in b4 => r1c1<>3
Locked Candidates Type 1 (Pointing): 3 in b6 => r12c7<>3
Avoidable Rectangle Type 1: 8/3 in r5c45,r9c45 => r9c5<>8
Naked Single: r9c5=4
Full House: r1c5=8
Empty Rectangle: 8 in b1 (r9c39) => r3c9<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r2c3<>8
AIC: 7 7- r1c4 -4- r1c2 =4= r3c2 =8= r3c3 -8- r9c3 =8= r9c9 -8- r2c9 =8= r2c7 =4= r2c6 -4- r4c6 -7 => r23c6,r46c4<>7
XY-Wing: 3/4/7 in r1c4,r2c36 => r1c123<>7
Finned Swordfish: 7 r259 c389 fr2c7 => r13c9,r3c8<>7
XY-Chain: 5 5- r5c3 -7- r2c3 -3- r2c6 -4- r4c6 -7- r6c6 -1- r6c4 -5 => r6c1<>5
Hidden Rectangle: 3/7 in r4c17,r6c17 => r4c7<>7
Continuous Nice Loop: 1/3/4/5 3= r1c3 =1= r1c1 -1- r7c1 =1= r7c6 -1- r6c6 -7- r4c6 -4- r2c6 =4= r2c7 -4- r3c8 -5- r3c9 -3- r1c9 =3= r1c3 =1 => r8c16<>1, r2c9<>3, r1c7,r3c6<>4, r1c37,r3c23<>5
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c9<>5
Empty Rectangle: 5 in b6 (r58c3) => r8c7<>5
XYZ-Wing: 2/7/8 in r29c9,r9c8 => r7c9<>7
Hidden Rectangle: 6/8 in r7c69,r8c69 => r7c9<>8
XY-Wing: 3/5/6 in r3c69,r7c9 => r7c6<>6
Hidden Single: r7c9=6
Swordfish: 5 c389 r358 => r8c1<>5
Naked Single: r8c1=8
Naked Single: r8c6=6
Naked Single: r3c6=3
Naked Single: r8c4=1
Full House: r7c6=8
Naked Single: r2c6=4
Naked Single: r3c9=5
Naked Single: r6c4=5
Naked Single: r1c4=7
Full House: r3c4=6
Full House: r4c4=4
Naked Single: r4c6=7
Full House: r6c6=1
Naked Single: r3c8=4
Naked Single: r1c7=9
Naked Single: r4c8=9
Naked Single: r1c9=3
Naked Single: r8c7=4
Naked Single: r1c3=1
Naked Single: r1c1=5
Full House: r1c2=4
Naked Single: r4c1=3
Naked Single: r4c7=5
Full House: r4c2=8
Naked Single: r6c1=7
Full House: r5c3=5
Full House: r6c7=3
Full House: r7c1=1
Naked Single: r7c7=7
Full House: r2c7=8
Full House: r7c2=5
Full House: r3c2=7
Full House: r2c9=7
Full House: r2c3=3
Full House: r3c3=8
Naked Single: r8c3=2
Full House: r9c3=7
Naked Single: r9c8=2
Full House: r9c9=8
Naked Single: r5c9=2
Full House: r8c9=9
Full House: r8c8=5
Full House: r5c8=7
|
sudoku_normal_hard_116
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.26.5....4..2.9..6..98467.......183...89.2..71......6.6...2...4.5...4.....43...7.
|
826157943417239586539846721965471832348962157172583469681725394753694218294318675
|
. 2 6 . 5 . . . .
4 . . 2 . 9 . . 6
. . 9 8 4 6 7 . .
. . . . . 1 8 3 .
. . 8 9 . 2 . . 7
1 . . . . . . 6 .
6 . . . 2 . . . 4
. 5 . . . 4 . . .
. . 4 3 . . . 7 .
|
8 2 6 1 5 7 9 4 3
4 1 7 2 3 9 5 8 6
5 3 9 8 4 6 7 2 1
9 6 5 4 7 1 8 3 2
3 4 8 9 6 2 1 5 7
1 7 2 5 8 3 4 6 9
6 8 1 7 2 5 3 9 4
7 5 3 6 9 4 2 1 8
2 9 4 3 1 8 6 7 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7692_hard
|
826157943417239586539846721965471832348962157172583469681725394753694218294318675 #1 Extreme (19906) bf
Brute Force: r5c6=2
Hidden Single: r2c4=2
Naked Pair: 3,5 in r35c1 => r18c1<>3, r4c1<>5
Grouped Discontinuous Nice Loop: 4 r5c5 -4- r3c5 =4= r3c8 =2= r3c9 -2- r46c9 =2= r6c7 =4= r5c78 -4- r5c5 => r5c5<>4
W-Wing: 6/3 in r3c6,r5c5 connected by 3 in r35c1 => r3c5<>6
Almost Locked Set XY-Wing: A=r3c1256 {13456}, B=r6c23479 {234579}, C=r5c1 {35}, X,Y=3,5, Z=4 => r6c5<>4
Almost Locked Set Chain: 14- r3c1256 {13456} -5- r5c1 {35} -3- r5c25 {346} -4- r5c78 {145} -5- r46c9 {259} -2- r1c789,r2c78,r3c9 {1234589} -14 => r3c8<>1, r1c4,r3c8<>4
Hidden Single: r3c5=4
Grouped Discontinuous Nice Loop: 7 r1c3 -7- r1c46 =7= r2c5 -7- r4c5 -6- r4c3 =6= r1c3 => r1c3<>7
Grouped Discontinuous Nice Loop: 5 r2c8 -5- r2c3 =5= r3c1 =3= r5c1 -3- r5c5 -6- r4c5 -7- r2c5 =7= r1c46 -7- r1c1 -8- r2c2 =8= r2c8 => r2c8<>5
2-String Kite: 5 in r2c7,r5c1 (connected by r2c3,r3c1) => r5c7<>5
Hidden Rectangle: 1/4 in r1c78,r5c78 => r1c8<>1
Forcing Chain Contradiction in r2 => r1c3<>3
r1c3=3 r2c2<>3
r1c3=3 r2c3<>3
r1c3=3 r1c3<>6 r3c2=6 r3c6<>6 r3c6=3 r2c5<>3
r1c3=3 r3c1<>3 r3c1=5 r2c3<>5 r2c7=5 r2c7<>3
Forcing Chain Contradiction in r7c7 => r2c3<>3
r2c3=3 r2c3<>5 r3c1=5 r5c1<>5 r5c8=5 r5c8<>1 r5c7=1 r7c7<>1
r2c3=3 r8c3<>3 r7c23=3 r7c7<>3
r2c3=3 r2c3<>5 r2c7=5 r7c7<>5
r2c3=3 r2c3<>5 r3c1=5 r5c1<>5 r5c8=5 r5c8<>4 r1c8=4 r1c8<>9 r78c8=9 r7c7<>9
Forcing Chain Contradiction in r5c2 => r6c3<>5
r6c3=5 r5c1<>5 r5c1=3 r5c2<>3
r6c3=5 r6c46<>5 r4c4=5 r4c4<>4 r4c2=4 r5c2<>4
r6c3=5 r5c1<>5 r5c1=3 r5c5<>3 r5c5=6 r5c2<>6
AIC: 6 6- r1c3 =6= r4c3 =5= r2c3 -5- r3c1 -3- r3c6 -6 => r1c46,r3c2<>6
Hidden Single: r1c3=6
Hidden Single: r3c6=6
Almost Locked Set XZ-Rule: A=r1c4 {17}, B=r7c46,r9c6 {1578}, X=1, Z=7 => r8c4<>7
Forcing Chain Contradiction in r8 => r1c7<>3
r1c7=3 r1c6<>3 r1c6=7 r1c1<>7 r1c1=8 r8c1<>8
r1c7=3 r1c6<>3 r6c6=3 r6c6<>8 r6c5=8 r8c5<>8
r1c7=3 r1c6<>3 r1c6=7 r1c1<>7 r1c1=8 r1c9<>8 r12c8=8 r8c8<>8
r1c7=3 r78c7<>3 r8c9=3 r8c9<>8
Forcing Chain Contradiction in r2 => r7c2<>7
r7c2=7 r2c2<>7
r7c2=7 r7c46<>7 r8c5=7 r4c5<>7 r4c5=6 r5c5<>6 r5c5=3 r5c1<>3 r5c1=5 r3c1<>5 r2c3=5 r2c3<>7
r7c2=7 r7c46<>7 r8c5=7 r2c5<>7
Forcing Chain Contradiction in r2c7 => r8c9<>9
r8c9=9 r78c8<>9 r1c8=9 r1c8<>4 r1c7=4 r5c7<>4 r5c7=1 r2c7<>1
r8c9=9 r8c9<>3 r78c7=3 r2c7<>3
r8c9=9 r78c8<>9 r1c8=9 r1c8<>4 r5c8=4 r5c8<>5 r5c1=5 r3c1<>5 r2c3=5 r2c7<>5
Forcing Chain Contradiction in r8c8 => r9c7<>2
r9c7=2 r9c7<>6 r9c5=6 r8c4<>6 r8c4=1 r8c8<>1
r9c7=2 r8c8<>2
r9c7=2 r9c7<>6 r9c5=6 r8c4<>6 r8c4=1 r1c4<>1 r2c5=1 r2c8<>1 r2c8=8 r8c8<>8
r9c7=2 r9c7<>6 r9c5=6 r9c5<>9 r8c5=9 r8c8<>9
Forcing Net Contradiction in r9 => r1c1=8
r1c1<>8 (r1c1=7 r1c4<>7 r1c4=1 r2c5<>1) r2c2=8 (r9c2<>8) r2c8<>8 r2c8=1 r3c9<>1 r3c2=1 r9c2<>1 r9c2=9 r9c5<>9 r8c5=9 r8c5<>1 r9c5=1
r1c1<>8 (r2c2=8 r2c8<>8 r2c8=1 r3c9<>1) (r2c2=8 r2c2<>3 r2c7=3 r8c7<>3) r1c1=7 (r1c4<>7 r1c4=1 r1c9<>1) (r8c1<>7) (r2c2<>7) r2c3<>7 r2c5=7 r8c5<>7 r8c3=7 r8c3<>3 r8c9=3 r8c9<>1 r9c9=1
Hidden Single: r2c8=8
Locked Candidates Type 1 (Pointing): 7 in b1 => r2c5<>7
Finned X-Wing: 7 c15 r48 fr6c5 => r4c4<>7
XY-Chain: 7 7- r1c4 -1- r2c5 -3- r5c5 -6- r4c5 -7 => r6c4<>7
Discontinuous Nice Loop: 7 r4c2 -7- r2c2 =7= r2c3 =5= r4c3 -5- r5c1 -3- r5c5 -6- r5c2 =6= r4c2 => r4c2<>7
Almost Locked Set Chain: 9- r7c34678 {135789} -8- r9c6 {58} -5- r178c4 {1567} -6- r125678c7 {1234569} -9 => r9c7<>9
Forcing Chain Contradiction in r9c2 => r8c9=8
r8c9<>8 r8c5=8 r6c5<>8 r6c6=8 r6c6<>3 r1c6=3 r2c5<>3 r2c5=1 r2c3<>1 r23c2=1 r9c2<>1
r8c9<>8 r9c9=8 r9c2<>8
r8c9<>8 r8c5=8 r8c5<>9 r9c5=9 r9c2<>9
Locked Candidates Type 1 (Pointing): 3 in b9 => r2c7<>3
2-String Kite: 3 in r2c5,r5c1 (connected by r2c2,r3c1) => r5c5<>3
Naked Single: r5c5=6
Naked Single: r4c5=7
Hidden Single: r8c4=6
Hidden Single: r4c2=6
Hidden Single: r9c7=6
Hidden Single: r8c1=7
Hidden Single: r4c4=4
Naked Single: r6c4=5
Locked Candidates Type 1 (Pointing): 3 in b5 => r6c23<>3
Locked Candidates Type 2 (Claiming): 3 in c3 => r7c2<>3
Skyscraper: 5 in r2c7,r4c9 (connected by r24c3) => r3c9<>5
X-Wing: 5 r35 c18 => r7c8<>5
W-Wing: 9/2 in r4c1,r6c9 connected by 2 in r9c19 => r4c9,r6c2<>9
Hidden Single: r4c1=9
Naked Single: r9c1=2
Locked Pair: 1,3 in r78c3 => r2c3,r79c2<>1
2-String Kite: 1 in r1c4,r9c9 (connected by r7c4,r9c5) => r1c9<>1
W-Wing: 9/1 in r7c8,r8c5 connected by 1 in r9c59 => r8c78<>9
Hidden Single: r8c5=9
Swordfish: 1 c259 r239 => r2c7<>1
Naked Single: r2c7=5
Naked Single: r2c3=7
Naked Single: r3c8=2
Naked Single: r6c3=2
Naked Single: r8c8=1
Naked Single: r4c3=5
Full House: r4c9=2
Naked Single: r6c9=9
Naked Single: r7c8=9
Naked Single: r8c3=3
Full House: r7c3=1
Full House: r8c7=2
Naked Single: r5c1=3
Full House: r3c1=5
Naked Single: r1c9=3
Naked Single: r6c7=4
Naked Single: r9c9=5
Full House: r7c7=3
Full House: r3c9=1
Full House: r3c2=3
Full House: r2c2=1
Full House: r2c5=3
Naked Single: r1c8=4
Full House: r5c8=5
Full House: r5c7=1
Full House: r5c2=4
Full House: r6c2=7
Full House: r1c7=9
Naked Single: r7c2=8
Full House: r9c2=9
Naked Single: r7c4=7
Full House: r1c4=1
Full House: r1c6=7
Full House: r7c6=5
Naked Single: r9c6=8
Full House: r6c6=3
Full House: r6c5=8
Full House: r9c5=1
|
sudoku_normal_extremely_hard_116
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2..5....4....9..6..98..7.......183...89....71......6.6...2...4.5...4.....43...7.
|
826157943417239586539846721965471832348962157172583469681725394753694218294318675
|
. 2 . . 5 . . . .
4 . . . . 9 . . 6
. . 9 8 . . 7 . .
. . . . . 1 8 3 .
. . 8 9 . . . . 7
1 . . . . . . 6 .
6 . . . 2 . . . 4
. 5 . . . 4 . . .
. . 4 3 . . . 7 .
|
8 2 6 1 5 7 9 4 3
4 1 7 2 3 9 5 8 6
5 3 9 8 4 6 7 2 1
9 6 5 4 7 1 8 3 2
3 4 8 9 6 2 1 5 7
1 7 2 5 8 3 4 6 9
6 8 1 7 2 5 3 9 4
7 5 3 6 9 4 2 1 8
2 9 4 3 1 8 6 7 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7692_hard
|
826157943417239586539846721965471832348962157172583469681725394753694218294318675 #1 Extreme (19906) bf
Brute Force: r5c6=2
Hidden Single: r2c4=2
Naked Pair: 3,5 in r35c1 => r18c1<>3, r4c1<>5
Grouped Discontinuous Nice Loop: 4 r5c5 -4- r3c5 =4= r3c8 =2= r3c9 -2- r46c9 =2= r6c7 =4= r5c78 -4- r5c5 => r5c5<>4
W-Wing: 6/3 in r3c6,r5c5 connected by 3 in r35c1 => r3c5<>6
Almost Locked Set XY-Wing: A=r3c1256 {13456}, B=r6c23479 {234579}, C=r5c1 {35}, X,Y=3,5, Z=4 => r6c5<>4
Almost Locked Set Chain: 14- r3c1256 {13456} -5- r5c1 {35} -3- r5c25 {346} -4- r5c78 {145} -5- r46c9 {259} -2- r1c789,r2c78,r3c9 {1234589} -14 => r3c8<>1, r1c4,r3c8<>4
Hidden Single: r3c5=4
Grouped Discontinuous Nice Loop: 7 r1c3 -7- r1c46 =7= r2c5 -7- r4c5 -6- r4c3 =6= r1c3 => r1c3<>7
Grouped Discontinuous Nice Loop: 5 r2c8 -5- r2c3 =5= r3c1 =3= r5c1 -3- r5c5 -6- r4c5 -7- r2c5 =7= r1c46 -7- r1c1 -8- r2c2 =8= r2c8 => r2c8<>5
2-String Kite: 5 in r2c7,r5c1 (connected by r2c3,r3c1) => r5c7<>5
Hidden Rectangle: 1/4 in r1c78,r5c78 => r1c8<>1
Forcing Chain Contradiction in r2 => r1c3<>3
r1c3=3 r2c2<>3
r1c3=3 r2c3<>3
r1c3=3 r1c3<>6 r3c2=6 r3c6<>6 r3c6=3 r2c5<>3
r1c3=3 r3c1<>3 r3c1=5 r2c3<>5 r2c7=5 r2c7<>3
Forcing Chain Contradiction in r7c7 => r2c3<>3
r2c3=3 r2c3<>5 r3c1=5 r5c1<>5 r5c8=5 r5c8<>1 r5c7=1 r7c7<>1
r2c3=3 r8c3<>3 r7c23=3 r7c7<>3
r2c3=3 r2c3<>5 r2c7=5 r7c7<>5
r2c3=3 r2c3<>5 r3c1=5 r5c1<>5 r5c8=5 r5c8<>4 r1c8=4 r1c8<>9 r78c8=9 r7c7<>9
Forcing Chain Contradiction in r5c2 => r6c3<>5
r6c3=5 r5c1<>5 r5c1=3 r5c2<>3
r6c3=5 r6c46<>5 r4c4=5 r4c4<>4 r4c2=4 r5c2<>4
r6c3=5 r5c1<>5 r5c1=3 r5c5<>3 r5c5=6 r5c2<>6
AIC: 6 6- r1c3 =6= r4c3 =5= r2c3 -5- r3c1 -3- r3c6 -6 => r1c46,r3c2<>6
Hidden Single: r1c3=6
Hidden Single: r3c6=6
Almost Locked Set XZ-Rule: A=r1c4 {17}, B=r7c46,r9c6 {1578}, X=1, Z=7 => r8c4<>7
Forcing Chain Contradiction in r8 => r1c7<>3
r1c7=3 r1c6<>3 r1c6=7 r1c1<>7 r1c1=8 r8c1<>8
r1c7=3 r1c6<>3 r6c6=3 r6c6<>8 r6c5=8 r8c5<>8
r1c7=3 r1c6<>3 r1c6=7 r1c1<>7 r1c1=8 r1c9<>8 r12c8=8 r8c8<>8
r1c7=3 r78c7<>3 r8c9=3 r8c9<>8
Forcing Chain Contradiction in r2 => r7c2<>7
r7c2=7 r2c2<>7
r7c2=7 r7c46<>7 r8c5=7 r4c5<>7 r4c5=6 r5c5<>6 r5c5=3 r5c1<>3 r5c1=5 r3c1<>5 r2c3=5 r2c3<>7
r7c2=7 r7c46<>7 r8c5=7 r2c5<>7
Forcing Chain Contradiction in r2c7 => r8c9<>9
r8c9=9 r78c8<>9 r1c8=9 r1c8<>4 r1c7=4 r5c7<>4 r5c7=1 r2c7<>1
r8c9=9 r8c9<>3 r78c7=3 r2c7<>3
r8c9=9 r78c8<>9 r1c8=9 r1c8<>4 r5c8=4 r5c8<>5 r5c1=5 r3c1<>5 r2c3=5 r2c7<>5
Forcing Chain Contradiction in r8c8 => r9c7<>2
r9c7=2 r9c7<>6 r9c5=6 r8c4<>6 r8c4=1 r8c8<>1
r9c7=2 r8c8<>2
r9c7=2 r9c7<>6 r9c5=6 r8c4<>6 r8c4=1 r1c4<>1 r2c5=1 r2c8<>1 r2c8=8 r8c8<>8
r9c7=2 r9c7<>6 r9c5=6 r9c5<>9 r8c5=9 r8c8<>9
Forcing Net Contradiction in r9 => r1c1=8
r1c1<>8 (r1c1=7 r1c4<>7 r1c4=1 r2c5<>1) r2c2=8 (r9c2<>8) r2c8<>8 r2c8=1 r3c9<>1 r3c2=1 r9c2<>1 r9c2=9 r9c5<>9 r8c5=9 r8c5<>1 r9c5=1
r1c1<>8 (r2c2=8 r2c8<>8 r2c8=1 r3c9<>1) (r2c2=8 r2c2<>3 r2c7=3 r8c7<>3) r1c1=7 (r1c4<>7 r1c4=1 r1c9<>1) (r8c1<>7) (r2c2<>7) r2c3<>7 r2c5=7 r8c5<>7 r8c3=7 r8c3<>3 r8c9=3 r8c9<>1 r9c9=1
Hidden Single: r2c8=8
Locked Candidates Type 1 (Pointing): 7 in b1 => r2c5<>7
Finned X-Wing: 7 c15 r48 fr6c5 => r4c4<>7
XY-Chain: 7 7- r1c4 -1- r2c5 -3- r5c5 -6- r4c5 -7 => r6c4<>7
Discontinuous Nice Loop: 7 r4c2 -7- r2c2 =7= r2c3 =5= r4c3 -5- r5c1 -3- r5c5 -6- r5c2 =6= r4c2 => r4c2<>7
Almost Locked Set Chain: 9- r7c34678 {135789} -8- r9c6 {58} -5- r178c4 {1567} -6- r125678c7 {1234569} -9 => r9c7<>9
Forcing Chain Contradiction in r9c2 => r8c9=8
r8c9<>8 r8c5=8 r6c5<>8 r6c6=8 r6c6<>3 r1c6=3 r2c5<>3 r2c5=1 r2c3<>1 r23c2=1 r9c2<>1
r8c9<>8 r9c9=8 r9c2<>8
r8c9<>8 r8c5=8 r8c5<>9 r9c5=9 r9c2<>9
Locked Candidates Type 1 (Pointing): 3 in b9 => r2c7<>3
2-String Kite: 3 in r2c5,r5c1 (connected by r2c2,r3c1) => r5c5<>3
Naked Single: r5c5=6
Naked Single: r4c5=7
Hidden Single: r8c4=6
Hidden Single: r4c2=6
Hidden Single: r9c7=6
Hidden Single: r8c1=7
Hidden Single: r4c4=4
Naked Single: r6c4=5
Locked Candidates Type 1 (Pointing): 3 in b5 => r6c23<>3
Locked Candidates Type 2 (Claiming): 3 in c3 => r7c2<>3
Skyscraper: 5 in r2c7,r4c9 (connected by r24c3) => r3c9<>5
X-Wing: 5 r35 c18 => r7c8<>5
W-Wing: 9/2 in r4c1,r6c9 connected by 2 in r9c19 => r4c9,r6c2<>9
Hidden Single: r4c1=9
Naked Single: r9c1=2
Locked Pair: 1,3 in r78c3 => r2c3,r79c2<>1
2-String Kite: 1 in r1c4,r9c9 (connected by r7c4,r9c5) => r1c9<>1
W-Wing: 9/1 in r7c8,r8c5 connected by 1 in r9c59 => r8c78<>9
Hidden Single: r8c5=9
Swordfish: 1 c259 r239 => r2c7<>1
Naked Single: r2c7=5
Naked Single: r2c3=7
Naked Single: r3c8=2
Naked Single: r6c3=2
Naked Single: r8c8=1
Naked Single: r4c3=5
Full House: r4c9=2
Naked Single: r6c9=9
Naked Single: r7c8=9
Naked Single: r8c3=3
Full House: r7c3=1
Full House: r8c7=2
Naked Single: r5c1=3
Full House: r3c1=5
Naked Single: r1c9=3
Naked Single: r6c7=4
Naked Single: r9c9=5
Full House: r7c7=3
Full House: r3c9=1
Full House: r3c2=3
Full House: r2c2=1
Full House: r2c5=3
Naked Single: r1c8=4
Full House: r5c8=5
Full House: r5c7=1
Full House: r5c2=4
Full House: r6c2=7
Full House: r1c7=9
Naked Single: r7c2=8
Full House: r9c2=9
Naked Single: r7c4=7
Full House: r1c4=1
Full House: r1c6=7
Full House: r7c6=5
Naked Single: r9c6=8
Full House: r6c6=3
Full House: r6c5=8
Full House: r9c5=1
|
sudoku_normal_hard_117
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
3...7.52.......867..75..31...143.9.2.....9.46.9.....53..2.1.6.5.4.6....86....8...
|
386971524915243867427586319561437982238159746794862153872314695143695278659728431
|
3 . . . 7 . 5 2 .
. . . . . . 8 6 7
. . 7 5 . . 3 1 .
. . 1 4 3 . 9 . 2
. . . . . 9 . 4 6
. 9 . . . . . 5 3
. . 2 . 1 . 6 . 5
. 4 . 6 . . . . 8
6 . . . . 8 . . .
|
3 8 6 9 7 1 5 2 4
9 1 5 2 4 3 8 6 7
4 2 7 5 8 6 3 1 9
5 6 1 4 3 7 9 8 2
2 3 8 1 5 9 7 4 6
7 9 4 8 6 2 1 5 3
8 7 2 3 1 4 6 9 5
1 4 3 6 9 5 2 7 8
6 5 9 7 2 8 4 3 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8206_hard
|
386971524915243867427586319561437982238159746794862153872314695143695278659728431 #1 Extreme (15290) bf
Locked Candidates Type 1 (Pointing): 3 in b6 => r89c9<>3
Brute Force: r5c9=6
Hidden Single: r6c9=3
Locked Candidates Type 1 (Pointing): 6 in b3 => r2c2356<>6
Locked Candidates Type 1 (Pointing): 1 in b6 => r89c7<>1
Skyscraper: 6 in r1c3,r3c5 (connected by r6c35) => r1c6,r3c2<>6
Forcing Net Verity => r2c7<>4
r2c5=4 r2c7<>4
r3c5=4 (r1c6<>4) r3c5<>6 r3c6=6 r4c6<>6 r4c2=6 r1c2<>6 r1c3=6 r1c3<>4 r1c9=4 r2c7<>4
r9c5=4 r7c6<>4 r7c7=4 r2c7<>4
Locked Candidates Type 1 (Pointing): 4 in b3 => r9c9<>4
Hidden Rectangle: 6/8 in r2c78,r7c78 => r7c8<>8
Forcing Net Verity => r2c8<>8
r1c3=8 (r3c1<>8) (r3c2<>8) r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 r3c5=6 r3c5<>8 r3c9=8 r2c8<>8
r2c3=8 r2c8<>8
r5c3=8 (r4c1<>8) r4c2<>8 r4c8=8 r2c8<>8
r6c3=8 (r4c1<>8) r4c2<>8 r4c8=8 r2c8<>8
r8c3=8 (r7c1<>8) r7c2<>8 r7c7=8 (r5c7<>8) r6c7<>8 r4c8=8 r2c8<>8
Forcing Net Contradiction in r8c3 => r1c3<>8
r1c3=8 (r5c3<>8) r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r4c6<>5 r8c6=5 (r8c5<>5) r9c5<>5 r5c5=5 r5c3<>5 r5c3=3 r8c3<>3
r1c3=8 r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r4c6<>5 r8c6=5 r8c3<>5
r1c3=8 r8c3<>8
r1c3=8 (r3c2<>8 r3c2=2 r3c6<>2) r1c3<>6 (r6c3=6 r6c3<>4 r2c3=4 r2c5<>4 r9c5=4 r9c5<>9) r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 (r3c5=6 r3c5<>9) r3c6=4 r7c6<>4 r7c7=4 r7c7<>6 r7c8=6 r2c8<>6 r2c8=9 r2c5<>9 r8c5=9 r8c3<>9
Forcing Net Contradiction in r7c8 => r1c3<>9
r1c3=9 (r3c1<>9) r1c3<>6 (r6c3=6 r6c3<>4 r6c1=4 r3c1<>4) r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 r3c5=6 (r3c5<>9) (r3c5<>4) r3c5<>9 r3c9=9 r3c9<>4 r3c6=4 r7c6<>4 r7c7=4 r7c7<>6 r7c8=6 r2c8<>6 r2c8=9 r3c9<>9 r3c1=9 r1c3<>9
Discontinuous Nice Loop: 1 r1c4 -1- r1c6 -4- r7c6 =4= r7c7 =6= r7c8 -6- r2c8 -9- r1c9 =9= r1c4 => r1c4<>1
Grouped Discontinuous Nice Loop: 9 r8c1 -9- r3c1 =9= r2c13 -9- r2c8 =9= r789c8 -9- r9c9 -1- r9c2 =1= r8c1 => r8c1<>9
Finned Franken Swordfish: 9 r17b1 c148 fr1c9 fr2c3 => r2c8<>9
Naked Single: r2c8=6
Naked Single: r2c7=8
Hidden Single: r7c7=6
Hidden Single: r8c9=8
Hidden Single: r4c8=8
Hidden Single: r7c6=4
Naked Single: r1c6=1
Hidden Single: r9c7=4
Hidden Single: r8c1=1
Hidden Single: r9c9=1
Hidden Single: r8c7=2
Hidden Single: r2c2=1
Locked Candidates Type 2 (Claiming): 8 in c3 => r5c12,r6c1<>8
Uniqueness Test 4: 1/7 in r5c47,r6c47 => r56c4<>7
Locked Candidates Type 1 (Pointing): 7 in b5 => r8c6<>7
Hidden Single: r8c8=7
Continuous Nice Loop: 2/4/6/9 8= r3c5 =6= r3c6 -6- r4c6 =6= r4c2 -6- r1c2 -8- r1c4 =8= r3c5 =6 => r3c5<>2, r3c5<>4, r6c6<>6, r3c5<>9
Hidden Single: r2c5=4
Locked Candidates Type 1 (Pointing): 9 in b2 => r79c4<>9
Naked Triple: 2,6,8 in r3c256 => r3c1<>2, r3c1<>8
Hidden Single: r7c1=8
Hidden Single: r7c8=9
Full House: r9c8=3
Locked Candidates Type 1 (Pointing): 7 in b7 => r45c2<>7
Locked Candidates Type 1 (Pointing): 9 in b7 => r2c3<>9
Naked Single: r2c3=5
Naked Single: r9c3=9
Naked Single: r8c3=3
Naked Single: r5c3=8
Naked Single: r7c2=7
Full House: r7c4=3
Full House: r9c2=5
Naked Single: r8c6=5
Full House: r8c5=9
Naked Single: r4c2=6
Naked Single: r9c5=2
Full House: r9c4=7
Naked Single: r1c2=8
Naked Single: r4c6=7
Full House: r4c1=5
Naked Single: r6c3=4
Full House: r1c3=6
Naked Single: r5c5=5
Naked Single: r1c4=9
Full House: r1c9=4
Full House: r3c9=9
Naked Single: r3c2=2
Full House: r5c2=3
Naked Single: r6c6=2
Naked Single: r2c4=2
Naked Single: r3c1=4
Full House: r2c1=9
Full House: r2c6=3
Full House: r3c6=6
Full House: r3c5=8
Full House: r6c5=6
Naked Single: r5c4=1
Full House: r6c4=8
Naked Single: r6c1=7
Full House: r5c1=2
Full House: r5c7=7
Full House: r6c7=1
|
sudoku_normal_extremely_hard_117
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
3...7.52.........7..75..31...143.9.2.....9.4..9.....5...2.1...5.4.6.....6....8...
|
386971524915243867427586319561437982238159746794862153872314695143695278659728431
|
3 . . . 7 . 5 2 .
. . . . . . . . 7
. . 7 5 . . 3 1 .
. . 1 4 3 . 9 . 2
. . . . . 9 . 4 .
. 9 . . . . . 5 .
. . 2 . 1 . . . 5
. 4 . 6 . . . . .
6 . . . . 8 . . .
|
3 8 6 9 7 1 5 2 4
9 1 5 2 4 3 8 6 7
4 2 7 5 8 6 3 1 9
5 6 1 4 3 7 9 8 2
2 3 8 1 5 9 7 4 6
7 9 4 8 6 2 1 5 3
8 7 2 3 1 4 6 9 5
1 4 3 6 9 5 2 7 8
6 5 9 7 2 8 4 3 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8206_hard
|
386971524915243867427586319561437982238159746794862153872314695143695278659728431 #1 Extreme (15290) bf
Locked Candidates Type 1 (Pointing): 3 in b6 => r89c9<>3
Brute Force: r5c9=6
Hidden Single: r6c9=3
Locked Candidates Type 1 (Pointing): 6 in b3 => r2c2356<>6
Locked Candidates Type 1 (Pointing): 1 in b6 => r89c7<>1
Skyscraper: 6 in r1c3,r3c5 (connected by r6c35) => r1c6,r3c2<>6
Forcing Net Verity => r2c7<>4
r2c5=4 r2c7<>4
r3c5=4 (r1c6<>4) r3c5<>6 r3c6=6 r4c6<>6 r4c2=6 r1c2<>6 r1c3=6 r1c3<>4 r1c9=4 r2c7<>4
r9c5=4 r7c6<>4 r7c7=4 r2c7<>4
Locked Candidates Type 1 (Pointing): 4 in b3 => r9c9<>4
Hidden Rectangle: 6/8 in r2c78,r7c78 => r7c8<>8
Forcing Net Verity => r2c8<>8
r1c3=8 (r3c1<>8) (r3c2<>8) r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 r3c5=6 r3c5<>8 r3c9=8 r2c8<>8
r2c3=8 r2c8<>8
r5c3=8 (r4c1<>8) r4c2<>8 r4c8=8 r2c8<>8
r6c3=8 (r4c1<>8) r4c2<>8 r4c8=8 r2c8<>8
r8c3=8 (r7c1<>8) r7c2<>8 r7c7=8 (r5c7<>8) r6c7<>8 r4c8=8 r2c8<>8
Forcing Net Contradiction in r8c3 => r1c3<>8
r1c3=8 (r5c3<>8) r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r4c6<>5 r8c6=5 (r8c5<>5) r9c5<>5 r5c5=5 r5c3<>5 r5c3=3 r8c3<>3
r1c3=8 r1c3<>6 r1c2=6 r4c2<>6 r4c6=6 r4c6<>5 r8c6=5 r8c3<>5
r1c3=8 r8c3<>8
r1c3=8 (r3c2<>8 r3c2=2 r3c6<>2) r1c3<>6 (r6c3=6 r6c3<>4 r2c3=4 r2c5<>4 r9c5=4 r9c5<>9) r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 (r3c5=6 r3c5<>9) r3c6=4 r7c6<>4 r7c7=4 r7c7<>6 r7c8=6 r2c8<>6 r2c8=9 r2c5<>9 r8c5=9 r8c3<>9
Forcing Net Contradiction in r7c8 => r1c3<>9
r1c3=9 (r3c1<>9) r1c3<>6 (r6c3=6 r6c3<>4 r6c1=4 r3c1<>4) r1c2=6 r4c2<>6 r4c6=6 r3c6<>6 r3c5=6 (r3c5<>9) (r3c5<>4) r3c5<>9 r3c9=9 r3c9<>4 r3c6=4 r7c6<>4 r7c7=4 r7c7<>6 r7c8=6 r2c8<>6 r2c8=9 r3c9<>9 r3c1=9 r1c3<>9
Discontinuous Nice Loop: 1 r1c4 -1- r1c6 -4- r7c6 =4= r7c7 =6= r7c8 -6- r2c8 -9- r1c9 =9= r1c4 => r1c4<>1
Grouped Discontinuous Nice Loop: 9 r8c1 -9- r3c1 =9= r2c13 -9- r2c8 =9= r789c8 -9- r9c9 -1- r9c2 =1= r8c1 => r8c1<>9
Finned Franken Swordfish: 9 r17b1 c148 fr1c9 fr2c3 => r2c8<>9
Naked Single: r2c8=6
Naked Single: r2c7=8
Hidden Single: r7c7=6
Hidden Single: r8c9=8
Hidden Single: r4c8=8
Hidden Single: r7c6=4
Naked Single: r1c6=1
Hidden Single: r9c7=4
Hidden Single: r8c1=1
Hidden Single: r9c9=1
Hidden Single: r8c7=2
Hidden Single: r2c2=1
Locked Candidates Type 2 (Claiming): 8 in c3 => r5c12,r6c1<>8
Uniqueness Test 4: 1/7 in r5c47,r6c47 => r56c4<>7
Locked Candidates Type 1 (Pointing): 7 in b5 => r8c6<>7
Hidden Single: r8c8=7
Continuous Nice Loop: 2/4/6/9 8= r3c5 =6= r3c6 -6- r4c6 =6= r4c2 -6- r1c2 -8- r1c4 =8= r3c5 =6 => r3c5<>2, r3c5<>4, r6c6<>6, r3c5<>9
Hidden Single: r2c5=4
Locked Candidates Type 1 (Pointing): 9 in b2 => r79c4<>9
Naked Triple: 2,6,8 in r3c256 => r3c1<>2, r3c1<>8
Hidden Single: r7c1=8
Hidden Single: r7c8=9
Full House: r9c8=3
Locked Candidates Type 1 (Pointing): 7 in b7 => r45c2<>7
Locked Candidates Type 1 (Pointing): 9 in b7 => r2c3<>9
Naked Single: r2c3=5
Naked Single: r9c3=9
Naked Single: r8c3=3
Naked Single: r5c3=8
Naked Single: r7c2=7
Full House: r7c4=3
Full House: r9c2=5
Naked Single: r8c6=5
Full House: r8c5=9
Naked Single: r4c2=6
Naked Single: r9c5=2
Full House: r9c4=7
Naked Single: r1c2=8
Naked Single: r4c6=7
Full House: r4c1=5
Naked Single: r6c3=4
Full House: r1c3=6
Naked Single: r5c5=5
Naked Single: r1c4=9
Full House: r1c9=4
Full House: r3c9=9
Naked Single: r3c2=2
Full House: r5c2=3
Naked Single: r6c6=2
Naked Single: r2c4=2
Naked Single: r3c1=4
Full House: r2c1=9
Full House: r2c6=3
Full House: r3c6=6
Full House: r3c5=8
Full House: r6c5=6
Naked Single: r5c4=1
Full House: r6c4=8
Naked Single: r6c1=7
Full House: r5c1=2
Full House: r5c7=7
Full House: r6c7=1
|
sudoku_normal_hard_118
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.6582.....2.1..65...9.65...25.9.1.6..81.562399.628...5..86.....6.25..3.4.1......6
|
165827943824139657739465182253941768481756239976283415348672591692518374517394826
|
. 6 5 8 2 . . . .
. 2 . 1 . . 6 5 .
. . 9 . 6 5 . . .
2 5 . 9 . 1 . 6 .
. 8 1 . 5 6 2 3 9
9 . 6 2 8 . . . 5
. . 8 6 . . . . .
6 . 2 5 . . 3 . 4
. 1 . . . . . . 6
|
1 6 5 8 2 7 9 4 3
8 2 4 1 3 9 6 5 7
7 3 9 4 6 5 1 8 2
2 5 3 9 4 1 7 6 8
4 8 1 7 5 6 2 3 9
9 7 6 2 8 3 4 1 5
3 4 8 6 7 2 5 9 1
6 9 2 5 1 8 3 7 4
5 1 7 3 9 4 8 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7201_hard
|
165827943824139657739465182253941768481756239976283415348672591692518374517394826 #1 Extreme (27050) bf
Hidden Single: r2c8=5
Hidden Single: r3c5=6
Hidden Single: r1c2=6
Hidden Single: r4c1=2
Hidden Single: r5c3=1
Hidden Single: r4c8=6
Hidden Single: r4c2=5
Hidden Single: r8c4=5
Brute Force: r5c9=9
Locked Candidates Type 1 (Pointing): 9 in b3 => r1c6<>9
Brute Force: r5c8=3
Finned Franken Swordfish: 3 c24b5 r367 fr4c5 fr9c4 => r7c5<>3
Sashimi Swordfish: 3 c345 r249 fr3c4 => r2c6<>3
Forcing Net Verity => r1c6<>3
r3c4=3 r1c6<>3
r3c4=4 (r3c4<>3 r9c4=3 r9c5<>3) (r3c4<>3 r9c4=3 r9c3<>3) (r2c5<>4) (r2c6<>4) r5c4<>4 r5c1=4 r2c1<>4 r2c3=4 r2c3<>3 r4c3=3 r4c5<>3 r2c5=3 r1c6<>3
r3c4=7 (r3c4<>3 r9c4=3 r9c5<>3) (r3c4<>3 r9c4=3 r9c3<>3) (r3c1<>7) (r3c2<>7) r5c4<>7 r5c1=7 (r1c1<>7) r2c1<>7 r2c3=7 r2c3<>3 r4c3=3 r4c5<>3 r2c5=3 r1c6<>3
Forcing Net Verity => r2c6=9
r9c4=3 r3c4<>3 r2c5=3 r2c5<>9 r2c6=9
r9c4=4 (r9c4<>3) (r9c4<>3 r3c4=3 r2c5<>3) (r7c5<>4) (r9c5<>4) (r9c3<>4) r5c4<>4 r5c1=4 r4c3<>4 r2c3=4 r2c5<>4 r4c5=4 (r6c6<>4 r6c6=3 r9c6<>3) r4c5<>3 r9c5=3 r9c1<>3 r9c3=3 (r7c1<>3) r7c2<>3 r7c6=3 (r7c6<>9) r7c6<>2 r9c6=2 (r9c6<>9) r9c6<>8 r8c6=8 r8c6<>9 r2c6=9
r9c4=7 (r9c4<>3 r3c4=3 r3c2<>3) (r9c3<>7) r5c4<>7 (r5c4=4 r6c6<>4) (r5c4=4 r5c1<>4) r5c1=7 (r6c2<>7) r4c3<>7 r2c3=7 (r2c3<>4) r3c2<>7 r3c2=4 r6c2<>4 r4c3=4 r4c3<>3 r4c5=3 r6c6<>3 r6c6=7 (r6c7<>7) r1c6<>7 r1c6=4 r2c6<>4 r2c1=4 (r2c6<>4) (r2c5<>4) r2c1<>8 r2c9=8 r4c9<>8 r4c9=7 r6c8<>7 r6c6=7 (r6c7<>7) r2c6<>7 r2c6=9
Forcing Net Verity => r2c1=8
r4c3=4 (r5c1<>4 r5c4=4 r9c4<>4) r4c3<>3 r4c5=3 r2c5<>3 r3c4=3 r9c4<>3 r9c4=7 (r7c5<>7) (r8c5<>7) (r9c5<>7) (r9c3<>7) r5c4<>7 r5c1=7 r4c3<>7 r2c3=7 r2c5<>7 r4c5=7 r4c9<>7 r4c9=8 r2c9<>8 r2c1=8
r4c5=4 (r9c5<>4) (r2c5<>4) (r4c5<>3 r4c3=3 r6c2<>3 r6c2=7 r3c2<>7) (r2c5<>4) r5c4<>4 (r5c4=7 r3c4<>7) r5c1=4 (r6c2<>4 r7c2=4 r7c6<>4 r7c6=2 r9c6<>2 r9c8=2 r9c8<>8) (r9c1<>4) r2c1<>4 r2c3=4 r3c2<>4 r3c2=3 r3c4<>3 r3c4=4 (r9c4<>4) r5c4<>4 (r5c4=7 r3c4<>7) r5c1=4 (r6c2<>4 r7c2=4 r7c6<>4 r7c6=2 r9c6<>2 r9c8=2 r9c8<>8) (r9c1<>4) r2c1<>4 r2c3=4 r9c3<>4 r9c6=4 r9c6<>8 r8c6=8 r8c8<>8 r3c8=8 r2c9<>8 r2c1=8
r4c7=4 r4c7<>8 r4c9=8 r2c9<>8 r2c1=8
Forcing Chain Contradiction in b2 => r1c1<>7
r1c1=7 r1c6<>7
r1c1=7 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c5<>7
r1c1=7 r5c1<>7 r5c4=7 r3c4<>7
Grouped Discontinuous Nice Loop: 7 r3c4 -7- r1c6 =7= r1c789 -7- r2c9 -3- r2c5 =3= r3c4 => r3c4<>7
Forcing Chain Contradiction in c3 => r1c1<>4
r1c1=4 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c3<>7
r1c1=4 r5c1<>4 r5c1=7 r4c3<>7
r1c1=4 r5c1<>4 r5c1=7 r5c4<>7 r9c4=7 r9c3<>7
Forcing Chain Contradiction in c3 => r3c1<>4
r3c1=4 r3c1<>1 r1c1=1 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c3<>7
r3c1=4 r5c1<>4 r5c1=7 r4c3<>7
r3c1=4 r5c1<>4 r5c1=7 r5c4<>7 r9c4=7 r9c3<>7
Finned Franken Swordfish: 4 c14b1 r359 fr2c3 fr7c1 => r9c3<>4
Discontinuous Nice Loop: 3 r2c3 -3- r9c3 -7- r9c4 =7= r5c4 =4= r5c1 -4- r4c3 =4= r2c3 => r2c3<>3
2-String Kite: 3 in r6c6,r9c3 (connected by r4c3,r6c2) => r9c6<>3
Empty Rectangle: 3 in b1 (r39c4) => r9c1<>3
Discontinuous Nice Loop: 7 r4c5 -7- r5c4 =7= r9c4 -7- r9c3 -3- r4c3 =3= r4c5 => r4c5<>7
AIC: 4/7 4- r2c3 =4= r4c3 -4- r5c1 -7- r5c4 =7= r6c6 -7- r1c6 =7= r2c5 -7 => r2c5<>4, r2c3<>7
Naked Single: r2c3=4
Locked Candidates Type 1 (Pointing): 7 in b1 => r3c789<>7
Skyscraper: 7 in r4c3,r5c4 (connected by r9c34) => r5c1<>7
Naked Single: r5c1=4
Full House: r5c4=7
Hidden Single: r7c2=4
Hidden Single: r8c2=9
2-String Kite: 3 in r3c4,r7c1 (connected by r7c6,r9c4) => r3c1<>3
W-Wing: 7/3 in r2c5,r9c3 connected by 3 in r4c35 => r9c5<>7
W-Wing: 4/3 in r3c4,r6c6 connected by 3 in r36c2 => r1c6<>4
Naked Single: r1c6=7
Naked Single: r2c5=3
Full House: r2c9=7
Full House: r3c4=4
Full House: r9c4=3
Naked Single: r8c6=8
Naked Single: r4c5=4
Full House: r6c6=3
Naked Single: r4c9=8
Naked Single: r7c6=2
Full House: r9c6=4
Naked Single: r9c3=7
Full House: r4c3=3
Full House: r6c2=7
Full House: r4c7=7
Full House: r3c2=3
Naked Single: r9c5=9
Naked Single: r7c9=1
Naked Single: r9c1=5
Full House: r7c1=3
Naked Single: r1c1=1
Full House: r3c1=7
Naked Single: r1c9=3
Full House: r3c9=2
Naked Single: r7c5=7
Full House: r8c5=1
Full House: r8c8=7
Naked Single: r9c7=8
Full House: r9c8=2
Naked Single: r7c8=9
Full House: r7c7=5
Naked Single: r3c7=1
Full House: r3c8=8
Naked Single: r1c8=4
Full House: r1c7=9
Full House: r6c7=4
Full House: r6c8=1
|
sudoku_normal_extremely_hard_118
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..582.....2.1..6....9..5......9.1....8..562..9.628...5..86.....6.2...3.4.1......6
|
165827943824139657739465182253941768481756239976283415348672591692518374517394826
|
. . 5 8 2 . . . .
. 2 . 1 . . 6 . .
. . 9 . . 5 . . .
. . . 9 . 1 . . .
. 8 . . 5 6 2 . .
9 . 6 2 8 . . . 5
. . 8 6 . . . . .
6 . 2 . . . 3 . 4
. 1 . . . . . . 6
|
1 6 5 8 2 7 9 4 3
8 2 4 1 3 9 6 5 7
7 3 9 4 6 5 1 8 2
2 5 3 9 4 1 7 6 8
4 8 1 7 5 6 2 3 9
9 7 6 2 8 3 4 1 5
3 4 8 6 7 2 5 9 1
6 9 2 5 1 8 3 7 4
5 1 7 3 9 4 8 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7201_hard
|
165827943824139657739465182253941768481756239976283415348672591692518374517394826 #1 Extreme (27050) bf
Hidden Single: r2c8=5
Hidden Single: r3c5=6
Hidden Single: r1c2=6
Hidden Single: r4c1=2
Hidden Single: r5c3=1
Hidden Single: r4c8=6
Hidden Single: r4c2=5
Hidden Single: r8c4=5
Brute Force: r5c9=9
Locked Candidates Type 1 (Pointing): 9 in b3 => r1c6<>9
Brute Force: r5c8=3
Finned Franken Swordfish: 3 c24b5 r367 fr4c5 fr9c4 => r7c5<>3
Sashimi Swordfish: 3 c345 r249 fr3c4 => r2c6<>3
Forcing Net Verity => r1c6<>3
r3c4=3 r1c6<>3
r3c4=4 (r3c4<>3 r9c4=3 r9c5<>3) (r3c4<>3 r9c4=3 r9c3<>3) (r2c5<>4) (r2c6<>4) r5c4<>4 r5c1=4 r2c1<>4 r2c3=4 r2c3<>3 r4c3=3 r4c5<>3 r2c5=3 r1c6<>3
r3c4=7 (r3c4<>3 r9c4=3 r9c5<>3) (r3c4<>3 r9c4=3 r9c3<>3) (r3c1<>7) (r3c2<>7) r5c4<>7 r5c1=7 (r1c1<>7) r2c1<>7 r2c3=7 r2c3<>3 r4c3=3 r4c5<>3 r2c5=3 r1c6<>3
Forcing Net Verity => r2c6=9
r9c4=3 r3c4<>3 r2c5=3 r2c5<>9 r2c6=9
r9c4=4 (r9c4<>3) (r9c4<>3 r3c4=3 r2c5<>3) (r7c5<>4) (r9c5<>4) (r9c3<>4) r5c4<>4 r5c1=4 r4c3<>4 r2c3=4 r2c5<>4 r4c5=4 (r6c6<>4 r6c6=3 r9c6<>3) r4c5<>3 r9c5=3 r9c1<>3 r9c3=3 (r7c1<>3) r7c2<>3 r7c6=3 (r7c6<>9) r7c6<>2 r9c6=2 (r9c6<>9) r9c6<>8 r8c6=8 r8c6<>9 r2c6=9
r9c4=7 (r9c4<>3 r3c4=3 r3c2<>3) (r9c3<>7) r5c4<>7 (r5c4=4 r6c6<>4) (r5c4=4 r5c1<>4) r5c1=7 (r6c2<>7) r4c3<>7 r2c3=7 (r2c3<>4) r3c2<>7 r3c2=4 r6c2<>4 r4c3=4 r4c3<>3 r4c5=3 r6c6<>3 r6c6=7 (r6c7<>7) r1c6<>7 r1c6=4 r2c6<>4 r2c1=4 (r2c6<>4) (r2c5<>4) r2c1<>8 r2c9=8 r4c9<>8 r4c9=7 r6c8<>7 r6c6=7 (r6c7<>7) r2c6<>7 r2c6=9
Forcing Net Verity => r2c1=8
r4c3=4 (r5c1<>4 r5c4=4 r9c4<>4) r4c3<>3 r4c5=3 r2c5<>3 r3c4=3 r9c4<>3 r9c4=7 (r7c5<>7) (r8c5<>7) (r9c5<>7) (r9c3<>7) r5c4<>7 r5c1=7 r4c3<>7 r2c3=7 r2c5<>7 r4c5=7 r4c9<>7 r4c9=8 r2c9<>8 r2c1=8
r4c5=4 (r9c5<>4) (r2c5<>4) (r4c5<>3 r4c3=3 r6c2<>3 r6c2=7 r3c2<>7) (r2c5<>4) r5c4<>4 (r5c4=7 r3c4<>7) r5c1=4 (r6c2<>4 r7c2=4 r7c6<>4 r7c6=2 r9c6<>2 r9c8=2 r9c8<>8) (r9c1<>4) r2c1<>4 r2c3=4 r3c2<>4 r3c2=3 r3c4<>3 r3c4=4 (r9c4<>4) r5c4<>4 (r5c4=7 r3c4<>7) r5c1=4 (r6c2<>4 r7c2=4 r7c6<>4 r7c6=2 r9c6<>2 r9c8=2 r9c8<>8) (r9c1<>4) r2c1<>4 r2c3=4 r9c3<>4 r9c6=4 r9c6<>8 r8c6=8 r8c8<>8 r3c8=8 r2c9<>8 r2c1=8
r4c7=4 r4c7<>8 r4c9=8 r2c9<>8 r2c1=8
Forcing Chain Contradiction in b2 => r1c1<>7
r1c1=7 r1c6<>7
r1c1=7 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c5<>7
r1c1=7 r5c1<>7 r5c4=7 r3c4<>7
Grouped Discontinuous Nice Loop: 7 r3c4 -7- r1c6 =7= r1c789 -7- r2c9 -3- r2c5 =3= r3c4 => r3c4<>7
Forcing Chain Contradiction in c3 => r1c1<>4
r1c1=4 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c3<>7
r1c1=4 r5c1<>4 r5c1=7 r4c3<>7
r1c1=4 r5c1<>4 r5c1=7 r5c4<>7 r9c4=7 r9c3<>7
Forcing Chain Contradiction in c3 => r3c1<>4
r3c1=4 r3c1<>1 r1c1=1 r1c1<>3 r1c9=3 r2c9<>3 r2c9=7 r2c3<>7
r3c1=4 r5c1<>4 r5c1=7 r4c3<>7
r3c1=4 r5c1<>4 r5c1=7 r5c4<>7 r9c4=7 r9c3<>7
Finned Franken Swordfish: 4 c14b1 r359 fr2c3 fr7c1 => r9c3<>4
Discontinuous Nice Loop: 3 r2c3 -3- r9c3 -7- r9c4 =7= r5c4 =4= r5c1 -4- r4c3 =4= r2c3 => r2c3<>3
2-String Kite: 3 in r6c6,r9c3 (connected by r4c3,r6c2) => r9c6<>3
Empty Rectangle: 3 in b1 (r39c4) => r9c1<>3
Discontinuous Nice Loop: 7 r4c5 -7- r5c4 =7= r9c4 -7- r9c3 -3- r4c3 =3= r4c5 => r4c5<>7
AIC: 4/7 4- r2c3 =4= r4c3 -4- r5c1 -7- r5c4 =7= r6c6 -7- r1c6 =7= r2c5 -7 => r2c5<>4, r2c3<>7
Naked Single: r2c3=4
Locked Candidates Type 1 (Pointing): 7 in b1 => r3c789<>7
Skyscraper: 7 in r4c3,r5c4 (connected by r9c34) => r5c1<>7
Naked Single: r5c1=4
Full House: r5c4=7
Hidden Single: r7c2=4
Hidden Single: r8c2=9
2-String Kite: 3 in r3c4,r7c1 (connected by r7c6,r9c4) => r3c1<>3
W-Wing: 7/3 in r2c5,r9c3 connected by 3 in r4c35 => r9c5<>7
W-Wing: 4/3 in r3c4,r6c6 connected by 3 in r36c2 => r1c6<>4
Naked Single: r1c6=7
Naked Single: r2c5=3
Full House: r2c9=7
Full House: r3c4=4
Full House: r9c4=3
Naked Single: r8c6=8
Naked Single: r4c5=4
Full House: r6c6=3
Naked Single: r4c9=8
Naked Single: r7c6=2
Full House: r9c6=4
Naked Single: r9c3=7
Full House: r4c3=3
Full House: r6c2=7
Full House: r4c7=7
Full House: r3c2=3
Naked Single: r9c5=9
Naked Single: r7c9=1
Naked Single: r9c1=5
Full House: r7c1=3
Naked Single: r1c1=1
Full House: r3c1=7
Naked Single: r1c9=3
Full House: r3c9=2
Naked Single: r7c5=7
Full House: r8c5=1
Full House: r8c8=7
Naked Single: r9c7=8
Full House: r9c8=2
Naked Single: r7c8=9
Full House: r7c7=5
Naked Single: r3c7=1
Full House: r3c8=8
Naked Single: r1c8=4
Full House: r1c7=9
Full House: r6c7=4
Full House: r6c8=1
|
sudoku_normal_hard_119
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.5..4..7...7..94..8.47.52....61.4....4.976.3..7..5264.7...2.3.4.2.4.....4..5.7.2.
|
652843179317269485894715263236184597145976832978352641789621354523498716461537928
|
. 5 . . 4 . . 7 .
. . 7 . . 9 4 . .
8 . 4 7 . 5 2 . .
. . 6 1 . 4 . . .
. 4 . 9 7 6 . 3 .
. 7 . . 5 2 6 4 .
7 . . . 2 . 3 . 4
. 2 . 4 . . . . .
4 . . 5 . 7 . 2 .
|
6 5 2 8 4 3 1 7 9
3 1 7 2 6 9 4 8 5
8 9 4 7 1 5 2 6 3
2 3 6 1 8 4 5 9 7
1 4 5 9 7 6 8 3 2
9 7 8 3 5 2 6 4 1
7 8 9 6 2 1 3 5 4
5 2 3 4 9 8 7 1 6
4 6 1 5 3 7 9 2 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4880_hard
|
652843179317269485894715263236184597145976832978352641789621354523498716461537928 #1 Extreme (20230) bf
Hidden Single: r6c8=4
Hidden Single: r4c6=4
Hidden Single: r3c6=5
Hidden Single: r3c4=7
Hidden Single: r7c1=7
Hidden Single: r3c3=4
Hidden Single: r2c7=4
Hidden Single: r9c1=4
Almost Locked Set XZ-Rule: A=r4c258 {3589}, B=r159c7 {1589}, X=5, Z=8,9 => r4c7<>8, r4c7<>9
Hidden Rectangle: 5/7 in r4c79,r8c79 => r8c9<>5
Forcing Chain Contradiction in c3 => r8c1<>3
r8c1=3 r8c6<>3 r1c6=3 r1c3<>3
r8c1=3 r8c6<>3 r1c6=3 r12c4<>3 r6c4=3 r6c3<>3
r8c1=3 r8c3<>3
r8c1=3 r9c3<>3
Brute Force: r5c4=9
Hidden Single: r5c6=6
Grouped Discontinuous Nice Loop: 9 r9c2 -9- r3c2 =9= r1c13 -9- r1c7 =9= r89c7 -9- r7c8 =9= r7c23 -9- r9c2 => r9c2<>9
Forcing Net Verity => r2c9<>1
r4c8=8 (r4c2<>8) r4c5<>8 r4c5=3 r4c2<>3 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9 r7c3<>5 r7c8=5 r2c8<>5 r2c9=5 r2c9<>1
r4c9=8 (r4c9<>5) (r5c9<>8 r5c3=8 r5c3<>2) r4c9<>2 r4c1=2 r5c1<>2 r5c9=2 r5c9<>5 r2c9=5 r2c9<>1
r5c7=8 r5c7<>1 r56c9=1 r2c9<>1
r5c9=8 (r5c9<>5) r5c9<>2 r4c9=2 r4c9<>5 r2c9=5 r2c9<>1
r6c9=8 (r2c9<>8) (r5c7<>8) r5c9<>8 r5c3=8 (r4c2<>8 r4c5=8 r2c5<>8) r5c3<>2 r1c3=2 r2c1<>2 r2c4=2 r2c4<>8 r2c8=8 r2c8<>5 r2c9=5 r2c9<>1
Forcing Net Contradiction in r7c3 => r4c1<>3
r4c1=3 (r4c2<>3) r4c5<>3 r4c5=8 (r4c8<>8) r4c2<>8 r4c2=9 r4c8<>9 r4c8=5 r7c8<>5 r7c3=5
r4c1=3 (r4c2<>3) r4c5<>3 r4c5=8 r4c2<>8 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9
Forcing Net Contradiction in r1 => r1c3<>3
r1c3=3 (r1c6<>3 r8c6=3 r9c5<>3 r9c2=3 r9c2<>6) (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r7c2<>6 r8c1=6 r1c1<>6
r1c3=3 (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r1c4<>6
r1c3=3 (r1c6<>3 r8c6=3 r9c5<>3 r9c2=3 r9c2<>6) (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r9c5<>6 r9c9=6 r1c9<>6
Forcing Net Contradiction in r9 => r2c4<>8
r2c4=8 (r6c4<>8 r6c4=3 r6c1<>3) r2c4<>2 r2c1=2 (r2c1<>6) r2c1<>3 r1c1=3 r1c1<>6 r8c1=6 r9c2<>6
r2c4=8 r7c4<>8 r7c4=6 r9c5<>6
r2c4=8 (r7c4<>8 r7c4=6 r1c4<>6) (r6c4<>8 r6c4=3 r6c1<>3) r2c4<>2 r2c1=2 r2c1<>3 r1c1=3 r1c1<>6 r1c9=6 r9c9<>6
Forcing Net Contradiction in r7c3 => r4c9<>8
r4c9=8 (r4c9<>2 r4c1=2 r4c1<>5) (r4c9<>5) r4c9<>7 r4c7=7 r4c7<>5 r4c8=5 r7c8<>5 r7c3=5
r4c9=8 (r4c2<>8) r4c5<>8 r4c5=3 r4c2<>3 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9
Forcing Net Contradiction in r1 => r6c3<>3
r6c3=3 (r4c2<>3 r4c5=3 r9c5<>3 r9c2=3 r9c2<>6) r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r7c2<>6 r8c1=6 r1c1<>6
r6c3=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r1c4<>6
r6c3=3 (r4c2<>3 r4c5=3 r9c5<>3 r9c2=3 r9c2<>6) r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r9c5<>6 r9c9=6 r1c9<>6
Locked Candidates Type 2 (Claiming): 3 in c3 => r9c2<>3
Grouped Discontinuous Nice Loop: 8 r9c3 -8- r79c2 =8= r4c2 =3= r4c5 -3- r9c5 =3= r9c3 => r9c3<>8
Forcing Net Contradiction in r1 => r7c3<>8
r7c3=8 (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r1c7<>9) (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r1c9<>9) (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r6c9<>9) (r7c2<>8) r9c2<>8 r4c2=8 r4c5<>8 r4c5=3 r6c4<>3 r6c1=3 r6c1<>9 r6c3=9 r1c3<>9 r1c1=9 r1c1<>6
r7c3=8 r7c4<>8 r7c4=6 r1c4<>6
r7c3=8 (r7c6<>8 r7c6=1 r7c2<>1 r7c2=9 r3c2<>9) (r9c2<>8 r4c2=8 r4c8<>8) r7c3<>5 r7c8=5 (r2c8<>5 r2c9=5 r2c9<>3) r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r3c9<>3 r1c9=3 r1c9<>6
Forcing Net Contradiction in r1 => r8c5<>6
r8c5=6 (r7c4<>6) (r9c5<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c2<>6 r9c9=6 r7c8<>6 r7c2=6 (r2c2<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r6c4=3 r4c5<>3 r4c2=3 r2c2<>3 r2c2=1 r1c1<>1
r8c5=6 (r7c4<>6) (r9c5<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c2<>6 r9c9=6 r7c8<>6 r7c2=6 (r2c2<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r6c4=3 r4c5<>3 r4c2=3 r2c2<>3 r2c2=1 r1c3<>1
r8c5=6 r7c4<>6 r7c4=8 r7c6<>8 r7c6=1 r1c6<>1
r8c5=6 (r8c5<>9 r9c5=9 r9c7<>9) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c7<>8 r9c7=1 r1c7<>1
r8c5=6 (r8c5<>9 r9c5=9 r9c7<>9) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c7<>8 r9c7=1 r5c7<>1 r56c9=1 r1c9<>1
Finned Franken Swordfish: 6 r18b8 c149 fr8c8 fr9c5 => r9c9<>6
Forcing Chain Contradiction in c2 => r8c6<>1
r8c6=1 r8c6<>3 r89c5=3 r4c5<>3 r4c5=8 r4c2<>8
r8c6=1 r7c6<>1 r7c6=8 r7c2<>8
r8c6=1 r7c6<>1 r7c6=8 r7c4<>8 r7c4=6 r9c5<>6 r9c2=6 r9c2<>8
Forcing Chain Contradiction in c2 => r9c2<>1
r9c2=1 r9c2<>6 r9c5=6 r7c4<>6 r7c4=8 r6c4<>8 r4c5=8 r4c2<>8
r9c2=1 r9c2<>6 r9c5=6 r7c4<>6 r7c4=8 r7c2<>8
r9c2=1 r9c2<>8
Sashimi X-Wing: 1 c26 r17 fr2c2 fr3c2 => r1c13<>1
Forcing Chain Verity => r7c4=6
r9c3=1 r9c3<>3 r9c5=3 r9c5<>6 r7c4=6
r9c5=1 r9c5<>6 r7c4=6
r9c7=1 r78c8<>1 r23c8=1 r1c79<>1 r1c6=1 r1c6<>8 r78c6=8 r7c4<>8 r7c4=6
r9c9=1 r78c8<>1 r23c8=1 r1c79<>1 r1c6=1 r1c6<>8 r78c6=8 r7c4<>8 r7c4=6
Hidden Single: r9c2=6
Finned Franken Swordfish: 8 r49b7 c258 fr8c3 fr9c7 fr9c9 => r8c8<>8
Finned Swordfish: 8 c258 r247 fr8c5 fr9c5 => r7c6<>8
Naked Single: r7c6=1
Locked Candidates Type 2 (Claiming): 1 in r1 => r23c8,r3c9<>1
Hidden Single: r8c8=1
Hidden Single: r9c3=1
Hidden Single: r8c9=6
Hidden Single: r9c5=3
Naked Single: r4c5=8
Full House: r6c4=3
Naked Single: r8c6=8
Full House: r8c5=9
Full House: r1c6=3
Naked Single: r2c4=2
Full House: r1c4=8
Naked Single: r8c1=5
Naked Single: r7c3=9
Naked Single: r8c3=3
Full House: r8c7=7
Full House: r7c2=8
Full House: r7c8=5
Naked Single: r1c3=2
Naked Single: r6c3=8
Full House: r5c3=5
Naked Single: r4c7=5
Naked Single: r4c8=9
Naked Single: r3c8=6
Full House: r2c8=8
Naked Single: r4c1=2
Naked Single: r4c2=3
Full House: r4c9=7
Naked Single: r6c9=1
Full House: r6c1=9
Full House: r5c1=1
Naked Single: r3c5=1
Full House: r2c5=6
Naked Single: r2c2=1
Full House: r3c2=9
Full House: r3c9=3
Naked Single: r1c9=9
Naked Single: r5c7=8
Full House: r5c9=2
Naked Single: r1c1=6
Full House: r2c1=3
Full House: r2c9=5
Full House: r1c7=1
Full House: r9c9=8
Full House: r9c7=9
|
sudoku_normal_extremely_hard_119
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.5..4..7...7..9...8.....2....61......4..7..3..7..526......2.3.4.2.4........5.7.2.
|
652843179317269485894715263236184597145976832978352641789621354523498716461537928
|
. 5 . . 4 . . 7 .
. . 7 . . 9 . . .
8 . . . . . 2 . .
. . 6 1 . . . . .
. 4 . . 7 . . 3 .
. 7 . . 5 2 6 . .
. . . . 2 . 3 . 4
. 2 . 4 . . . . .
. . . 5 . 7 . 2 .
|
6 5 2 8 4 3 1 7 9
3 1 7 2 6 9 4 8 5
8 9 4 7 1 5 2 6 3
2 3 6 1 8 4 5 9 7
1 4 5 9 7 6 8 3 2
9 7 8 3 5 2 6 4 1
7 8 9 6 2 1 3 5 4
5 2 3 4 9 8 7 1 6
4 6 1 5 3 7 9 2 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4880_hard
|
652843179317269485894715263236184597145976832978352641789621354523498716461537928 #1 Extreme (20230) bf
Hidden Single: r6c8=4
Hidden Single: r4c6=4
Hidden Single: r3c6=5
Hidden Single: r3c4=7
Hidden Single: r7c1=7
Hidden Single: r3c3=4
Hidden Single: r2c7=4
Hidden Single: r9c1=4
Almost Locked Set XZ-Rule: A=r4c258 {3589}, B=r159c7 {1589}, X=5, Z=8,9 => r4c7<>8, r4c7<>9
Hidden Rectangle: 5/7 in r4c79,r8c79 => r8c9<>5
Forcing Chain Contradiction in c3 => r8c1<>3
r8c1=3 r8c6<>3 r1c6=3 r1c3<>3
r8c1=3 r8c6<>3 r1c6=3 r12c4<>3 r6c4=3 r6c3<>3
r8c1=3 r8c3<>3
r8c1=3 r9c3<>3
Brute Force: r5c4=9
Hidden Single: r5c6=6
Grouped Discontinuous Nice Loop: 9 r9c2 -9- r3c2 =9= r1c13 -9- r1c7 =9= r89c7 -9- r7c8 =9= r7c23 -9- r9c2 => r9c2<>9
Forcing Net Verity => r2c9<>1
r4c8=8 (r4c2<>8) r4c5<>8 r4c5=3 r4c2<>3 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9 r7c3<>5 r7c8=5 r2c8<>5 r2c9=5 r2c9<>1
r4c9=8 (r4c9<>5) (r5c9<>8 r5c3=8 r5c3<>2) r4c9<>2 r4c1=2 r5c1<>2 r5c9=2 r5c9<>5 r2c9=5 r2c9<>1
r5c7=8 r5c7<>1 r56c9=1 r2c9<>1
r5c9=8 (r5c9<>5) r5c9<>2 r4c9=2 r4c9<>5 r2c9=5 r2c9<>1
r6c9=8 (r2c9<>8) (r5c7<>8) r5c9<>8 r5c3=8 (r4c2<>8 r4c5=8 r2c5<>8) r5c3<>2 r1c3=2 r2c1<>2 r2c4=2 r2c4<>8 r2c8=8 r2c8<>5 r2c9=5 r2c9<>1
Forcing Net Contradiction in r7c3 => r4c1<>3
r4c1=3 (r4c2<>3) r4c5<>3 r4c5=8 (r4c8<>8) r4c2<>8 r4c2=9 r4c8<>9 r4c8=5 r7c8<>5 r7c3=5
r4c1=3 (r4c2<>3) r4c5<>3 r4c5=8 r4c2<>8 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9
Forcing Net Contradiction in r1 => r1c3<>3
r1c3=3 (r1c6<>3 r8c6=3 r9c5<>3 r9c2=3 r9c2<>6) (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r7c2<>6 r8c1=6 r1c1<>6
r1c3=3 (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r1c4<>6
r1c3=3 (r1c6<>3 r8c6=3 r9c5<>3 r9c2=3 r9c2<>6) (r1c1<>3) r2c1<>3 r6c1=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r9c5<>6 r9c9=6 r1c9<>6
Forcing Net Contradiction in r9 => r2c4<>8
r2c4=8 (r6c4<>8 r6c4=3 r6c1<>3) r2c4<>2 r2c1=2 (r2c1<>6) r2c1<>3 r1c1=3 r1c1<>6 r8c1=6 r9c2<>6
r2c4=8 r7c4<>8 r7c4=6 r9c5<>6
r2c4=8 (r7c4<>8 r7c4=6 r1c4<>6) (r6c4<>8 r6c4=3 r6c1<>3) r2c4<>2 r2c1=2 r2c1<>3 r1c1=3 r1c1<>6 r1c9=6 r9c9<>6
Forcing Net Contradiction in r7c3 => r4c9<>8
r4c9=8 (r4c9<>2 r4c1=2 r4c1<>5) (r4c9<>5) r4c9<>7 r4c7=7 r4c7<>5 r4c8=5 r7c8<>5 r7c3=5
r4c9=8 (r4c2<>8) r4c5<>8 r4c5=3 r4c2<>3 r4c2=9 (r7c2<>9) (r3c2<>9) (r6c1<>9) r6c3<>9 r6c9=9 r3c9<>9 r3c8=9 r7c8<>9 r7c3=9
Forcing Net Contradiction in r1 => r6c3<>3
r6c3=3 (r4c2<>3 r4c5=3 r9c5<>3 r9c2=3 r9c2<>6) r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r7c2<>6 r8c1=6 r1c1<>6
r6c3=3 r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r1c4<>6
r6c3=3 (r4c2<>3 r4c5=3 r9c5<>3 r9c2=3 r9c2<>6) r6c4<>3 r6c4=8 r7c4<>8 r7c4=6 r9c5<>6 r9c9=6 r1c9<>6
Locked Candidates Type 2 (Claiming): 3 in c3 => r9c2<>3
Grouped Discontinuous Nice Loop: 8 r9c3 -8- r79c2 =8= r4c2 =3= r4c5 -3- r9c5 =3= r9c3 => r9c3<>8
Forcing Net Contradiction in r1 => r7c3<>8
r7c3=8 (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r1c7<>9) (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r1c9<>9) (r7c3<>5 r7c8=5 r4c8<>5 r4c8=9 r6c9<>9) (r7c2<>8) r9c2<>8 r4c2=8 r4c5<>8 r4c5=3 r6c4<>3 r6c1=3 r6c1<>9 r6c3=9 r1c3<>9 r1c1=9 r1c1<>6
r7c3=8 r7c4<>8 r7c4=6 r1c4<>6
r7c3=8 (r7c6<>8 r7c6=1 r7c2<>1 r7c2=9 r3c2<>9) (r9c2<>8 r4c2=8 r4c8<>8) r7c3<>5 r7c8=5 (r2c8<>5 r2c9=5 r2c9<>3) r4c8<>5 r4c8=9 r3c8<>9 r3c9=9 r3c9<>3 r1c9=3 r1c9<>6
Forcing Net Contradiction in r1 => r8c5<>6
r8c5=6 (r7c4<>6) (r9c5<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c2<>6 r9c9=6 r7c8<>6 r7c2=6 (r2c2<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r6c4=3 r4c5<>3 r4c2=3 r2c2<>3 r2c2=1 r1c1<>1
r8c5=6 (r7c4<>6) (r9c5<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c2<>6 r9c9=6 r7c8<>6 r7c2=6 (r2c2<>6) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r6c4=3 r4c5<>3 r4c2=3 r2c2<>3 r2c2=1 r1c3<>1
r8c5=6 r7c4<>6 r7c4=8 r7c6<>8 r7c6=1 r1c6<>1
r8c5=6 (r8c5<>9 r9c5=9 r9c7<>9) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c7<>8 r9c7=1 r1c7<>1
r8c5=6 (r8c5<>9 r9c5=9 r9c7<>9) r7c4<>6 r7c4=8 (r7c2<>8) r6c4<>8 r4c5=8 r4c2<>8 r9c2=8 r9c7<>8 r9c7=1 r5c7<>1 r56c9=1 r1c9<>1
Finned Franken Swordfish: 6 r18b8 c149 fr8c8 fr9c5 => r9c9<>6
Forcing Chain Contradiction in c2 => r8c6<>1
r8c6=1 r8c6<>3 r89c5=3 r4c5<>3 r4c5=8 r4c2<>8
r8c6=1 r7c6<>1 r7c6=8 r7c2<>8
r8c6=1 r7c6<>1 r7c6=8 r7c4<>8 r7c4=6 r9c5<>6 r9c2=6 r9c2<>8
Forcing Chain Contradiction in c2 => r9c2<>1
r9c2=1 r9c2<>6 r9c5=6 r7c4<>6 r7c4=8 r6c4<>8 r4c5=8 r4c2<>8
r9c2=1 r9c2<>6 r9c5=6 r7c4<>6 r7c4=8 r7c2<>8
r9c2=1 r9c2<>8
Sashimi X-Wing: 1 c26 r17 fr2c2 fr3c2 => r1c13<>1
Forcing Chain Verity => r7c4=6
r9c3=1 r9c3<>3 r9c5=3 r9c5<>6 r7c4=6
r9c5=1 r9c5<>6 r7c4=6
r9c7=1 r78c8<>1 r23c8=1 r1c79<>1 r1c6=1 r1c6<>8 r78c6=8 r7c4<>8 r7c4=6
r9c9=1 r78c8<>1 r23c8=1 r1c79<>1 r1c6=1 r1c6<>8 r78c6=8 r7c4<>8 r7c4=6
Hidden Single: r9c2=6
Finned Franken Swordfish: 8 r49b7 c258 fr8c3 fr9c7 fr9c9 => r8c8<>8
Finned Swordfish: 8 c258 r247 fr8c5 fr9c5 => r7c6<>8
Naked Single: r7c6=1
Locked Candidates Type 2 (Claiming): 1 in r1 => r23c8,r3c9<>1
Hidden Single: r8c8=1
Hidden Single: r9c3=1
Hidden Single: r8c9=6
Hidden Single: r9c5=3
Naked Single: r4c5=8
Full House: r6c4=3
Naked Single: r8c6=8
Full House: r8c5=9
Full House: r1c6=3
Naked Single: r2c4=2
Full House: r1c4=8
Naked Single: r8c1=5
Naked Single: r7c3=9
Naked Single: r8c3=3
Full House: r8c7=7
Full House: r7c2=8
Full House: r7c8=5
Naked Single: r1c3=2
Naked Single: r6c3=8
Full House: r5c3=5
Naked Single: r4c7=5
Naked Single: r4c8=9
Naked Single: r3c8=6
Full House: r2c8=8
Naked Single: r4c1=2
Naked Single: r4c2=3
Full House: r4c9=7
Naked Single: r6c9=1
Full House: r6c1=9
Full House: r5c1=1
Naked Single: r3c5=1
Full House: r2c5=6
Naked Single: r2c2=1
Full House: r3c2=9
Full House: r3c9=3
Naked Single: r1c9=9
Naked Single: r5c7=8
Full House: r5c9=2
Naked Single: r1c1=6
Full House: r2c1=3
Full House: r2c9=5
Full House: r1c7=1
Full House: r9c9=8
Full House: r9c7=9
|
sudoku_normal_hard_120
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....2..95...3.....1.7..3...6.41..7...4..89.....6..4..9......5...8.....2.7..6.1..
|
743182569586934217219756384362419875154378926897625431921847653638591742475263198
|
. . . . . 2 . . 9
5 . . . 3 . . . .
. 1 . 7 . . 3 . .
. 6 . 4 1 . . 7 .
. . 4 . . 8 9 . .
. . . 6 . . 4 . .
9 . . . . . . 5 .
. . 8 . . . . . 2
. 7 . . 6 . 1 . .
|
7 4 3 1 8 2 5 6 9
5 8 6 9 3 4 2 1 7
2 1 9 7 5 6 3 8 4
3 6 2 4 1 9 8 7 5
1 5 4 3 7 8 9 2 6
8 9 7 6 2 5 4 3 1
9 2 1 8 4 7 6 5 3
6 3 8 5 9 1 7 4 2
4 7 5 2 6 3 1 9 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3736_hard
|
743182569586934217219756384362419875154378926897625431921847653638591742475263198 #1 Extreme (29284) bf
Hidden Pair: 1,6 in r7c3,r8c1 => r7c3<>2, r7c3,r8c1<>3, r8c1<>4
Forcing Net Contradiction in r8 => r6c8<>1
r6c8=1 (r5c8<>1) r5c9<>1 r5c1=1 r5c1<>7 r5c5=7 r8c5<>7
r6c8=1 (r1c8<>1 r1c4=1 r8c4<>1) (r5c8<>1) r5c9<>1 r5c1=1 r8c1<>1 r8c6=1 r8c6<>7
r6c8=1 (r2c8<>1) r1c8<>1 r1c4=1 (r2c4<>1) r2c6<>1 r2c9=1 r2c9<>7 r7c9=7 r8c7<>7
Brute Force: r5c7=9
2-String Kite: 9 in r2c2,r4c6 (connected by r4c3,r6c2) => r2c6<>9
Grouped Discontinuous Nice Loop: 9 r8c6 -9- r4c6 =9= r4c3 -9- r3c3 =9= r2c23 -9- r2c4 =9= r89c4 -9- r8c6 => r8c6<>9
Grouped Discontinuous Nice Loop: 9 r9c6 -9- r4c6 =9= r4c3 -9- r3c3 =9= r2c23 -9- r2c4 =9= r89c4 -9- r9c6 => r9c6<>9
Forcing Chain Contradiction in r5 => r8c8<>6
r8c8=6 r8c1<>6 r8c1=1 r5c1<>1
r8c8=6 r8c7<>6 r8c7=7 r7c9<>7 r2c9=7 r2c9<>1 r12c8=1 r5c8<>1
r8c8=6 r5c8<>6 r5c9=6 r5c9<>1
Forcing Net Contradiction in c2 => r1c7<>6
r1c7=6 r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 r2c2<>2
r1c7=6 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r5c2<>2
r1c7=6 (r3c8<>6 r5c8=6 r5c8<>2) r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 (r2c8<>2) r3c8<>2 r6c8=2 r6c2<>2
r1c7=6 (r7c7<>6) r8c7<>6 r8c7=7 r7c7<>7 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
Forcing Net Contradiction in c2 => r1c7<>7
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 r2c2<>2
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r5c2<>2
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r6c2<>2
r1c7=7 (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
Locked Candidates Type 1 (Pointing): 7 in b3 => r2c3<>7
Forcing Net Contradiction in r4 => r1c1<>8
r1c1=8 r4c1<>8
r1c1=8 (r2c2<>8 r6c2=8 r6c2<>9 r2c2=9 r2c3<>9) (r1c5<>8) r1c7<>8 r1c7=5 (r1c4<>5 r1c4=1 r2c6<>1) r1c5<>5 r1c5=4 r2c6<>4 r2c6=6 r2c3<>6 r2c3=2 r2c7<>2 r4c7=2 r4c7<>8
r1c1=8 (r1c7<>8 r1c7=5 r3c9<>5) (r1c1<>7 r1c3=7 r1c3<>6 r1c8=6 r3c9<>6) (r1c1<>4) (r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r1c2<>4) (r1c2<>8) r2c2<>8 r6c2=8 r6c2<>9 r2c2=9 r2c2<>4 r3c1=4 r3c9<>4 r3c9=8 r4c9<>8
Forcing Net Contradiction in r5 => r2c9<>8
r2c9=8 r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r8c1<>6 r8c1=1 r5c1<>1
r2c9=8 r2c9<>1 r12c8=1 r5c8<>1
r2c9=8 (r1c8<>8) (r1c7<>8) (r1c8<>8) (r3c8<>8) (r3c9<>8) (r4c9<>8) r2c9<>7 r2c7=7 (r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 r9c9<>8 r9c4=8 r1c4<>8 r1c4=1 r1c8<>1) (r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 r9c8<>8 r9c4=8 r1c4<>8) r2c7<>2 r4c7=2 r4c7<>8 r4c1=8 r3c1<>8 r3c5=8 (r1c5<>8) r1c5<>8 r1c2=8 r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r1c8<>4 r1c8=6 r5c8<>6 r5c9=6 r5c9<>1
Forcing Net Contradiction in r2 => r3c6<>9
r3c6=9 (r2c4<>9) r4c6<>9 r4c3=9 r2c3<>9 r2c2=9 r2c2<>4
r3c6=9 r3c6<>6 r2c6=6 r2c6<>4
r3c6=9 (r3c3<>9) (r4c6<>9 r4c3=9 r2c3<>9) r3c6<>6 r2c6=6 (r2c6<>1) r2c3<>6 r2c3=2 r3c3<>2 r3c3=6 (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>1 r2c8=1 r2c8<>4
r3c6=9 (r3c3<>9) (r4c6<>9 r4c3=9 r2c3<>9) r3c6<>6 r2c6=6 r2c3<>6 r2c3=2 r3c3<>2 r3c3=6 (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>4
Locked Candidates Type 2 (Claiming): 9 in c6 => r6c5<>9
Forcing Chain Contradiction in r3 => r4c6<>5
r4c6=5 r4c6<>9 r4c3=9 r3c3<>9 r3c5=9 r3c5<>5
r4c6=5 r3c6<>5
r4c6=5 r4c7<>5 r1c7=5 r3c9<>5
Forcing Net Contradiction in c7 => r6c2<>2
r6c2=2 (r4c1<>2) r4c3<>2 r4c7=2 r4c7<>5 r1c7=5 r1c7<>8
r6c2=2 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c4<>8) r1c5<>8 r7c5=8 (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8
r6c2=2 (r4c1<>2) r4c3<>2 r4c7=2 r4c7<>8
r6c2=2 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 r1c5<>8 r7c5=8 r7c7<>8
Forcing Net Contradiction in r2c3 => r6c2<>3
r6c2=3 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c7<>8) (r1c4<>8) r1c5<>8 r7c5=8 (r7c7<>8) (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8 r4c7=8 r4c7<>2 r2c7=2 r2c3<>2
r6c2=3 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>5) r2c2<>8 r1c2=8 r1c7<>8 r1c7=5 r3c9<>5 r3c6=5 r3c6<>6 r2c6=6 r2c3<>6
r6c2=3 r6c2<>9 r2c2=9 r2c3<>9
Forcing Net Contradiction in r2c3 => r6c2<>5
r6c2=5 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c7<>8) (r1c4<>8) r1c5<>8 r7c5=8 (r7c7<>8) (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8 r4c7=8 r4c7<>2 r2c7=2 r2c3<>2
r6c2=5 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>5) r2c2<>8 r1c2=8 r1c7<>8 r1c7=5 r3c9<>5 r3c6=5 r3c6<>6 r2c6=6 r2c3<>6
r6c2=5 r6c2<>9 r2c2=9 r2c3<>9
Forcing Net Contradiction in c8 => r4c6=9
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 (r2c3<>9) r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 r4c7<>2 r2c7=2 r2c3<>2 r2c3=6 (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>8
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 (r2c3<>9) r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 r4c7<>2 r2c7=2 r2c3<>2 r2c3=6 (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1) (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c6<>1) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>1 r2c8=1 r2c8<>8
r4c6<>9 r4c3=9 r6c2<>9 r6c2=8 (r4c1<>8) r6c1<>8 r3c1=8 r3c8<>8
r4c6<>9 r4c3=9 r6c2<>9 r6c2=8 r6c8<>8
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 (r9c1<>2) (r5c2<>2) r4c7<>2 r2c7=2 r2c2<>2 r7c2=2 r9c3<>2 r9c4=2 r9c4<>9 r9c8=9 r9c8<>8
Forcing Net Contradiction in r8c8 => r7c4<>1
r7c4=1 (r1c4<>1 r1c8=1 r2c9<>1 r2c6=1 r2c6<>6) (r1c4<>1 r1c8=1 r5c8<>1) r7c3<>1 (r7c3=6 r2c3<>6) r6c3=1 r5c1<>1 r5c9=1 r5c9<>6 r5c8=6 r2c8<>6 r2c9=6 r2c9<>7 r2c7=7 (r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r1c4<>5) (r7c7<>7) r8c7<>7 r8c7=6 (r2c7<>6) r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r1c4<>8 r1c4=1 r7c4<>1
Forcing Net Contradiction in r3 => r1c4<>5
r1c4=5 (r1c4<>1 r1c8=1 r1c8<>6) (r1c4<>1) (r3c6<>5) (r1c5<>5) r1c7<>5 r1c7=8 (r1c2<>8) r1c5<>8 r1c5=4 (r1c1<>4) (r1c2<>4) (r2c6<>4) r3c6<>4 r3c6=6 r2c6<>6 r2c6=1 r2c4<>1 r8c4=1 r8c1<>1 r8c1=6 r1c1<>6 r1c3=6 r1c3<>7 r6c3=7 r6c3<>9 r6c2=9 r6c2<>8 r2c2=8 r2c2<>4 r3c1=4
r1c4=5 (r3c6<>5) (r1c5<>5) r1c7<>5 (r4c7=5 r4c7<>2 r2c7=2 r3c8<>2) r1c7=8 (r3c8<>8) r1c5<>8 r1c5=4 r3c6<>4 r3c6=6 r3c8<>6 r3c8=4
Finned X-Wing: 5 c24 r58 fr9c4 => r8c56<>5
Forcing Net Contradiction in r2 => r2c6<>1
r2c6=1 (r2c4<>1) r1c4<>1 r1c4=8 (r1c2<>8) r2c4<>8 r2c4=9 r2c2<>9 r6c2=9 r6c2<>8 r2c2=8
r2c6=1 (r1c4<>1) r2c4<>1 r8c4=1 (r8c1<>1 r8c1=6 r8c7<>6 r8c7=7 r7c7<>7 r7c7=6 r2c7<>6) (r8c1<>1 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7) (r8c1<>1 r8c1=6 r1c1<>6) r1c4<>1 (r1c4=8 r2c4<>8 r2c4=9 r2c3<>9) r1c8=1 r1c8<>6 r1c3=6 r2c3<>6 r2c3=2 r2c7<>2 r2c7=8
Locked Candidates Type 1 (Pointing): 1 in b2 => r8c4<>1
Forcing Net Contradiction in r7c2 => r2c7<>6
r2c7=6 (r7c7<>6) r8c7<>6 r8c7=7 r7c7<>7 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
r2c7=6 (r1c8<>6) r8c7<>6 r8c1=6 r1c1<>6 r1c3=6 (r1c3<>3) r1c3<>7 r1c1=7 r1c1<>3 r1c2=3 r7c2<>3
r2c7=6 (r2c6<>6 r2c6=4 r3c5<>4) (r8c7<>6 r8c1=6 r1c1<>6 r1c3=6 r1c3<>7 r6c3=7 r6c3<>9 r6c2=9 r2c2<>9) (r2c6<>6 r3c6=6 r3c6<>5) r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r3c5<>9 (r8c5=9 r8c5<>4) r3c3=9 r2c3<>9 r2c4=9 r2c4<>1 r1c4=1 r1c4<>8 r1c5=8 (r2c4<>8) (r3c5<>8) r1c5<>4 r7c5=4 r7c2<>4
Locked Candidates Type 2 (Claiming): 6 in c7 => r7c9<>6
Forcing Net Contradiction in r7c2 => r2c9<>6
r2c9=6 r2c9<>7 r2c7=7 (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
r2c9=6 (r1c8<>6) r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r7c7<>6 r7c3=6 r1c3<>6 r1c1=6 (r1c1<>3) r1c1<>7 r1c3=7 r1c3<>3 r1c2=3 r7c2<>3
r2c9=6 (r2c6<>6 r2c6=4 r3c5<>4) (r2c6<>6 r3c6=6 r3c6<>5) r2c9<>7 r2c7=7 r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r3c5<>9 (r8c5=9 r8c5<>4) r3c3=9 (r2c2<>9) r2c3<>9 r2c4=9 r2c4<>1 r1c4=1 r1c4<>8 r1c5=8 (r2c4<>8) (r3c5<>8) r1c5<>4 r7c5=4 r7c2<>4
Forcing Net Contradiction in r3c8 => r3c3<>6
r3c3=6 (r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7) (r3c3<>9 r3c5=9 r2c4<>9) (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1 r2c4=8 r2c7<>8 r2c7=2 r3c8<>2
r3c3=6 (r1c3<>6 r1c8=6 r2c8<>6 r2c6=6 r2c6<>4) (r7c3<>6 r7c3=1 r8c1<>1 r8c6=1 r8c6<>4) (r3c3<>9 r3c5=9 r8c5<>9) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r8c5<>7 r8c5=4 (r7c6<>4) r9c6<>4 r3c6=4 r3c8<>4
r3c3=6 r3c8<>6
r3c3=6 (r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r8c5<>7 r8c5=4 r1c5<>4) (r3c3<>9 r3c5=9 r2c4<>9) (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1 r2c4=8 r1c5<>8 r1c5=5 r1c7<>5 r1c7=8 r3c8<>8
Forcing Net Contradiction in r2 => r2c2<>2
r2c2=2 (r2c3<>2) r3c3<>2 r3c3=9 r2c3<>9 r2c3=6
r2c2=2 (r2c2<>8) r3c3<>2 r3c3=9 r6c3<>9 r6c2=9 r6c2<>8 r1c2=8 (r1c5<>8) r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r2c6<>4 r2c6=6
Empty Rectangle: 2 in b5 (r57c2) => r7c5<>2
Locked Candidates Type 1 (Pointing): 2 in b8 => r5c4<>2
Forcing Chain Contradiction in r9c3 => r9c8<>3
r9c8=3 r9c8<>9 r9c4=9 r2c4<>9 r3c5=9 r3c3<>9 r3c3=2 r9c3<>2
r9c8=3 r9c3<>3
r9c8=3 r9c8<>9 r9c4=9 r9c4<>2 r7c4=2 r7c2<>2 r5c2=2 r5c2<>5 r8c2=5 r9c3<>5
Forcing Net Contradiction in c3 => r2c9=7
r2c9<>7 r2c7=7 (r7c7<>7) (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c9<>8 r9c4=8 r9c4<>2 r7c4=2 r7c4<>3) r7c7<>6 r7c3=6 r8c1<>6 (r8c1=1 r7c3<>1 r7c6=1 r7c6<>3) r8c7=6 r8c7<>7 r2c7=7 (r7c7<>7) (r7c7<>7) r2c9<>7 r7c9=7 r7c9<>3 r7c2=3 (r9c3<>3) r7c2<>2 r5c2=2 r5c2<>5 r8c2=5 r9c3<>5 r9c3=2 (r2c3<>2) r3c3<>2 r3c3=9 r2c3<>9 r2c3=6
r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r7c7<>6 r7c3=6
Locked Candidates Type 1 (Pointing): 1 in b3 => r5c8<>1
Naked Triple: 2,5,8 in r124c7 => r7c7<>8
Hidden Rectangle: 1/8 in r1c48,r2c48 => r2c8<>8
Discontinuous Nice Loop: 6 r3c1 -6- r3c9 =6= r5c9 =1= r5c1 -1- r8c1 -6- r3c1 => r3c1<>6
Grouped Discontinuous Nice Loop: 8 r3c9 -8- r2c7 -2- r4c7 =2= r4c13 -2- r5c2 =2= r7c2 -2- r7c4 =2= r9c4 =9= r9c8 =8= r79c9 -8- r3c9 => r3c9<>8
Almost Locked Set XY-Wing: A=r2c6 {46}, B=r135689c8 {1234689}, C=r1c457 {1458}, X,Y=1,4, Z=6 => r2c8<>6
Almost Locked Set XY-Wing: A=r1c457 {1458}, B=r2c23,r3c13 {24689}, C=r2c6 {46}, X,Y=4,6, Z=8 => r1c2<>8
Hidden Pair: 8,9 in r26c2 => r2c2<>4
XY-Wing: 8/9/2 in r2c27,r3c3 => r2c3,r3c8<>2
Discontinuous Nice Loop: 4 r3c5 -4- r2c6 -6- r2c3 -9- r2c4 =9= r3c5 => r3c5<>4
Discontinuous Nice Loop: 2 r6c3 -2- r6c5 =2= r5c5 =7= r5c1 =1= r5c9 =6= r3c9 -6- r3c6 =6= r2c6 -6- r2c3 -9- r3c3 -2- r6c3 => r6c3<>2
Grouped Continuous Nice Loop: 2/4/8 6= r1c8 =1= r2c8 =4= r2c6 =6= r2c3 -6- r1c13 =6= r1c8 =1 => r2c8<>2, r1c8<>4, r1c8<>8
Hidden Single: r2c7=2
Locked Candidates Type 2 (Claiming): 2 in r4 => r5c12,r6c1<>2
Hidden Single: r7c2=2
Hidden Single: r9c4=2
Hidden Single: r9c8=9
Hidden Single: r9c9=8
Naked Pair: 3,5 in r5c24 => r5c189<>3, r5c59<>5
Skyscraper: 8 in r2c2,r3c8 (connected by r6c28) => r3c1<>8
Hidden Single: r2c2=8
Naked Single: r6c2=9
2-String Kite: 4 in r2c6,r7c9 (connected by r2c8,r3c9) => r7c6<>4
Turbot Fish: 3 r5c4 =3= r6c6 -3- r6c8 =3= r8c8 => r8c4<>3
Empty Rectangle: 4 in b2 (r18c2) => r8c6<>4
Empty Rectangle: 4 in b2 (r9c16) => r1c1<>4
XY-Chain: 6 6- r1c8 -1- r1c4 -8- r7c4 -3- r5c4 -5- r5c2 -3- r1c2 -4- r3c1 -2- r3c3 -9- r2c3 -6 => r1c13<>6
Hidden Single: r8c1=6
Naked Single: r7c3=1
Naked Single: r8c7=7
Naked Single: r7c7=6
Hidden Single: r1c8=6
Naked Single: r5c8=2
Naked Single: r5c5=7
Naked Single: r5c1=1
Naked Single: r5c9=6
Hidden Single: r2c3=6
Naked Single: r2c6=4
Naked Single: r2c8=1
Full House: r2c4=9
Naked Single: r8c4=5
Naked Single: r5c4=3
Full House: r5c2=5
Naked Single: r9c6=3
Naked Single: r6c6=5
Full House: r6c5=2
Naked Single: r7c4=8
Full House: r1c4=1
Naked Single: r7c6=7
Naked Single: r8c6=1
Full House: r3c6=6
Naked Single: r9c1=4
Full House: r9c3=5
Full House: r8c2=3
Full House: r1c2=4
Naked Single: r7c5=4
Full House: r7c9=3
Full House: r8c8=4
Full House: r8c5=9
Naked Single: r3c1=2
Naked Single: r4c9=5
Naked Single: r6c9=1
Full House: r3c9=4
Naked Single: r3c8=8
Full House: r1c7=5
Full House: r4c7=8
Full House: r6c8=3
Naked Single: r3c3=9
Full House: r3c5=5
Full House: r1c5=8
Naked Single: r4c1=3
Full House: r4c3=2
Naked Single: r6c3=7
Full House: r1c3=3
Full House: r1c1=7
Full House: r6c1=8
|
sudoku_normal_extremely_hard_120
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....2..95...3.....1.7..3...6.41..7...4..8......6..4..9......5...8.....2.7..6.1..
|
743182569586934217219756384362419875154378926897625431921847653638591742475263198
|
. . . . . 2 . . 9
5 . . . 3 . . . .
. 1 . 7 . . 3 . .
. 6 . 4 1 . . 7 .
. . 4 . . 8 . . .
. . . 6 . . 4 . .
9 . . . . . . 5 .
. . 8 . . . . . 2
. 7 . . 6 . 1 . .
|
7 4 3 1 8 2 5 6 9
5 8 6 9 3 4 2 1 7
2 1 9 7 5 6 3 8 4
3 6 2 4 1 9 8 7 5
1 5 4 3 7 8 9 2 6
8 9 7 6 2 5 4 3 1
9 2 1 8 4 7 6 5 3
6 3 8 5 9 1 7 4 2
4 7 5 2 6 3 1 9 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3736_hard
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743182569586934217219756384362419875154378926897625431921847653638591742475263198 #1 Extreme (29284) bf
Hidden Pair: 1,6 in r7c3,r8c1 => r7c3<>2, r7c3,r8c1<>3, r8c1<>4
Forcing Net Contradiction in r8 => r6c8<>1
r6c8=1 (r5c8<>1) r5c9<>1 r5c1=1 r5c1<>7 r5c5=7 r8c5<>7
r6c8=1 (r1c8<>1 r1c4=1 r8c4<>1) (r5c8<>1) r5c9<>1 r5c1=1 r8c1<>1 r8c6=1 r8c6<>7
r6c8=1 (r2c8<>1) r1c8<>1 r1c4=1 (r2c4<>1) r2c6<>1 r2c9=1 r2c9<>7 r7c9=7 r8c7<>7
Brute Force: r5c7=9
2-String Kite: 9 in r2c2,r4c6 (connected by r4c3,r6c2) => r2c6<>9
Grouped Discontinuous Nice Loop: 9 r8c6 -9- r4c6 =9= r4c3 -9- r3c3 =9= r2c23 -9- r2c4 =9= r89c4 -9- r8c6 => r8c6<>9
Grouped Discontinuous Nice Loop: 9 r9c6 -9- r4c6 =9= r4c3 -9- r3c3 =9= r2c23 -9- r2c4 =9= r89c4 -9- r9c6 => r9c6<>9
Forcing Chain Contradiction in r5 => r8c8<>6
r8c8=6 r8c1<>6 r8c1=1 r5c1<>1
r8c8=6 r8c7<>6 r8c7=7 r7c9<>7 r2c9=7 r2c9<>1 r12c8=1 r5c8<>1
r8c8=6 r5c8<>6 r5c9=6 r5c9<>1
Forcing Net Contradiction in c2 => r1c7<>6
r1c7=6 r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 r2c2<>2
r1c7=6 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r5c2<>2
r1c7=6 (r3c8<>6 r5c8=6 r5c8<>2) r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 (r2c8<>2) r3c8<>2 r6c8=2 r6c2<>2
r1c7=6 (r7c7<>6) r8c7<>6 r8c7=7 r7c7<>7 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
Forcing Net Contradiction in c2 => r1c7<>7
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r2c7=2 r2c2<>2
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r5c2<>2
r1c7=7 r1c7<>5 r4c7=5 r4c7<>2 r4c13=2 r6c2<>2
r1c7=7 (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
Locked Candidates Type 1 (Pointing): 7 in b3 => r2c3<>7
Forcing Net Contradiction in r4 => r1c1<>8
r1c1=8 r4c1<>8
r1c1=8 (r2c2<>8 r6c2=8 r6c2<>9 r2c2=9 r2c3<>9) (r1c5<>8) r1c7<>8 r1c7=5 (r1c4<>5 r1c4=1 r2c6<>1) r1c5<>5 r1c5=4 r2c6<>4 r2c6=6 r2c3<>6 r2c3=2 r2c7<>2 r4c7=2 r4c7<>8
r1c1=8 (r1c7<>8 r1c7=5 r3c9<>5) (r1c1<>7 r1c3=7 r1c3<>6 r1c8=6 r3c9<>6) (r1c1<>4) (r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r1c2<>4) (r1c2<>8) r2c2<>8 r6c2=8 r6c2<>9 r2c2=9 r2c2<>4 r3c1=4 r3c9<>4 r3c9=8 r4c9<>8
Forcing Net Contradiction in r5 => r2c9<>8
r2c9=8 r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r8c1<>6 r8c1=1 r5c1<>1
r2c9=8 r2c9<>1 r12c8=1 r5c8<>1
r2c9=8 (r1c8<>8) (r1c7<>8) (r1c8<>8) (r3c8<>8) (r3c9<>8) (r4c9<>8) r2c9<>7 r2c7=7 (r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 r9c9<>8 r9c4=8 r1c4<>8 r1c4=1 r1c8<>1) (r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 r9c8<>8 r9c4=8 r1c4<>8) r2c7<>2 r4c7=2 r4c7<>8 r4c1=8 r3c1<>8 r3c5=8 (r1c5<>8) r1c5<>8 r1c2=8 r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r1c8<>4 r1c8=6 r5c8<>6 r5c9=6 r5c9<>1
Forcing Net Contradiction in r2 => r3c6<>9
r3c6=9 (r2c4<>9) r4c6<>9 r4c3=9 r2c3<>9 r2c2=9 r2c2<>4
r3c6=9 r3c6<>6 r2c6=6 r2c6<>4
r3c6=9 (r3c3<>9) (r4c6<>9 r4c3=9 r2c3<>9) r3c6<>6 r2c6=6 (r2c6<>1) r2c3<>6 r2c3=2 r3c3<>2 r3c3=6 (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>1 r2c8=1 r2c8<>4
r3c6=9 (r3c3<>9) (r4c6<>9 r4c3=9 r2c3<>9) r3c6<>6 r2c6=6 r2c3<>6 r2c3=2 r3c3<>2 r3c3=6 (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>4
Locked Candidates Type 2 (Claiming): 9 in c6 => r6c5<>9
Forcing Chain Contradiction in r3 => r4c6<>5
r4c6=5 r4c6<>9 r4c3=9 r3c3<>9 r3c5=9 r3c5<>5
r4c6=5 r3c6<>5
r4c6=5 r4c7<>5 r1c7=5 r3c9<>5
Forcing Net Contradiction in c7 => r6c2<>2
r6c2=2 (r4c1<>2) r4c3<>2 r4c7=2 r4c7<>5 r1c7=5 r1c7<>8
r6c2=2 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c4<>8) r1c5<>8 r7c5=8 (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8
r6c2=2 (r4c1<>2) r4c3<>2 r4c7=2 r4c7<>8
r6c2=2 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 r1c5<>8 r7c5=8 r7c7<>8
Forcing Net Contradiction in r2c3 => r6c2<>3
r6c2=3 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c7<>8) (r1c4<>8) r1c5<>8 r7c5=8 (r7c7<>8) (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8 r4c7=8 r4c7<>2 r2c7=2 r2c3<>2
r6c2=3 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>5) r2c2<>8 r1c2=8 r1c7<>8 r1c7=5 r3c9<>5 r3c6=5 r3c6<>6 r2c6=6 r2c3<>6
r6c2=3 r6c2<>9 r2c2=9 r2c3<>9
Forcing Net Contradiction in r2c3 => r6c2<>5
r6c2=5 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>8) r2c2<>8 r1c2=8 (r1c7<>8) (r1c4<>8) r1c5<>8 r7c5=8 (r7c7<>8) (r7c4<>8) r9c4<>8 r2c4=8 r2c7<>8 r4c7=8 r4c7<>2 r2c7=2 r2c3<>2
r6c2=5 (r6c2<>8) r6c2<>9 r2c2=9 (r3c3<>9 r3c5=9 r3c5<>5) r2c2<>8 r1c2=8 r1c7<>8 r1c7=5 r3c9<>5 r3c6=5 r3c6<>6 r2c6=6 r2c3<>6
r6c2=5 r6c2<>9 r2c2=9 r2c3<>9
Forcing Net Contradiction in c8 => r4c6=9
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 (r2c3<>9) r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 r4c7<>2 r2c7=2 r2c3<>2 r2c3=6 (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>8
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 (r2c3<>9) r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 r4c7<>2 r2c7=2 r2c3<>2 r2c3=6 (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1) (r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c6<>1) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7 r2c9=7 r2c9<>1 r2c8=1 r2c8<>8
r4c6<>9 r4c3=9 r6c2<>9 r6c2=8 (r4c1<>8) r6c1<>8 r3c1=8 r3c8<>8
r4c6<>9 r4c3=9 r6c2<>9 r6c2=8 r6c8<>8
r4c6<>9 (r4c6=3 r4c1<>3) r4c3=9 r6c2<>9 r6c2=8 r4c1<>8 r4c1=2 (r9c1<>2) (r5c2<>2) r4c7<>2 r2c7=2 r2c2<>2 r7c2=2 r9c3<>2 r9c4=2 r9c4<>9 r9c8=9 r9c8<>8
Forcing Net Contradiction in r8c8 => r7c4<>1
r7c4=1 (r1c4<>1 r1c8=1 r2c9<>1 r2c6=1 r2c6<>6) (r1c4<>1 r1c8=1 r5c8<>1) r7c3<>1 (r7c3=6 r2c3<>6) r6c3=1 r5c1<>1 r5c9=1 r5c9<>6 r5c8=6 r2c8<>6 r2c9=6 r2c9<>7 r2c7=7 (r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r1c4<>5) (r7c7<>7) r8c7<>7 r8c7=6 (r2c7<>6) r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r1c4<>8 r1c4=1 r7c4<>1
Forcing Net Contradiction in r3 => r1c4<>5
r1c4=5 (r1c4<>1 r1c8=1 r1c8<>6) (r1c4<>1) (r3c6<>5) (r1c5<>5) r1c7<>5 r1c7=8 (r1c2<>8) r1c5<>8 r1c5=4 (r1c1<>4) (r1c2<>4) (r2c6<>4) r3c6<>4 r3c6=6 r2c6<>6 r2c6=1 r2c4<>1 r8c4=1 r8c1<>1 r8c1=6 r1c1<>6 r1c3=6 r1c3<>7 r6c3=7 r6c3<>9 r6c2=9 r6c2<>8 r2c2=8 r2c2<>4 r3c1=4
r1c4=5 (r3c6<>5) (r1c5<>5) r1c7<>5 (r4c7=5 r4c7<>2 r2c7=2 r3c8<>2) r1c7=8 (r3c8<>8) r1c5<>8 r1c5=4 r3c6<>4 r3c6=6 r3c8<>6 r3c8=4
Finned X-Wing: 5 c24 r58 fr9c4 => r8c56<>5
Forcing Net Contradiction in r2 => r2c6<>1
r2c6=1 (r2c4<>1) r1c4<>1 r1c4=8 (r1c2<>8) r2c4<>8 r2c4=9 r2c2<>9 r6c2=9 r6c2<>8 r2c2=8
r2c6=1 (r1c4<>1) r2c4<>1 r8c4=1 (r8c1<>1 r8c1=6 r8c7<>6 r8c7=7 r7c7<>7 r7c7=6 r2c7<>6) (r8c1<>1 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7) (r8c1<>1 r8c1=6 r1c1<>6) r1c4<>1 (r1c4=8 r2c4<>8 r2c4=9 r2c3<>9) r1c8=1 r1c8<>6 r1c3=6 r2c3<>6 r2c3=2 r2c7<>2 r2c7=8
Locked Candidates Type 1 (Pointing): 1 in b2 => r8c4<>1
Forcing Net Contradiction in r7c2 => r2c7<>6
r2c7=6 (r7c7<>6) r8c7<>6 r8c7=7 r7c7<>7 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
r2c7=6 (r1c8<>6) r8c7<>6 r8c1=6 r1c1<>6 r1c3=6 (r1c3<>3) r1c3<>7 r1c1=7 r1c1<>3 r1c2=3 r7c2<>3
r2c7=6 (r2c6<>6 r2c6=4 r3c5<>4) (r8c7<>6 r8c1=6 r1c1<>6 r1c3=6 r1c3<>7 r6c3=7 r6c3<>9 r6c2=9 r2c2<>9) (r2c6<>6 r3c6=6 r3c6<>5) r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r3c5<>9 (r8c5=9 r8c5<>4) r3c3=9 r2c3<>9 r2c4=9 r2c4<>1 r1c4=1 r1c4<>8 r1c5=8 (r2c4<>8) (r3c5<>8) r1c5<>4 r7c5=4 r7c2<>4
Locked Candidates Type 2 (Claiming): 6 in c7 => r7c9<>6
Forcing Net Contradiction in r7c2 => r2c9<>6
r2c9=6 r2c9<>7 r2c7=7 (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c8<>8) r9c9<>8 r9c4=8 r9c4<>2 r7c45=2 r7c2<>2
r2c9=6 (r1c8<>6) r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r7c7<>6 r7c3=6 r1c3<>6 r1c1=6 (r1c1<>3) r1c1<>7 r1c3=7 r1c3<>3 r1c2=3 r7c2<>3
r2c9=6 (r2c6<>6 r2c6=4 r3c5<>4) (r2c6<>6 r3c6=6 r3c6<>5) r2c9<>7 r2c7=7 r2c7<>2 r4c7=2 r4c7<>5 r1c7=5 r3c9<>5 r3c5=5 r3c5<>9 (r8c5=9 r8c5<>4) r3c3=9 (r2c2<>9) r2c3<>9 r2c4=9 r2c4<>1 r1c4=1 r1c4<>8 r1c5=8 (r2c4<>8) (r3c5<>8) r1c5<>4 r7c5=4 r7c2<>4
Forcing Net Contradiction in r3c8 => r3c3<>6
r3c3=6 (r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r2c7<>7) (r3c3<>9 r3c5=9 r2c4<>9) (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1 r2c4=8 r2c7<>8 r2c7=2 r3c8<>2
r3c3=6 (r1c3<>6 r1c8=6 r2c8<>6 r2c6=6 r2c6<>4) (r7c3<>6 r7c3=1 r8c1<>1 r8c6=1 r8c6<>4) (r3c3<>9 r3c5=9 r8c5<>9) (r1c1<>6) r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r8c5<>7 r8c5=4 (r7c6<>4) r9c6<>4 r3c6=4 r3c8<>4
r3c3=6 r3c8<>6
r3c3=6 (r3c1<>6 r8c1=6 r8c7<>6 r8c7=7 r8c5<>7 r8c5=4 r1c5<>4) (r3c3<>9 r3c5=9 r2c4<>9) (r1c1<>6) r1c3<>6 r1c8=6 r1c8<>1 r1c4=1 r2c4<>1 r2c4=8 r1c5<>8 r1c5=5 r1c7<>5 r1c7=8 r3c8<>8
Forcing Net Contradiction in r2 => r2c2<>2
r2c2=2 (r2c3<>2) r3c3<>2 r3c3=9 r2c3<>9 r2c3=6
r2c2=2 (r2c2<>8) r3c3<>2 r3c3=9 r6c3<>9 r6c2=9 r6c2<>8 r1c2=8 (r1c5<>8) r1c7<>8 r1c7=5 r1c5<>5 r1c5=4 r2c6<>4 r2c6=6
Empty Rectangle: 2 in b5 (r57c2) => r7c5<>2
Locked Candidates Type 1 (Pointing): 2 in b8 => r5c4<>2
Forcing Chain Contradiction in r9c3 => r9c8<>3
r9c8=3 r9c8<>9 r9c4=9 r2c4<>9 r3c5=9 r3c3<>9 r3c3=2 r9c3<>2
r9c8=3 r9c3<>3
r9c8=3 r9c8<>9 r9c4=9 r9c4<>2 r7c4=2 r7c2<>2 r5c2=2 r5c2<>5 r8c2=5 r9c3<>5
Forcing Net Contradiction in c3 => r2c9=7
r2c9<>7 r2c7=7 (r7c7<>7) (r7c7<>7) r8c7<>7 r8c7=6 r7c7<>6 r7c7=8 (r9c9<>8 r9c4=8 r9c4<>2 r7c4=2 r7c4<>3) r7c7<>6 r7c3=6 r8c1<>6 (r8c1=1 r7c3<>1 r7c6=1 r7c6<>3) r8c7=6 r8c7<>7 r2c7=7 (r7c7<>7) (r7c7<>7) r2c9<>7 r7c9=7 r7c9<>3 r7c2=3 (r9c3<>3) r7c2<>2 r5c2=2 r5c2<>5 r8c2=5 r9c3<>5 r9c3=2 (r2c3<>2) r3c3<>2 r3c3=9 r2c3<>9 r2c3=6
r2c9<>7 r2c7=7 r8c7<>7 r8c7=6 r7c7<>6 r7c3=6
Locked Candidates Type 1 (Pointing): 1 in b3 => r5c8<>1
Naked Triple: 2,5,8 in r124c7 => r7c7<>8
Hidden Rectangle: 1/8 in r1c48,r2c48 => r2c8<>8
Discontinuous Nice Loop: 6 r3c1 -6- r3c9 =6= r5c9 =1= r5c1 -1- r8c1 -6- r3c1 => r3c1<>6
Grouped Discontinuous Nice Loop: 8 r3c9 -8- r2c7 -2- r4c7 =2= r4c13 -2- r5c2 =2= r7c2 -2- r7c4 =2= r9c4 =9= r9c8 =8= r79c9 -8- r3c9 => r3c9<>8
Almost Locked Set XY-Wing: A=r2c6 {46}, B=r135689c8 {1234689}, C=r1c457 {1458}, X,Y=1,4, Z=6 => r2c8<>6
Almost Locked Set XY-Wing: A=r1c457 {1458}, B=r2c23,r3c13 {24689}, C=r2c6 {46}, X,Y=4,6, Z=8 => r1c2<>8
Hidden Pair: 8,9 in r26c2 => r2c2<>4
XY-Wing: 8/9/2 in r2c27,r3c3 => r2c3,r3c8<>2
Discontinuous Nice Loop: 4 r3c5 -4- r2c6 -6- r2c3 -9- r2c4 =9= r3c5 => r3c5<>4
Discontinuous Nice Loop: 2 r6c3 -2- r6c5 =2= r5c5 =7= r5c1 =1= r5c9 =6= r3c9 -6- r3c6 =6= r2c6 -6- r2c3 -9- r3c3 -2- r6c3 => r6c3<>2
Grouped Continuous Nice Loop: 2/4/8 6= r1c8 =1= r2c8 =4= r2c6 =6= r2c3 -6- r1c13 =6= r1c8 =1 => r2c8<>2, r1c8<>4, r1c8<>8
Hidden Single: r2c7=2
Locked Candidates Type 2 (Claiming): 2 in r4 => r5c12,r6c1<>2
Hidden Single: r7c2=2
Hidden Single: r9c4=2
Hidden Single: r9c8=9
Hidden Single: r9c9=8
Naked Pair: 3,5 in r5c24 => r5c189<>3, r5c59<>5
Skyscraper: 8 in r2c2,r3c8 (connected by r6c28) => r3c1<>8
Hidden Single: r2c2=8
Naked Single: r6c2=9
2-String Kite: 4 in r2c6,r7c9 (connected by r2c8,r3c9) => r7c6<>4
Turbot Fish: 3 r5c4 =3= r6c6 -3- r6c8 =3= r8c8 => r8c4<>3
Empty Rectangle: 4 in b2 (r18c2) => r8c6<>4
Empty Rectangle: 4 in b2 (r9c16) => r1c1<>4
XY-Chain: 6 6- r1c8 -1- r1c4 -8- r7c4 -3- r5c4 -5- r5c2 -3- r1c2 -4- r3c1 -2- r3c3 -9- r2c3 -6 => r1c13<>6
Hidden Single: r8c1=6
Naked Single: r7c3=1
Naked Single: r8c7=7
Naked Single: r7c7=6
Hidden Single: r1c8=6
Naked Single: r5c8=2
Naked Single: r5c5=7
Naked Single: r5c1=1
Naked Single: r5c9=6
Hidden Single: r2c3=6
Naked Single: r2c6=4
Naked Single: r2c8=1
Full House: r2c4=9
Naked Single: r8c4=5
Naked Single: r5c4=3
Full House: r5c2=5
Naked Single: r9c6=3
Naked Single: r6c6=5
Full House: r6c5=2
Naked Single: r7c4=8
Full House: r1c4=1
Naked Single: r7c6=7
Naked Single: r8c6=1
Full House: r3c6=6
Naked Single: r9c1=4
Full House: r9c3=5
Full House: r8c2=3
Full House: r1c2=4
Naked Single: r7c5=4
Full House: r7c9=3
Full House: r8c8=4
Full House: r8c5=9
Naked Single: r3c1=2
Naked Single: r4c9=5
Naked Single: r6c9=1
Full House: r3c9=4
Naked Single: r3c8=8
Full House: r1c7=5
Full House: r4c7=8
Full House: r6c8=3
Naked Single: r3c3=9
Full House: r3c5=5
Full House: r1c5=8
Naked Single: r4c1=3
Full House: r4c3=2
Naked Single: r6c3=7
Full House: r1c3=3
Full House: r1c1=7
Full House: r6c1=8
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sudoku_normal_hard_121
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.5....67...9.....28....1.4.7....8...4..3.521...2.9........5...6.....7.3....8.34..
|
253489671149736852867521943731268594496375218582194367314952786928647135675813429
|
. 5 . . . . 6 7 .
. . 9 . . . . . 2
8 . . . . 1 . 4 .
7 . . . . 8 . . .
4 . . 3 . 5 2 1 .
. . 2 . 9 . . . .
. . . . 5 . . . 6
. . . . . 7 . 3 .
. . . 8 . 3 4 . .
|
2 5 3 4 8 9 6 7 1
1 4 9 7 3 6 8 5 2
8 6 7 5 2 1 9 4 3
7 3 1 2 6 8 5 9 4
4 9 6 3 7 5 2 1 8
5 8 2 1 9 4 3 6 7
3 1 4 9 5 2 7 8 6
9 2 8 6 4 7 1 3 5
6 7 5 8 1 3 4 2 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5121_hard
|
253489671149736852867521943731268594496375218582194367314952786928647135675813429 #1 Extreme (39944) bf
Locked Candidates Type 1 (Pointing): 9 in b4 => r789c2<>9
Almost Locked Set XY-Wing: A=r1c13469 {123489}, B=r34589c5 {123467}, C=r2c8,r3c79 {3589}, X,Y=3,8, Z=2,4 => r1c5<>2, r1c5<>4
Brute Force: r5c6=5
Naked Pair: 4,6 in r26c6 => r17c6<>4
Turbot Fish: 2 r3c2 =2= r1c1 -2- r1c6 =2= r7c6 => r7c2<>2
Empty Rectangle: 4 in b8 (r1c34) => r8c3<>4
Forcing Net Contradiction in r1 => r1c9<>9
r1c9=9 (r1c9<>1 r2c7=1 r2c1<>1) (r1c4<>9) r1c6<>9 r1c6=2 r1c4<>2 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r1c1<>3
r1c9=9 (r1c9<>1 r2c7=1 r2c1<>1) (r1c4<>9) r1c6<>9 r1c6=2 r1c4<>2 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r1c3<>3
r1c9=9 r1c9<>8 r1c5=8 r1c5<>3
r1c9=9 r1c9<>3
Locked Candidates Type 1 (Pointing): 9 in b3 => r3c4<>9
Forcing Net Contradiction in r7c7 => r3c2<>3
r3c2=3 (r1c3<>3) r3c2<>2 r1c1=2 (r1c4<>2) r1c6<>2 r1c6=9 r1c4<>9 r1c4=4 r1c3<>4 r1c3=1 (r2c1<>1) r1c3<>4 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r3c2<>3
Forcing Net Contradiction in c1 => r6c2<>6
r6c2=6 (r5c3<>6 r5c5=6 r4c4<>6) (r6c4<>6) r6c6<>6 r2c6=6 (r2c4<>6) r3c4<>6 r8c4=6 r8c4<>9 r7c46=9 r7c1<>9
r6c2=6 (r6c6<>6 r2c6=6 r3c4<>6 r3c3=6 r9c3<>6 r9c1=6 r9c1<>5) (r6c2<>1) (r5c2<>6) r5c3<>6 r5c5=6 r5c5<>7 r6c4=7 r6c4<>1 r6c1=1 r6c1<>5 r8c1=5 r8c1<>9
r6c2=6 (r9c2<>6) (r5c3<>6 r5c5=6 r9c5<>6) (r3c2<>6) (r5c3<>6 r5c5=6 r3c5<>6) r6c6<>6 r2c6=6 r3c4<>6 r3c3=6 r9c3<>6 r9c1=6 r9c1<>9
Forcing Net Contradiction in c1 => r7c7<>2
r7c7=2 (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c1<>6
r7c7=2 (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>6 r6c8=6 r6c1<>6
r7c7=2 (r7c6<>2 r7c6=9 r8c4<>9) (r7c6<>2 r7c6=9 r7c8<>9) (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>9 r9c8=9 (r8c7<>9) r8c9<>9 r8c1=9 r8c1<>6
r7c7=2 (r5c7<>2 r5c5=2 r9c5<>2) (r9c8<>2) (r5c7<>2 r5c5=2 r3c5<>2) r7c6<>2 r1c6=2 r3c4<>2 r3c2=2 r9c2<>2 r9c1=2 r9c1<>6
Forcing Net Contradiction in r3 => r7c7<>9
r7c7=9 (r7c7<>7 r9c9=7 r5c9<>7 r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) (r7c8<>9) r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 (r3c4<>6) r3c5<>6 r3c2=6 r3c2<>2
r7c7=9 (r3c7<>9 r3c9=9 r3c9<>5) (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r7c8=8 r2c8<>8 r2c8=5 r3c7<>5 r3c4=5 r3c4<>2
r7c7=9 (r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6) (r7c8<>9) r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 (r6c4<>6) r6c6<>6 r2c6=6 (r2c4<>6) r3c4<>6 r4c4=6 r4c4<>2 r45c5=2 r3c5<>2
Brute Force: r5c7=2
Finned Swordfish: 2 r348 c245 fr8c1 => r9c2<>2
Almost Locked Set XY-Wing: A=r2c6 {46}, B=r14678c4 {124679}, C=r5c5,r6c6 {467}, X,Y=4,7, Z=6 => r23c4<>6
Finned Swordfish: 6 r359 c235 fr9c1 => r8c23<>6
Forcing Net Contradiction in r7c8 => r3c4<>2
r3c4=2 (r3c4<>7) r3c4<>5 r2c4=5 r2c4<>7 r6c4=7 (r6c4<>6) r5c5<>7 r5c5=6 r4c4<>6 r8c4=6 r8c4<>9 r7c46=9 r7c8<>9
r3c4=2 (r1c6<>2 r7c6=2 r7c8<>2) r3c4<>5 r2c4=5 r2c8<>5 r2c8=8 r7c8<>8 r7c8=9
Almost Locked Set XZ-Rule: A=r3c479 {3579}, B=r34589c5 {123467}, X=3, Z=7 => r2c5<>7
Forcing Chain Verity => r4c3<>6
r3c2=6 r3c2<>2 r3c5=2 r3c5<>7 r5c5=7 r5c5<>6 r5c23=6 r4c3<>6
r3c3=6 r4c3<>6
r3c5=6 r5c5<>6 r5c23=6 r4c3<>6
Forcing Net Contradiction in r9c5 => r4c2<>6
r4c2=6 (r9c2<>6) (r5c2<>6) r5c3<>6 r5c5=6 r5c5<>7 r3c5=7 r2c4<>7 r2c2=7 r9c2<>7 r9c2=1 r9c5<>1
r4c2=6 (r4c2<>9 r5c2=9 r5c9<>9 r5c9=7 r6c7<>7 r7c7=7 r7c7<>8) (r5c2<>6) r5c3<>6 (r5c3=8 r7c3<>8) r5c5=6 r5c5<>7 r3c5=7 (r2c4<>7) r3c4<>7 r3c4=5 r2c4<>5 r2c4=4 (r7c4<>4) r1c4<>4 r1c3=4 r7c3<>4 r7c2=4 r7c2<>8 r7c8=8 r7c8<>2 r9c8=2 r9c5<>2
r4c2=6 (r5c2<>6) r5c3<>6 r5c5=6 r9c5<>6
Forcing Net Contradiction in c8 => r5c5=7
r5c5<>7 r5c5=6 (r4c4<>6) r4c5<>6 r4c8=6
r5c5<>7 (r5c5=6 r5c3<>6 r5c3=8 r7c3<>8) (r5c9=7 r6c7<>7 r7c7=7 r7c7<>8) r3c5=7 (r2c4<>7) r3c4<>7 r3c4=5 r2c4<>5 r2c4=4 (r7c4<>4) r1c4<>4 r1c3=4 r7c3<>4 r7c2=4 r7c2<>8 r7c8=8 (r6c8<>8) r2c8<>8 r2c8=5 r6c8<>5 r6c8=6
Locked Candidates Type 2 (Claiming): 6 in r5 => r6c1<>6
Hidden Pair: 5,7 in r23c4 => r2c4<>4
Almost Locked Set XY-Wing: A=r6c46 {146}, B=r8c379 {1589}, C=r2679c8 {25689}, X,Y=6,9, Z=1 => r8c4<>1
Forcing Net Verity => r2c2<>6
r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c2<>6
r7c8=9 (r7c4<>9) r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6 r89c5=6 r23c5<>6 r2c6=6 r2c2<>6
r9c8=9 (r9c1<>9) (r8c7<>9) (r8c9<>9) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r8c4<>9 r8c1=9 r8c1<>2 r9c1=2 (r9c1<>6) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r7c1<>9 r8c1=9 r8c1<>6 r2c1=6 r2c2<>6
Forcing Net Verity => r2c5<>6
r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c5<>6
r7c8=9 (r7c4<>9) r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6 r89c5=6 r2c5<>6
r9c8=9 (r9c1<>9) (r8c7<>9) (r8c9<>9) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r8c4<>9 r8c1=9 r8c1<>2 r9c1=2 (r9c1<>6) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r7c1<>9 r8c1=9 r8c1<>6 r2c1=6 r2c5<>6
Forcing Net Verity => r4c4<>4
r7c4=1 (r8c5<>1) r9c5<>1 r4c5=1 r4c5<>2 r4c4=2 r4c4<>4
r7c4=2 (r4c4<>2 r4c5=2 r4c5<>6) (r7c6<>2 r7c6=9 r7c8<>9) r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r4c4=6 r4c4<>4
r7c4=4 r4c4<>4
r7c4=9 (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r6c6=4 r4c4<>4
Forcing Net Contradiction in r6 => r4c9<>9
r4c9=9 (r3c9<>9 r3c7=9 r8c7<>9) (r8c9<>9) (r4c8<>9) r4c9<>4 r4c5=4 (r6c6<>4 r2c6=4 r1c4<>4) r4c5<>2 r4c4=2 r1c4<>2 r1c4=9 r1c6<>9 (r1c6=2 r1c1<>2) r7c6=9 r7c8<>9 r9c8=9 r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 r7c6=9 r8c4<>9 r8c1=9 (r9c1<>9) r8c1<>2 r9c1=2 (r9c1<>5) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 r7c6=9 r7c1<>9 r8c1=9 (r9c1<>9) r8c1<>5 r6c1=5
r4c9=9 (r5c9<>9 r5c9=8 r6c8<>8) r4c9<>4 r4c5=4 r6c6<>4 r6c6=6 r6c8<>6 r6c8=5
Forcing Net Contradiction in r7c7 => r7c1<>2
r7c1=2 (r7c6<>2 r7c6=9 r7c8<>9) r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 (r5c9<>9 r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r3c5<>6 r3c2=6 r3c2<>2 r8c2=2 r7c1<>2
Forcing Net Contradiction in r7c4 => r7c1<>9
r7c1=9 (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 (r6c4<>6) r6c6<>6 r6c6=4 r6c4<>4 r6c4=1 r7c4<>1
r7c1=9 r7c6<>9 r7c6=2 r7c4<>2
r7c1=9 (r9c1<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r9c9=9 r5c9<>9 (r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) r5c2=9 r4c2<>9 r4c8=9 (r4c7<>9) r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r3c5<>6 r3c2=6 r3c2<>2 r3c5=2 (r1c4<>2) r1c6<>2 r1c6=9 r1c4<>9 r1c4=4 r7c4<>4
r7c1=9 r7c4<>9
Almost Locked Set XZ-Rule: A=r3c23479 {235679}, B=r1267c1 {12356}, X=2,6 => r3c5<>3, r89c1<>1, r4c3,r6c789,r89c1<>5
Hidden Single: r6c1=5
Hidden Pair: 3,8 in r12c5 => r2c5<>4
AIC: 5 5- r2c8 -8- r6c8 -6- r6c6 -4- r2c6 =4= r2c2 =7= r2c4 =5= r3c4 -5 => r2c4,r3c79<>5
Naked Single: r2c4=7
Naked Single: r3c4=5
Locked Pair: 3,9 in r3c79 => r1c9,r2c7,r3c3<>3
Discontinuous Nice Loop: 6 r4c4 -6- r6c6 =6= r2c6 -6- r3c5 -2- r4c5 =2= r4c4 => r4c4<>6
AIC: 4/6 6- r8c4 =6= r6c4 -6- r6c6 -4- r4c5 =4= r8c5 -4 => r8c4<>4, r8c5<>6
Discontinuous Nice Loop: 3 r4c9 -3- r3c9 -9- r5c9 -8- r6c8 -6- r6c6 -4- r6c9 =4= r4c9 => r4c9<>3
Discontinuous Nice Loop: 7 r7c3 -7- r3c3 -6- r3c5 =6= r2c6 =4= r2c2 -4- r1c3 =4= r7c3 => r7c3<>7
Discontinuous Nice Loop: 2 r8c4 -2- r8c2 =2= r3c2 -2- r3c5 -6- r9c5 =6= r8c4 => r8c4<>2
Discontinuous Nice Loop: 5 r9c8 -5- r2c8 -8- r6c8 -6- r6c6 =6= r2c6 -6- r3c5 -2- r1c6 =2= r7c6 -2- r7c8 =2= r9c8 => r9c8<>5
Almost Locked Set XY-Wing: A=r9c18 {269}, B=r2c6,r3c5 {246}, C=r2c12578 {134568}, X,Y=4,6, Z=2 => r9c5<>2
Discontinuous Nice Loop: 1 r8c5 -1- r9c5 -6- r3c5 -2- r3c2 =2= r8c2 =4= r8c5 => r8c5<>1
2-String Kite: 1 in r6c2,r9c5 (connected by r4c5,r6c4) => r9c2<>1
W-Wing: 7/6 in r3c3,r9c2 connected by 6 in r5c23 => r3c2,r9c3<>7
Hidden Single: r3c3=7
AIC: 9 9- r3c7 -3- r3c9 =3= r6c9 =7= r9c9 -7- r9c2 -6- r3c2 =6= r3c5 -6- r4c5 =6= r4c8 -6- r6c8 -8- r5c9 -9 => r3c9,r4c7<>9
Naked Single: r3c9=3
Naked Single: r3c7=9
Discontinuous Nice Loop: 8 r6c9 -8- r6c8 -6- r6c6 =6= r2c6 -6- r2c1 =6= r3c2 -6- r9c2 -7- r9c9 =7= r6c9 => r6c9<>8
Almost Locked Set XY-Wing: A=r14c3 {134}, B=r1239c5 {12368}, C=r1c46 {249}, X,Y=2,4, Z=1 => r9c3<>1
Almost Locked Set XY-Wing: A=r4c234 {1239}, B=r7c68 {289}, C=r246c8 {5689}, X,Y=8,9, Z=2 => r7c4<>2
Almost Locked Set XY-Wing: A=r8c379 {1589}, B=r4c23,r56c2 {13689}, C=r5c39 {689}, X,Y=6,9, Z=8 => r8c2<>8
Almost Locked Set Chain: 2- r1c1359 {12348} -4- r1c46 {249} -2- r3c5 {26} -6- r4c234579 {1234569} -9- r5c23 {689} -8- r5c9 {89} -9- r8c23579 {124589} -2 => r8c1<>2
Naked Pair: 6,9 in r8c14 => r8c9<>9
Naked Triple: 1,5,8 in r8c379 => r8c2<>1
X-Wing: 2 r38 c25 => r4c5<>2
Hidden Single: r4c4=2
Sue de Coq: r78c4 - {1469} (r1c4 - {49}, r9c5 - {16}) => r6c4<>4
X-Wing: 4 c34 r17 => r7c2<>4
AIC: 6 6- r5c3 =6= r5c2 -6- r3c2 =6= r3c5 -6- r2c6 -4- r6c6 =4= r6c9 =7= r9c9 -7- r9c2 -6 => r5c2,r9c3<>6
Naked Single: r9c3=5
Hidden Single: r5c3=6
Locked Candidates Type 1 (Pointing): 8 in b4 => r7c2<>8
Discontinuous Nice Loop: 3 r2c2 -3- r6c2 =3= r6c7 =7= r6c9 =4= r6c6 -4- r2c6 =4= r2c2 => r2c2<>3
AIC: 1 1- r6c4 =1= r7c4 -1- r7c1 -3- r2c1 =3= r2c5 =8= r1c5 -8- r1c9 -1- r9c9 =1= r9c5 -1 => r4c5,r7c4<>1
Hidden Single: r9c5=1
Hidden Single: r6c4=1
Hidden Single: r8c4=6
Naked Single: r8c1=9
Locked Candidates Type 1 (Pointing): 9 in b8 => r7c8<>9
XY-Chain: 1 1- r1c9 -8- r5c9 -9- r9c9 -7- r9c2 -6- r9c1 -2- r8c2 -4- r2c2 -1 => r1c13,r2c7<>1
Hidden Single: r1c9=1
Hidden Single: r1c5=8
Naked Single: r2c5=3
W-Wing: 1/3 in r4c3,r7c1 connected by 3 in r1c13 => r78c3<>1
Naked Single: r8c3=8
Naked Single: r8c9=5
Naked Single: r4c9=4
Naked Single: r8c7=1
Naked Single: r4c5=6
Full House: r6c6=4
Naked Single: r6c9=7
Naked Single: r3c5=2
Full House: r3c2=6
Full House: r8c5=4
Full House: r8c2=2
Naked Single: r2c6=6
Naked Single: r9c9=9
Full House: r5c9=8
Full House: r5c2=9
Naked Single: r1c6=9
Full House: r1c4=4
Full House: r7c4=9
Full House: r7c6=2
Naked Single: r2c1=1
Naked Single: r9c2=7
Naked Single: r9c1=6
Full House: r9c8=2
Naked Single: r6c7=3
Naked Single: r6c8=6
Full House: r6c2=8
Naked Single: r1c3=3
Full House: r1c1=2
Full House: r2c2=4
Full House: r7c1=3
Naked Single: r7c8=8
Full House: r7c7=7
Naked Single: r4c7=5
Full House: r2c7=8
Full House: r2c8=5
Full House: r4c8=9
Naked Single: r4c3=1
Full House: r7c3=4
Full House: r7c2=1
Full House: r4c2=3
|
sudoku_normal_extremely_hard_121
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.5....67...9.....28....1.4.7....8...4..3...1...2.9........5...6.....7.3....8.34..
|
253489671149736852867521943731268594496375218582194367314952786928647135675813429
|
. 5 . . . . 6 7 .
. . 9 . . . . . 2
8 . . . . 1 . 4 .
7 . . . . 8 . . .
4 . . 3 . . . 1 .
. . 2 . 9 . . . .
. . . . 5 . . . 6
. . . . . 7 . 3 .
. . . 8 . 3 4 . .
|
2 5 3 4 8 9 6 7 1
1 4 9 7 3 6 8 5 2
8 6 7 5 2 1 9 4 3
7 3 1 2 6 8 5 9 4
4 9 6 3 7 5 2 1 8
5 8 2 1 9 4 3 6 7
3 1 4 9 5 2 7 8 6
9 2 8 6 4 7 1 3 5
6 7 5 8 1 3 4 2 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5121_hard
|
253489671149736852867521943731268594496375218582194367314952786928647135675813429 #1 Extreme (39944) bf
Locked Candidates Type 1 (Pointing): 9 in b4 => r789c2<>9
Almost Locked Set XY-Wing: A=r1c13469 {123489}, B=r34589c5 {123467}, C=r2c8,r3c79 {3589}, X,Y=3,8, Z=2,4 => r1c5<>2, r1c5<>4
Brute Force: r5c6=5
Naked Pair: 4,6 in r26c6 => r17c6<>4
Turbot Fish: 2 r3c2 =2= r1c1 -2- r1c6 =2= r7c6 => r7c2<>2
Empty Rectangle: 4 in b8 (r1c34) => r8c3<>4
Forcing Net Contradiction in r1 => r1c9<>9
r1c9=9 (r1c9<>1 r2c7=1 r2c1<>1) (r1c4<>9) r1c6<>9 r1c6=2 r1c4<>2 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r1c1<>3
r1c9=9 (r1c9<>1 r2c7=1 r2c1<>1) (r1c4<>9) r1c6<>9 r1c6=2 r1c4<>2 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r1c3<>3
r1c9=9 r1c9<>8 r1c5=8 r1c5<>3
r1c9=9 r1c9<>3
Locked Candidates Type 1 (Pointing): 9 in b3 => r3c4<>9
Forcing Net Contradiction in r7c7 => r3c2<>3
r3c2=3 (r1c3<>3) r3c2<>2 r1c1=2 (r1c4<>2) r1c6<>2 r1c6=9 r1c4<>9 r1c4=4 r1c3<>4 r1c3=1 (r2c1<>1) r1c3<>4 r1c4=4 r2c6<>4 r2c6=6 r2c1<>6 r2c1=3 r3c2<>3
Forcing Net Contradiction in c1 => r6c2<>6
r6c2=6 (r5c3<>6 r5c5=6 r4c4<>6) (r6c4<>6) r6c6<>6 r2c6=6 (r2c4<>6) r3c4<>6 r8c4=6 r8c4<>9 r7c46=9 r7c1<>9
r6c2=6 (r6c6<>6 r2c6=6 r3c4<>6 r3c3=6 r9c3<>6 r9c1=6 r9c1<>5) (r6c2<>1) (r5c2<>6) r5c3<>6 r5c5=6 r5c5<>7 r6c4=7 r6c4<>1 r6c1=1 r6c1<>5 r8c1=5 r8c1<>9
r6c2=6 (r9c2<>6) (r5c3<>6 r5c5=6 r9c5<>6) (r3c2<>6) (r5c3<>6 r5c5=6 r3c5<>6) r6c6<>6 r2c6=6 r3c4<>6 r3c3=6 r9c3<>6 r9c1=6 r9c1<>9
Forcing Net Contradiction in c1 => r7c7<>2
r7c7=2 (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c1<>6
r7c7=2 (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>6 r6c8=6 r6c1<>6
r7c7=2 (r7c6<>2 r7c6=9 r8c4<>9) (r7c6<>2 r7c6=9 r7c8<>9) (r4c7<>2) r5c7<>2 r5c5=2 (r4c4<>2) r4c5<>2 r4c8=2 r4c8<>9 r9c8=9 (r8c7<>9) r8c9<>9 r8c1=9 r8c1<>6
r7c7=2 (r5c7<>2 r5c5=2 r9c5<>2) (r9c8<>2) (r5c7<>2 r5c5=2 r3c5<>2) r7c6<>2 r1c6=2 r3c4<>2 r3c2=2 r9c2<>2 r9c1=2 r9c1<>6
Forcing Net Contradiction in r3 => r7c7<>9
r7c7=9 (r7c7<>7 r9c9=7 r5c9<>7 r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) (r7c8<>9) r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 (r3c4<>6) r3c5<>6 r3c2=6 r3c2<>2
r7c7=9 (r3c7<>9 r3c9=9 r3c9<>5) (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r7c8=8 r2c8<>8 r2c8=5 r3c7<>5 r3c4=5 r3c4<>2
r7c7=9 (r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6) (r7c8<>9) r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 (r6c4<>6) r6c6<>6 r2c6=6 (r2c4<>6) r3c4<>6 r4c4=6 r4c4<>2 r45c5=2 r3c5<>2
Brute Force: r5c7=2
Finned Swordfish: 2 r348 c245 fr8c1 => r9c2<>2
Almost Locked Set XY-Wing: A=r2c6 {46}, B=r14678c4 {124679}, C=r5c5,r6c6 {467}, X,Y=4,7, Z=6 => r23c4<>6
Finned Swordfish: 6 r359 c235 fr9c1 => r8c23<>6
Forcing Net Contradiction in r7c8 => r3c4<>2
r3c4=2 (r3c4<>7) r3c4<>5 r2c4=5 r2c4<>7 r6c4=7 (r6c4<>6) r5c5<>7 r5c5=6 r4c4<>6 r8c4=6 r8c4<>9 r7c46=9 r7c8<>9
r3c4=2 (r1c6<>2 r7c6=2 r7c8<>2) r3c4<>5 r2c4=5 r2c8<>5 r2c8=8 r7c8<>8 r7c8=9
Almost Locked Set XZ-Rule: A=r3c479 {3579}, B=r34589c5 {123467}, X=3, Z=7 => r2c5<>7
Forcing Chain Verity => r4c3<>6
r3c2=6 r3c2<>2 r3c5=2 r3c5<>7 r5c5=7 r5c5<>6 r5c23=6 r4c3<>6
r3c3=6 r4c3<>6
r3c5=6 r5c5<>6 r5c23=6 r4c3<>6
Forcing Net Contradiction in r9c5 => r4c2<>6
r4c2=6 (r9c2<>6) (r5c2<>6) r5c3<>6 r5c5=6 r5c5<>7 r3c5=7 r2c4<>7 r2c2=7 r9c2<>7 r9c2=1 r9c5<>1
r4c2=6 (r4c2<>9 r5c2=9 r5c9<>9 r5c9=7 r6c7<>7 r7c7=7 r7c7<>8) (r5c2<>6) r5c3<>6 (r5c3=8 r7c3<>8) r5c5=6 r5c5<>7 r3c5=7 (r2c4<>7) r3c4<>7 r3c4=5 r2c4<>5 r2c4=4 (r7c4<>4) r1c4<>4 r1c3=4 r7c3<>4 r7c2=4 r7c2<>8 r7c8=8 r7c8<>2 r9c8=2 r9c5<>2
r4c2=6 (r5c2<>6) r5c3<>6 r5c5=6 r9c5<>6
Forcing Net Contradiction in c8 => r5c5=7
r5c5<>7 r5c5=6 (r4c4<>6) r4c5<>6 r4c8=6
r5c5<>7 (r5c5=6 r5c3<>6 r5c3=8 r7c3<>8) (r5c9=7 r6c7<>7 r7c7=7 r7c7<>8) r3c5=7 (r2c4<>7) r3c4<>7 r3c4=5 r2c4<>5 r2c4=4 (r7c4<>4) r1c4<>4 r1c3=4 r7c3<>4 r7c2=4 r7c2<>8 r7c8=8 (r6c8<>8) r2c8<>8 r2c8=5 r6c8<>5 r6c8=6
Locked Candidates Type 2 (Claiming): 6 in r5 => r6c1<>6
Hidden Pair: 5,7 in r23c4 => r2c4<>4
Almost Locked Set XY-Wing: A=r6c46 {146}, B=r8c379 {1589}, C=r2679c8 {25689}, X,Y=6,9, Z=1 => r8c4<>1
Forcing Net Verity => r2c2<>6
r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c2<>6
r7c8=9 (r7c4<>9) r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6 r89c5=6 r23c5<>6 r2c6=6 r2c2<>6
r9c8=9 (r9c1<>9) (r8c7<>9) (r8c9<>9) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r8c4<>9 r8c1=9 r8c1<>2 r9c1=2 (r9c1<>6) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r7c1<>9 r8c1=9 r8c1<>6 r2c1=6 r2c2<>6
Forcing Net Verity => r2c5<>6
r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r2c5<>6
r7c8=9 (r7c4<>9) r7c6<>9 r1c6=9 r1c4<>9 r8c4=9 r8c4<>6 r89c5=6 r2c5<>6
r9c8=9 (r9c1<>9) (r8c7<>9) (r8c9<>9) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r8c4<>9 r8c1=9 r8c1<>2 r9c1=2 (r9c1<>6) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 (r1c6=2 r1c1<>2) r7c6=9 r7c1<>9 r8c1=9 r8c1<>6 r2c1=6 r2c5<>6
Forcing Net Verity => r4c4<>4
r7c4=1 (r8c5<>1) r9c5<>1 r4c5=1 r4c5<>2 r4c4=2 r4c4<>4
r7c4=2 (r4c4<>2 r4c5=2 r4c5<>6) (r7c6<>2 r7c6=9 r7c8<>9) r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r4c4=6 r4c4<>4
r7c4=4 r4c4<>4
r7c4=9 (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 r6c6<>6 r6c6=4 r4c4<>4
Forcing Net Contradiction in r6 => r4c9<>9
r4c9=9 (r3c9<>9 r3c7=9 r8c7<>9) (r8c9<>9) (r4c8<>9) r4c9<>4 r4c5=4 (r6c6<>4 r2c6=4 r1c4<>4) r4c5<>2 r4c4=2 r1c4<>2 r1c4=9 r1c6<>9 (r1c6=2 r1c1<>2) r7c6=9 r7c8<>9 r9c8=9 r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 r7c6=9 r8c4<>9 r8c1=9 (r9c1<>9) r8c1<>2 r9c1=2 (r9c1<>5) r9c8<>2 r7c8=2 (r7c1<>2) r7c6<>2 r7c6=9 r7c1<>9 r8c1=9 (r9c1<>9) r8c1<>5 r6c1=5
r4c9=9 (r5c9<>9 r5c9=8 r6c8<>8) r4c9<>4 r4c5=4 r6c6<>4 r6c6=6 r6c8<>6 r6c8=5
Forcing Net Contradiction in r7c7 => r7c1<>2
r7c1=2 (r7c6<>2 r7c6=9 r7c8<>9) r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 (r5c9<>9 r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r3c5<>6 r3c2=6 r3c2<>2 r8c2=2 r7c1<>2
Forcing Net Contradiction in r7c4 => r7c1<>9
r7c1=9 (r7c8<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r4c8=9 r4c8<>6 r6c8=6 (r6c4<>6) r6c6<>6 r6c6=4 r6c4<>4 r6c4=1 r7c4<>1
r7c1=9 r7c6<>9 r7c6=2 r7c4<>2
r7c1=9 (r9c1<>9) r7c6<>9 r7c6=2 r7c8<>2 r9c8=2 r9c8<>9 r9c9=9 r5c9<>9 (r5c9=8 r5c3<>8 r5c3=6 r3c3<>6) r5c2=9 r4c2<>9 r4c8=9 (r4c7<>9) r4c8<>6 r6c8=6 r6c6<>6 r2c6=6 r3c5<>6 r3c2=6 r3c2<>2 r3c5=2 (r1c4<>2) r1c6<>2 r1c6=9 r1c4<>9 r1c4=4 r7c4<>4
r7c1=9 r7c4<>9
Almost Locked Set XZ-Rule: A=r3c23479 {235679}, B=r1267c1 {12356}, X=2,6 => r3c5<>3, r89c1<>1, r4c3,r6c789,r89c1<>5
Hidden Single: r6c1=5
Hidden Pair: 3,8 in r12c5 => r2c5<>4
AIC: 5 5- r2c8 -8- r6c8 -6- r6c6 -4- r2c6 =4= r2c2 =7= r2c4 =5= r3c4 -5 => r2c4,r3c79<>5
Naked Single: r2c4=7
Naked Single: r3c4=5
Locked Pair: 3,9 in r3c79 => r1c9,r2c7,r3c3<>3
Discontinuous Nice Loop: 6 r4c4 -6- r6c6 =6= r2c6 -6- r3c5 -2- r4c5 =2= r4c4 => r4c4<>6
AIC: 4/6 6- r8c4 =6= r6c4 -6- r6c6 -4- r4c5 =4= r8c5 -4 => r8c4<>4, r8c5<>6
Discontinuous Nice Loop: 3 r4c9 -3- r3c9 -9- r5c9 -8- r6c8 -6- r6c6 -4- r6c9 =4= r4c9 => r4c9<>3
Discontinuous Nice Loop: 7 r7c3 -7- r3c3 -6- r3c5 =6= r2c6 =4= r2c2 -4- r1c3 =4= r7c3 => r7c3<>7
Discontinuous Nice Loop: 2 r8c4 -2- r8c2 =2= r3c2 -2- r3c5 -6- r9c5 =6= r8c4 => r8c4<>2
Discontinuous Nice Loop: 5 r9c8 -5- r2c8 -8- r6c8 -6- r6c6 =6= r2c6 -6- r3c5 -2- r1c6 =2= r7c6 -2- r7c8 =2= r9c8 => r9c8<>5
Almost Locked Set XY-Wing: A=r9c18 {269}, B=r2c6,r3c5 {246}, C=r2c12578 {134568}, X,Y=4,6, Z=2 => r9c5<>2
Discontinuous Nice Loop: 1 r8c5 -1- r9c5 -6- r3c5 -2- r3c2 =2= r8c2 =4= r8c5 => r8c5<>1
2-String Kite: 1 in r6c2,r9c5 (connected by r4c5,r6c4) => r9c2<>1
W-Wing: 7/6 in r3c3,r9c2 connected by 6 in r5c23 => r3c2,r9c3<>7
Hidden Single: r3c3=7
AIC: 9 9- r3c7 -3- r3c9 =3= r6c9 =7= r9c9 -7- r9c2 -6- r3c2 =6= r3c5 -6- r4c5 =6= r4c8 -6- r6c8 -8- r5c9 -9 => r3c9,r4c7<>9
Naked Single: r3c9=3
Naked Single: r3c7=9
Discontinuous Nice Loop: 8 r6c9 -8- r6c8 -6- r6c6 =6= r2c6 -6- r2c1 =6= r3c2 -6- r9c2 -7- r9c9 =7= r6c9 => r6c9<>8
Almost Locked Set XY-Wing: A=r14c3 {134}, B=r1239c5 {12368}, C=r1c46 {249}, X,Y=2,4, Z=1 => r9c3<>1
Almost Locked Set XY-Wing: A=r4c234 {1239}, B=r7c68 {289}, C=r246c8 {5689}, X,Y=8,9, Z=2 => r7c4<>2
Almost Locked Set XY-Wing: A=r8c379 {1589}, B=r4c23,r56c2 {13689}, C=r5c39 {689}, X,Y=6,9, Z=8 => r8c2<>8
Almost Locked Set Chain: 2- r1c1359 {12348} -4- r1c46 {249} -2- r3c5 {26} -6- r4c234579 {1234569} -9- r5c23 {689} -8- r5c9 {89} -9- r8c23579 {124589} -2 => r8c1<>2
Naked Pair: 6,9 in r8c14 => r8c9<>9
Naked Triple: 1,5,8 in r8c379 => r8c2<>1
X-Wing: 2 r38 c25 => r4c5<>2
Hidden Single: r4c4=2
Sue de Coq: r78c4 - {1469} (r1c4 - {49}, r9c5 - {16}) => r6c4<>4
X-Wing: 4 c34 r17 => r7c2<>4
AIC: 6 6- r5c3 =6= r5c2 -6- r3c2 =6= r3c5 -6- r2c6 -4- r6c6 =4= r6c9 =7= r9c9 -7- r9c2 -6 => r5c2,r9c3<>6
Naked Single: r9c3=5
Hidden Single: r5c3=6
Locked Candidates Type 1 (Pointing): 8 in b4 => r7c2<>8
Discontinuous Nice Loop: 3 r2c2 -3- r6c2 =3= r6c7 =7= r6c9 =4= r6c6 -4- r2c6 =4= r2c2 => r2c2<>3
AIC: 1 1- r6c4 =1= r7c4 -1- r7c1 -3- r2c1 =3= r2c5 =8= r1c5 -8- r1c9 -1- r9c9 =1= r9c5 -1 => r4c5,r7c4<>1
Hidden Single: r9c5=1
Hidden Single: r6c4=1
Hidden Single: r8c4=6
Naked Single: r8c1=9
Locked Candidates Type 1 (Pointing): 9 in b8 => r7c8<>9
XY-Chain: 1 1- r1c9 -8- r5c9 -9- r9c9 -7- r9c2 -6- r9c1 -2- r8c2 -4- r2c2 -1 => r1c13,r2c7<>1
Hidden Single: r1c9=1
Hidden Single: r1c5=8
Naked Single: r2c5=3
W-Wing: 1/3 in r4c3,r7c1 connected by 3 in r1c13 => r78c3<>1
Naked Single: r8c3=8
Naked Single: r8c9=5
Naked Single: r4c9=4
Naked Single: r8c7=1
Naked Single: r4c5=6
Full House: r6c6=4
Naked Single: r6c9=7
Naked Single: r3c5=2
Full House: r3c2=6
Full House: r8c5=4
Full House: r8c2=2
Naked Single: r2c6=6
Naked Single: r9c9=9
Full House: r5c9=8
Full House: r5c2=9
Naked Single: r1c6=9
Full House: r1c4=4
Full House: r7c4=9
Full House: r7c6=2
Naked Single: r2c1=1
Naked Single: r9c2=7
Naked Single: r9c1=6
Full House: r9c8=2
Naked Single: r6c7=3
Naked Single: r6c8=6
Full House: r6c2=8
Naked Single: r1c3=3
Full House: r1c1=2
Full House: r2c2=4
Full House: r7c1=3
Naked Single: r7c8=8
Full House: r7c7=7
Naked Single: r4c7=5
Full House: r2c7=8
Full House: r2c8=5
Full House: r4c8=9
Naked Single: r4c3=1
Full House: r7c3=4
Full House: r7c2=1
Full House: r4c2=3
|
sudoku_normal_hard_122
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....54....98....3.4..3.86....5..798.92687....7..9...61....8.3.93..1.6..2.43....1
|
783265419629841573541739862416523798392687145875194326167958234938412657254376981
|
. . . . . 5 4 . .
. . 9 8 . . . . 3
. 4 . . 3 . 8 6 .
. . . 5 . . 7 9 8
. 9 2 6 8 7 . . .
. 7 . . 9 . . . 6
1 . . . . 8 . 3 .
9 3 . . 1 . 6 . .
2 . 4 3 . . . . 1
|
7 8 3 2 6 5 4 1 9
6 2 9 8 4 1 5 7 3
5 4 1 7 3 9 8 6 2
4 1 6 5 2 3 7 9 8
3 9 2 6 8 7 1 4 5
8 7 5 1 9 4 3 2 6
1 6 7 9 5 8 2 3 4
9 3 8 4 1 2 6 5 7
2 5 4 3 7 6 9 8 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5280_hard
|
783265419629841573541739862416523798392687145875194326167958234938412657254376981 #1 Extreme (25748) bf
Brute Force: r5c5=8
Hidden Single: r5c6=7
Forcing Net Contradiction in c8 => r4c9<>4
r4c9=4 (r6c8<>4 r8c8=4 r8c8<>5) (r5c8<>4) r5c9<>4 (r5c9=5 r5c2<>5) (r5c9=5 r8c9<>5) r5c1=4 r5c1<>9 r8c1=9 r8c1<>5 r8c3=5 (r7c2<>5) r9c2<>5 r2c2=5 r2c8<>5
r4c9=4 r5c9<>4 r5c9=5 r5c8<>5
r4c9=4 r5c9<>4 r5c9=5 r6c8<>5
r4c9=4 (r5c8<>4) r6c8<>4 r8c8=4 r8c8<>5
r4c9=4 (r6c8<>4 r8c8=4 r8c4<>4) (r6c8<>4 r8c8=4 r8c6<>4) (r5c8<>4) r5c9<>4 r5c1=4 r5c1<>9 r8c1=9 (r8c4<>9) r8c6<>9 r8c6=2 r8c4<>2 r8c4=7 r9c5<>7 r9c8=7 r9c8<>5
Brute Force: r5c2=9
Hidden Single: r8c1=9
Locked Candidates Type 1 (Pointing): 7 in b7 => r13c3<>7
Locked Candidates Type 2 (Claiming): 1 in r5 => r6c78<>1
W-Wing: 2/4 in r4c5,r8c6 connected by 4 in r2c56 => r46c6,r7c5<>2
Discontinuous Nice Loop: 8 r1c9 -8- r4c9 -2- r4c5 -4- r2c5 =4= r2c6 =6= r9c6 =9= r3c6 -9- r1c4 =9= r1c9 => r1c9<>8
Almost Locked Set XZ-Rule: A=r7c235 {4567}, B=r8c46 {247}, X=4, Z=7 => r7c4<>7
Almost Locked Set XY-Wing: A=r7c235 {4567}, B=r9c2678 {56789}, C=r1249c5 {24567}, X,Y=4,5, Z=7 => r7c9<>7
Forcing Chain Contradiction in c8 => r4c5=2
r4c5<>2 r12c5=2 r3c46<>2 r3c79=2 r1c8<>2
r4c5<>2 r12c5=2 r3c46<>2 r3c79=2 r2c8<>2
r4c5<>2 r4c9=2 r6c8<>2
r4c5<>2 r6c4=2 r7c4<>2 r7c79=2 r8c8<>2
Naked Single: r4c9=8
Skyscraper: 8 in r1c2,r3c7 (connected by r9c27) => r1c8,r3c13<>8
Hidden Single: r3c7=8
Locked Candidates Type 1 (Pointing): 9 in b3 => r7c9<>9
AIC: 6 6- r7c2 -5- r7c5 =5= r9c5 -5- r9c7 -9- r9c6 -6 => r7c5,r9c2<>6
Discontinuous Nice Loop: 6 r1c2 -6- r1c5 -7- r7c5 =7= r7c3 =6= r7c2 -6- r1c2 => r1c2<>6
Discontinuous Nice Loop: 7 r1c9 -7- r1c5 -6- r9c5 =6= r9c6 =9= r3c6 -9- r3c9 =9= r1c9 => r1c9<>7
AIC: 1 1- r3c3 -5- r3c1 -7- r3c9 =7= r8c9 -7- r8c3 =7= r7c3 =6= r7c2 -6- r4c2 -1 => r12c2,r46c3<>1
Hidden Single: r4c2=1
AIC: 9 9- r1c9 -2- r1c2 -8- r9c2 -5- r9c7 -9- r9c6 =9= r3c6 -9 => r1c4,r3c9<>9
Hidden Single: r1c9=9
Discontinuous Nice Loop: 1 r3c6 -1- r3c3 -5- r3c1 -7- r3c9 =7= r8c9 -7- r9c8 =7= r9c5 =6= r9c6 =9= r3c6 => r3c6<>1
AIC: 3/6 3- r1c3 =3= r1c1 -3- r5c1 =3= r5c7 =1= r2c7 -1- r2c6 =1= r6c6 =3= r4c6 -3- r4c3 -6 => r4c3<>3, r1c3<>6
Naked Single: r4c3=6
Hidden Single: r7c2=6
AIC: 3/4 4- r4c1 -3- r5c1 =3= r5c7 =1= r2c7 -1- r2c6 =1= r6c6 =3= r4c6 -3 => r4c1<>3, r4c6<>4
Naked Single: r4c1=4
Full House: r4c6=3
Locked Candidates Type 1 (Pointing): 4 in b5 => r6c8<>4
Discontinuous Nice Loop: 2/4 r7c4 =9= r7c7 -9- r9c7 -5- r9c2 =5= r2c2 -5- r3c1 -7- r3c9 =7= r8c9 -7- r9c8 =7= r9c5 =6= r9c6 =9= r7c4 => r7c4<>2, r7c4<>4
Naked Single: r7c4=9
Naked Single: r9c6=6
Hidden Single: r3c6=9
Hidden Single: r9c7=9
Locked Candidates Type 1 (Pointing): 2 in b8 => r8c89<>2
XYZ-Wing: 2/4/5 in r57c9,r7c7 => r8c9<>5
Naked Triple: 2,4,7 in r8c469 => r8c38<>7, r8c8<>4
Hidden Single: r7c3=7
Hidden Single: r5c8=4
Naked Single: r5c9=5
Naked Single: r5c1=3
Full House: r5c7=1
Naked Single: r6c8=2
Full House: r6c7=3
Hidden Single: r1c3=3
Hidden Single: r3c3=1
Hidden Single: r3c1=5
Naked Single: r2c2=2
Naked Single: r6c1=8
Full House: r6c3=5
Full House: r8c3=8
Full House: r9c2=5
Full House: r1c2=8
Naked Single: r2c7=5
Full House: r7c7=2
Naked Single: r8c8=5
Naked Single: r9c5=7
Full House: r9c8=8
Naked Single: r7c9=4
Full House: r7c5=5
Full House: r8c9=7
Full House: r3c9=2
Full House: r3c4=7
Naked Single: r1c5=6
Full House: r2c5=4
Naked Single: r1c1=7
Full House: r2c1=6
Naked Single: r2c6=1
Full House: r1c4=2
Full House: r1c8=1
Full House: r2c8=7
Naked Single: r6c6=4
Full House: r6c4=1
Full House: r8c4=4
Full House: r8c6=2
|
sudoku_normal_extremely_hard_122
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....54....98....3.4..3..6....5..79...26......7..9...61....8.3..3..1.6..2.43....1
|
783265419629841573541739862416523798392687145875194326167958234938412657254376981
|
. . . . . 5 4 . .
. . 9 8 . . . . 3
. 4 . . 3 . . 6 .
. . . 5 . . 7 9 .
. . 2 6 . . . . .
. 7 . . 9 . . . 6
1 . . . . 8 . 3 .
. 3 . . 1 . 6 . .
2 . 4 3 . . . . 1
|
7 8 3 2 6 5 4 1 9
6 2 9 8 4 1 5 7 3
5 4 1 7 3 9 8 6 2
4 1 6 5 2 3 7 9 8
3 9 2 6 8 7 1 4 5
8 7 5 1 9 4 3 2 6
1 6 7 9 5 8 2 3 4
9 3 8 4 1 2 6 5 7
2 5 4 3 7 6 9 8 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5280_hard
|
783265419629841573541739862416523798392687145875194326167958234938412657254376981 #1 Extreme (25748) bf
Brute Force: r5c5=8
Hidden Single: r5c6=7
Forcing Net Contradiction in c8 => r4c9<>4
r4c9=4 (r6c8<>4 r8c8=4 r8c8<>5) (r5c8<>4) r5c9<>4 (r5c9=5 r5c2<>5) (r5c9=5 r8c9<>5) r5c1=4 r5c1<>9 r8c1=9 r8c1<>5 r8c3=5 (r7c2<>5) r9c2<>5 r2c2=5 r2c8<>5
r4c9=4 r5c9<>4 r5c9=5 r5c8<>5
r4c9=4 r5c9<>4 r5c9=5 r6c8<>5
r4c9=4 (r5c8<>4) r6c8<>4 r8c8=4 r8c8<>5
r4c9=4 (r6c8<>4 r8c8=4 r8c4<>4) (r6c8<>4 r8c8=4 r8c6<>4) (r5c8<>4) r5c9<>4 r5c1=4 r5c1<>9 r8c1=9 (r8c4<>9) r8c6<>9 r8c6=2 r8c4<>2 r8c4=7 r9c5<>7 r9c8=7 r9c8<>5
Brute Force: r5c2=9
Hidden Single: r8c1=9
Locked Candidates Type 1 (Pointing): 7 in b7 => r13c3<>7
Locked Candidates Type 2 (Claiming): 1 in r5 => r6c78<>1
W-Wing: 2/4 in r4c5,r8c6 connected by 4 in r2c56 => r46c6,r7c5<>2
Discontinuous Nice Loop: 8 r1c9 -8- r4c9 -2- r4c5 -4- r2c5 =4= r2c6 =6= r9c6 =9= r3c6 -9- r1c4 =9= r1c9 => r1c9<>8
Almost Locked Set XZ-Rule: A=r7c235 {4567}, B=r8c46 {247}, X=4, Z=7 => r7c4<>7
Almost Locked Set XY-Wing: A=r7c235 {4567}, B=r9c2678 {56789}, C=r1249c5 {24567}, X,Y=4,5, Z=7 => r7c9<>7
Forcing Chain Contradiction in c8 => r4c5=2
r4c5<>2 r12c5=2 r3c46<>2 r3c79=2 r1c8<>2
r4c5<>2 r12c5=2 r3c46<>2 r3c79=2 r2c8<>2
r4c5<>2 r4c9=2 r6c8<>2
r4c5<>2 r6c4=2 r7c4<>2 r7c79=2 r8c8<>2
Naked Single: r4c9=8
Skyscraper: 8 in r1c2,r3c7 (connected by r9c27) => r1c8,r3c13<>8
Hidden Single: r3c7=8
Locked Candidates Type 1 (Pointing): 9 in b3 => r7c9<>9
AIC: 6 6- r7c2 -5- r7c5 =5= r9c5 -5- r9c7 -9- r9c6 -6 => r7c5,r9c2<>6
Discontinuous Nice Loop: 6 r1c2 -6- r1c5 -7- r7c5 =7= r7c3 =6= r7c2 -6- r1c2 => r1c2<>6
Discontinuous Nice Loop: 7 r1c9 -7- r1c5 -6- r9c5 =6= r9c6 =9= r3c6 -9- r3c9 =9= r1c9 => r1c9<>7
AIC: 1 1- r3c3 -5- r3c1 -7- r3c9 =7= r8c9 -7- r8c3 =7= r7c3 =6= r7c2 -6- r4c2 -1 => r12c2,r46c3<>1
Hidden Single: r4c2=1
AIC: 9 9- r1c9 -2- r1c2 -8- r9c2 -5- r9c7 -9- r9c6 =9= r3c6 -9 => r1c4,r3c9<>9
Hidden Single: r1c9=9
Discontinuous Nice Loop: 1 r3c6 -1- r3c3 -5- r3c1 -7- r3c9 =7= r8c9 -7- r9c8 =7= r9c5 =6= r9c6 =9= r3c6 => r3c6<>1
AIC: 3/6 3- r1c3 =3= r1c1 -3- r5c1 =3= r5c7 =1= r2c7 -1- r2c6 =1= r6c6 =3= r4c6 -3- r4c3 -6 => r4c3<>3, r1c3<>6
Naked Single: r4c3=6
Hidden Single: r7c2=6
AIC: 3/4 4- r4c1 -3- r5c1 =3= r5c7 =1= r2c7 -1- r2c6 =1= r6c6 =3= r4c6 -3 => r4c1<>3, r4c6<>4
Naked Single: r4c1=4
Full House: r4c6=3
Locked Candidates Type 1 (Pointing): 4 in b5 => r6c8<>4
Discontinuous Nice Loop: 2/4 r7c4 =9= r7c7 -9- r9c7 -5- r9c2 =5= r2c2 -5- r3c1 -7- r3c9 =7= r8c9 -7- r9c8 =7= r9c5 =6= r9c6 =9= r7c4 => r7c4<>2, r7c4<>4
Naked Single: r7c4=9
Naked Single: r9c6=6
Hidden Single: r3c6=9
Hidden Single: r9c7=9
Locked Candidates Type 1 (Pointing): 2 in b8 => r8c89<>2
XYZ-Wing: 2/4/5 in r57c9,r7c7 => r8c9<>5
Naked Triple: 2,4,7 in r8c469 => r8c38<>7, r8c8<>4
Hidden Single: r7c3=7
Hidden Single: r5c8=4
Naked Single: r5c9=5
Naked Single: r5c1=3
Full House: r5c7=1
Naked Single: r6c8=2
Full House: r6c7=3
Hidden Single: r1c3=3
Hidden Single: r3c3=1
Hidden Single: r3c1=5
Naked Single: r2c2=2
Naked Single: r6c1=8
Full House: r6c3=5
Full House: r8c3=8
Full House: r9c2=5
Full House: r1c2=8
Naked Single: r2c7=5
Full House: r7c7=2
Naked Single: r8c8=5
Naked Single: r9c5=7
Full House: r9c8=8
Naked Single: r7c9=4
Full House: r7c5=5
Full House: r8c9=7
Full House: r3c9=2
Full House: r3c4=7
Naked Single: r1c5=6
Full House: r2c5=4
Naked Single: r1c1=7
Full House: r2c1=6
Naked Single: r2c6=1
Full House: r1c4=2
Full House: r1c8=1
Full House: r2c8=7
Naked Single: r6c6=4
Full House: r6c4=1
Full House: r8c4=4
Full House: r8c6=2
|
sudoku_normal_hard_123
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..1.3.8..9....2.6..2......427..5..3...467...8...2..7...1..69.....7..56..6..3.7.5.
|
561734829948512367723986514279458136154673298836291745315869472497125683682347951
|
. . 1 . 3 . 8 . .
9 . . . . 2 . 6 .
. 2 . . . . . . 4
2 7 . . 5 . . 3 .
. . 4 6 7 . . . 8
. . . 2 . . 7 . .
. 1 . . 6 9 . . .
. . 7 . . 5 6 . .
6 . . 3 . 7 . 5 .
|
5 6 1 7 3 4 8 2 9
9 4 8 5 1 2 3 6 7
7 2 3 9 8 6 5 1 4
2 7 9 4 5 8 1 3 6
1 5 4 6 7 3 2 9 8
8 3 6 2 9 1 7 4 5
3 1 5 8 6 9 4 7 2
4 9 7 1 2 5 6 8 3
6 8 2 3 4 7 9 5 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3989_hard
|
561734829948512367723986514279458136154673298836291745315869472497125683682347951 #1 Extreme (16140) bf
Discontinuous Nice Loop: 5 r1c9 -5- r6c9 =5= r5c7 =2= r5c8 -2- r1c8 =2= r1c9 => r1c9<>5
Brute Force: r5c5=7
Hidden Single: r4c2=7
Skyscraper: 7 in r2c4,r9c6 (connected by r29c9) => r13c6,r7c4<>7
Hidden Single: r9c6=7
Forcing Chain Contradiction in c8 => r6c5<>1
r6c5=1 r456c6<>1 r3c6=1 r3c8<>1
r6c5=1 r6c1<>1 r5c1=1 r5c8<>1
r6c5=1 r6c8<>1
r6c5=1 r9c5<>1 r8c45=1 r8c8<>1
Forcing Chain Contradiction in r9 => r6c5<>4
r6c5=4 r46c6<>4 r1c6=4 r1c1<>4 r78c1=4 r9c2<>4
r6c5=4 r9c5<>4
r6c5=4 r6c8<>4 r4c7=4 r9c7<>4
Forcing Chain Contradiction in c1 => r6c5=9
r6c5<>9 r6c5=8 r46c6<>8 r3c6=8 r3c1<>8
r6c5<>9 r6c5=8 r6c1<>8
r6c5<>9 r6c5=8 r9c5<>8 r9c23=8 r7c1<>8
r6c5<>9 r6c5=8 r9c5<>8 r9c23=8 r8c1<>8
Hidden Triple: 5,7,9 in r123c4 => r12c4<>4, r13c4<>6, r23c4<>1, r23c4<>8
Locked Candidates Type 1 (Pointing): 6 in b2 => r456c6<>6
Almost Locked Set XZ-Rule: A=r5c1246 {13569}, B=r78c1,r89c2 {34589}, X=9, Z=5 => r6c1<>5
Almost Locked Set XZ-Rule: A=r5c146 {1356}, B=r6c12368 {134568}, X=5, Z=6 => r5c2<>6
Hidden Single: r5c4=6
Almost Locked Set Chain: 1- r5c16 {135} -5- r7c14789 {234578} -2- r23467c3 {235689} -9- r4c7,r6c8 {149} -1 => r5c78<>1
Forcing Chain Verity => r2c5<>8
r3c8=1 r3c5<>1 r3c5=8 r2c5<>8
r6c8=1 r6c8<>4 r6c6=4 r1c6<>4 r2c5=4 r2c5<>8
r8c8=1 r8c4<>1 r89c5=1 r3c5<>1 r3c5=8 r2c5<>8
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c13<>8
Finned Swordfish: 8 c148 r478 fr6c1 => r4c3<>8
Locked Candidates Type 1 (Pointing): 8 in b4 => r6c6<>8
Sue de Coq: r4c79 - {1469} (r4c3 - {69}, r6c8 - {14}) => r6c9<>1
Empty Rectangle: 1 in b6 (r48c4) => r8c8<>1
Discontinuous Nice Loop: 4 r4c6 -4- r4c7 =4= r6c8 =1= r3c8 -1- r3c5 -8- r3c6 =8= r4c6 => r4c6<>4
Grouped Discontinuous Nice Loop: 3/5 r5c1 =1= r5c6 -1- r4c6 -8- r4c4 =8= r78c4 -8- r9c5 =8= r9c23 -8- r78c1 =8= r6c1 =1= r5c1 => r5c1<>3, r5c1<>5
Naked Single: r5c1=1
Naked Single: r5c6=3
2-String Kite: 5 in r2c9,r5c2 (connected by r5c7,r6c9) => r2c2<>5
Discontinuous Nice Loop: 5 r1c2 -5- r5c2 -9- r4c3 -6- r3c3 =6= r1c2 => r1c2<>5
Locked Candidates Type 2 (Claiming): 5 in c2 => r6c3<>5
Naked Pair: 4,6 in r1c26 => r1c1<>4
Locked Candidates Type 1 (Pointing): 4 in b1 => r89c2<>4
Skyscraper: 4 in r4c4,r9c5 (connected by r49c7) => r78c4<>4
Naked Single: r7c4=8
Naked Single: r8c4=1
Naked Single: r4c4=4
Naked Single: r6c6=1
Full House: r4c6=8
Naked Single: r6c8=4
Naked Single: r3c6=6
Full House: r1c6=4
Naked Single: r1c2=6
Naked Single: r2c5=1
Naked Single: r3c5=8
Hidden Single: r8c8=8
Hidden Single: r3c8=1
Hidden Single: r2c2=4
Hidden Single: r6c1=8
Hidden Single: r2c3=8
Hidden Single: r9c2=8
Locked Candidates Type 1 (Pointing): 3 in b1 => r3c7<>3
2-String Kite: 9 in r4c3,r8c9 (connected by r8c2,r9c3) => r4c9<>9
W-Wing: 5/7 in r1c1,r2c4 connected by 7 in r3c14 => r1c4<>5
Hidden Single: r1c1=5
Naked Single: r3c3=3
Full House: r3c1=7
Naked Single: r6c3=6
Naked Single: r4c3=9
Naked Single: r6c9=5
Full House: r6c2=3
Full House: r5c2=5
Full House: r8c2=9
Naked Single: r4c7=1
Full House: r4c9=6
Naked Single: r9c3=2
Full House: r7c3=5
Naked Single: r9c5=4
Full House: r8c5=2
Naked Single: r9c7=9
Full House: r9c9=1
Naked Single: r8c9=3
Full House: r8c1=4
Full House: r7c1=3
Naked Single: r3c7=5
Full House: r3c4=9
Naked Single: r5c7=2
Full House: r5c8=9
Naked Single: r2c9=7
Naked Single: r2c7=3
Full House: r7c7=4
Full House: r2c4=5
Full House: r1c4=7
Naked Single: r1c8=2
Full House: r1c9=9
Full House: r7c9=2
Full House: r7c8=7
|
sudoku_normal_extremely_hard_123
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..1.3.8..9....2.6..2......42...5..3...4.....8...2..7...1..69.....7..56..6..3...5.
|
561734829948512367723986514279458136154673298836291745315869472497125683682347951
|
. . 1 . 3 . 8 . .
9 . . . . 2 . 6 .
. 2 . . . . . . 4
2 . . . 5 . . 3 .
. . 4 . . . . . 8
. . . 2 . . 7 . .
. 1 . . 6 9 . . .
. . 7 . . 5 6 . .
6 . . 3 . . . 5 .
|
5 6 1 7 3 4 8 2 9
9 4 8 5 1 2 3 6 7
7 2 3 9 8 6 5 1 4
2 7 9 4 5 8 1 3 6
1 5 4 6 7 3 2 9 8
8 3 6 2 9 1 7 4 5
3 1 5 8 6 9 4 7 2
4 9 7 1 2 5 6 8 3
6 8 2 3 4 7 9 5 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3989_hard
|
561734829948512367723986514279458136154673298836291745315869472497125683682347951 #1 Extreme (16140) bf
Discontinuous Nice Loop: 5 r1c9 -5- r6c9 =5= r5c7 =2= r5c8 -2- r1c8 =2= r1c9 => r1c9<>5
Brute Force: r5c5=7
Hidden Single: r4c2=7
Skyscraper: 7 in r2c4,r9c6 (connected by r29c9) => r13c6,r7c4<>7
Hidden Single: r9c6=7
Forcing Chain Contradiction in c8 => r6c5<>1
r6c5=1 r456c6<>1 r3c6=1 r3c8<>1
r6c5=1 r6c1<>1 r5c1=1 r5c8<>1
r6c5=1 r6c8<>1
r6c5=1 r9c5<>1 r8c45=1 r8c8<>1
Forcing Chain Contradiction in r9 => r6c5<>4
r6c5=4 r46c6<>4 r1c6=4 r1c1<>4 r78c1=4 r9c2<>4
r6c5=4 r9c5<>4
r6c5=4 r6c8<>4 r4c7=4 r9c7<>4
Forcing Chain Contradiction in c1 => r6c5=9
r6c5<>9 r6c5=8 r46c6<>8 r3c6=8 r3c1<>8
r6c5<>9 r6c5=8 r6c1<>8
r6c5<>9 r6c5=8 r9c5<>8 r9c23=8 r7c1<>8
r6c5<>9 r6c5=8 r9c5<>8 r9c23=8 r8c1<>8
Hidden Triple: 5,7,9 in r123c4 => r12c4<>4, r13c4<>6, r23c4<>1, r23c4<>8
Locked Candidates Type 1 (Pointing): 6 in b2 => r456c6<>6
Almost Locked Set XZ-Rule: A=r5c1246 {13569}, B=r78c1,r89c2 {34589}, X=9, Z=5 => r6c1<>5
Almost Locked Set XZ-Rule: A=r5c146 {1356}, B=r6c12368 {134568}, X=5, Z=6 => r5c2<>6
Hidden Single: r5c4=6
Almost Locked Set Chain: 1- r5c16 {135} -5- r7c14789 {234578} -2- r23467c3 {235689} -9- r4c7,r6c8 {149} -1 => r5c78<>1
Forcing Chain Verity => r2c5<>8
r3c8=1 r3c5<>1 r3c5=8 r2c5<>8
r6c8=1 r6c8<>4 r6c6=4 r1c6<>4 r2c5=4 r2c5<>8
r8c8=1 r8c4<>1 r89c5=1 r3c5<>1 r3c5=8 r2c5<>8
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c13<>8
Finned Swordfish: 8 c148 r478 fr6c1 => r4c3<>8
Locked Candidates Type 1 (Pointing): 8 in b4 => r6c6<>8
Sue de Coq: r4c79 - {1469} (r4c3 - {69}, r6c8 - {14}) => r6c9<>1
Empty Rectangle: 1 in b6 (r48c4) => r8c8<>1
Discontinuous Nice Loop: 4 r4c6 -4- r4c7 =4= r6c8 =1= r3c8 -1- r3c5 -8- r3c6 =8= r4c6 => r4c6<>4
Grouped Discontinuous Nice Loop: 3/5 r5c1 =1= r5c6 -1- r4c6 -8- r4c4 =8= r78c4 -8- r9c5 =8= r9c23 -8- r78c1 =8= r6c1 =1= r5c1 => r5c1<>3, r5c1<>5
Naked Single: r5c1=1
Naked Single: r5c6=3
2-String Kite: 5 in r2c9,r5c2 (connected by r5c7,r6c9) => r2c2<>5
Discontinuous Nice Loop: 5 r1c2 -5- r5c2 -9- r4c3 -6- r3c3 =6= r1c2 => r1c2<>5
Locked Candidates Type 2 (Claiming): 5 in c2 => r6c3<>5
Naked Pair: 4,6 in r1c26 => r1c1<>4
Locked Candidates Type 1 (Pointing): 4 in b1 => r89c2<>4
Skyscraper: 4 in r4c4,r9c5 (connected by r49c7) => r78c4<>4
Naked Single: r7c4=8
Naked Single: r8c4=1
Naked Single: r4c4=4
Naked Single: r6c6=1
Full House: r4c6=8
Naked Single: r6c8=4
Naked Single: r3c6=6
Full House: r1c6=4
Naked Single: r1c2=6
Naked Single: r2c5=1
Naked Single: r3c5=8
Hidden Single: r8c8=8
Hidden Single: r3c8=1
Hidden Single: r2c2=4
Hidden Single: r6c1=8
Hidden Single: r2c3=8
Hidden Single: r9c2=8
Locked Candidates Type 1 (Pointing): 3 in b1 => r3c7<>3
2-String Kite: 9 in r4c3,r8c9 (connected by r8c2,r9c3) => r4c9<>9
W-Wing: 5/7 in r1c1,r2c4 connected by 7 in r3c14 => r1c4<>5
Hidden Single: r1c1=5
Naked Single: r3c3=3
Full House: r3c1=7
Naked Single: r6c3=6
Naked Single: r4c3=9
Naked Single: r6c9=5
Full House: r6c2=3
Full House: r5c2=5
Full House: r8c2=9
Naked Single: r4c7=1
Full House: r4c9=6
Naked Single: r9c3=2
Full House: r7c3=5
Naked Single: r9c5=4
Full House: r8c5=2
Naked Single: r9c7=9
Full House: r9c9=1
Naked Single: r8c9=3
Full House: r8c1=4
Full House: r7c1=3
Naked Single: r3c7=5
Full House: r3c4=9
Naked Single: r5c7=2
Full House: r5c8=9
Naked Single: r2c9=7
Naked Single: r2c7=3
Full House: r7c7=4
Full House: r2c4=5
Full House: r1c4=7
Naked Single: r1c8=2
Full House: r1c9=9
Full House: r7c9=2
Full House: r7c8=7
|
sudoku_normal_hard_124
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
5.6.....7.9.5..3..3....2.......2..7..65..12.8..96..4.1.4.2...1.6..9.45...5..8.7.4
|
516349827298517346374862195183425679465791238729638451847256913631974582952183764
|
5 . 6 . . . . . 7
. 9 . 5 . . 3 . .
3 . . . . 2 . . .
. . . . 2 . . 7 .
. 6 5 . . 1 2 . 8
. . 9 6 . . 4 . 1
. 4 . 2 . . . 1 .
6 . . 9 . 4 5 . .
. 5 . . 8 . 7 . 4
|
5 1 6 3 4 9 8 2 7
2 9 8 5 1 7 3 4 6
3 7 4 8 6 2 1 9 5
1 8 3 4 2 5 6 7 9
4 6 5 7 9 1 2 3 8
7 2 9 6 3 8 4 5 1
8 4 7 2 5 6 9 1 3
6 3 1 9 7 4 5 8 2
9 5 2 1 8 3 7 6 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8294_hard
|
516349827298517346374862195183425679465791238729638451847256913631974582952183764 #1 Extreme (26842) bf
Brute Force: r5c3=5
Hidden Single: r9c2=5
Forcing Net Contradiction in r5c1 => r5c5<>7
r5c5=7 (r5c5<>9 r4c6=9 r4c6<>5 r4c9=5 r6c8<>5) (r6c5<>7) (r6c6<>7) r5c4<>7 r3c4=7 r2c6<>7 r7c6=7 r7c6<>5 r7c5=5 r6c5<>5 r6c5=3 r6c8<>3 r6c8=2 (r6c2<>2) (r6c9<>2) r5c7<>2 r1c7=2 (r1c2<>2) r2c9<>2 r8c9=2 r8c2<>2 r5c2=2 r5c1<>2
r5c5=7 (r5c4<>7) (r6c5<>7) (r6c6<>7) r5c4<>7 r3c4=7 r2c6<>7 r7c6=7 r7c6<>5 r7c5=5 r6c5<>5 r6c5=3 r5c4<>3 r5c4=4 r5c1<>4
r5c5=7 r5c1<>7
Brute Force: r5c2=6
Hidden Triple: 5,6,9 in r4c679 => r4c69<>3, r4c6<>8, r4c79<>1
Hidden Single: r6c9=1
Locked Candidates Type 1 (Pointing): 3 in b6 => r89c8<>3
Empty Rectangle: 2 in b1 (r28c9) => r8c2<>2
Skyscraper: 2 in r5c7,r6c2 (connected by r1c27) => r5c1,r6c8<>2
Grouped Discontinuous Nice Loop: 2 r2c3 -2- r2c9 -6- r23c8 =6= r9c8 =9= r9c1 =2= r89c3 -2- r2c3 => r2c3<>2
Locked Candidates Type 2 (Claiming): 2 in c3 => r9c1<>2
Grouped Discontinuous Nice Loop: 4 r3c4 -4- r4c4 =4= r4c13 -4- r5c1 -7- r5c4 =7= r3c4 => r3c4<>4
Grouped Discontinuous Nice Loop: 3 r8c5 -3- r8c9 -2- r8c3 =2= r9c3 =3= r9c46 -3- r8c5 => r8c5<>3
Almost Locked Set XZ-Rule: A=r8c8 {28}, B=r457c7 {2689}, X=8, Z=2 => r5c8<>2
Hidden Single: r5c7=2
2-String Kite: 9 in r1c6,r5c8 (connected by r4c6,r5c5) => r1c8<>9
Forcing Chain Contradiction in r2c6 => r2c5<>7
r2c5=7 r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r2c6<>6
r2c5=7 r2c6<>7
r2c5=7 r3c4<>7 r5c4=7 r5c1<>7 r5c1=4 r4c13<>4 r4c4=4 r4c4<>8 r6c6=8 r2c6<>8
Forcing Chain Contradiction in r2c6 => r3c5<>7
r3c5=7 r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r2c6<>6
r3c5=7 r2c6<>7
r3c5=7 r3c4<>7 r5c4=7 r5c1<>7 r5c1=4 r4c13<>4 r4c4=4 r4c4<>8 r6c6=8 r2c6<>8
Turbot Fish: 7 r2c6 =7= r3c4 -7- r5c4 =7= r5c1 => r2c1<>7
Forcing Chain Contradiction in c2 => r2c6<>6
r2c6=6 r2c6<>7 r2c3=7 r3c2<>7
r2c6=6 r2c6<>7 r3c4=7 r5c4<>7 r5c1=7 r6c2<>7
r2c6=6 r9c6<>6 r9c6=3 r9c4<>3 r9c4=1 r8c5<>1 r8c5=7 r8c2<>7
Locked Candidates Type 1 (Pointing): 6 in b2 => r7c5<>6
Grouped Continuous Nice Loop: 3/8 8= r4c4 =4= r4c13 -4- r5c1 -7- r5c4 =7= r3c4 -7- r2c6 -8- r6c6 =8= r4c4 =4 => r4c4<>3, r1c6<>8
Locked Candidates Type 2 (Claiming): 3 in r4 => r6c2<>3
Grouped Discontinuous Nice Loop: 6 r3c9 -6- r23c8 =6= r9c8 -6- r9c6 -3- r1c6 -9- r4c6 -5- r4c9 =5= r3c9 => r3c9<>6
AIC: 9 9- r1c6 =9= r4c6 =5= r4c9 -5- r3c9 -9 => r1c7,r3c5<>9
Forcing Chain Contradiction in c2 => r8c5=7
r8c5<>7 r8c5=1 r2c5<>1 r2c13=1 r1c2<>1
r8c5<>7 r8c5=1 r2c5<>1 r2c13=1 r3c2<>1
r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r9c8<>6 r23c8=6 r2c9<>6 r2c9=2 r8c9<>2 r8c9=3 r8c2<>3 r4c2=3 r4c2<>1
r8c5<>7 r8c5=1 r8c2<>1
Hidden Single: r9c4=1
Naked Single: r9c1=9
Naked Pair: 7,8 in r2c6,r3c4 => r1c4<>8
Naked Pair: 3,5 in r6c58 => r6c6<>3, r6c6<>5
Naked Pair: 3,5 in r67c5 => r15c5<>3
Hidden Triple: 3,5,9 in r356c8 => r3c8<>4, r3c8<>6, r3c8<>8
Naked Pair: 5,9 in r3c89 => r3c7<>9
Skyscraper: 7 in r5c4,r6c2 (connected by r3c24) => r5c1,r6c6<>7
Naked Single: r5c1=4
Naked Single: r6c6=8
Naked Single: r5c5=9
Naked Single: r2c6=7
Naked Single: r4c4=4
Naked Single: r4c6=5
Naked Single: r5c8=3
Full House: r5c4=7
Full House: r6c5=3
Naked Single: r3c4=8
Full House: r1c4=3
Naked Single: r6c8=5
Naked Single: r7c5=5
Naked Single: r1c6=9
Naked Single: r3c8=9
Naked Single: r3c9=5
Uniqueness Test 3: 6/9 in r4c79,r7c79 => r7c6<>3
Naked Single: r7c6=6
Full House: r9c6=3
Naked Single: r9c3=2
Full House: r9c8=6
XY-Chain: 1 1- r3c2 -7- r6c2 -2- r6c1 -7- r7c1 -8- r7c7 -9- r4c7 -6- r3c7 -1 => r3c35<>1
XY-Wing: 4/6/1 in r13c5,r3c7 => r1c7<>1
Naked Single: r1c7=8
Naked Single: r7c7=9
Naked Single: r4c7=6
Full House: r3c7=1
Full House: r4c9=9
Naked Single: r7c9=3
Naked Single: r3c2=7
Naked Single: r8c9=2
Full House: r2c9=6
Full House: r8c8=8
Naked Single: r3c3=4
Full House: r3c5=6
Naked Single: r6c2=2
Full House: r6c1=7
Naked Single: r1c2=1
Naked Single: r7c1=8
Full House: r7c3=7
Naked Single: r1c5=4
Full House: r1c8=2
Full House: r2c5=1
Full House: r2c8=4
Naked Single: r2c3=8
Full House: r2c1=2
Full House: r4c1=1
Naked Single: r8c2=3
Full House: r4c2=8
Full House: r4c3=3
Full House: r8c3=1
|
sudoku_normal_extremely_hard_124
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
5.6.....7.9.5..3..3....2.......2..7......1..8..96..4...4.2...1.6..9.45......8.7.4
|
516349827298517346374862195183425679465791238729638451847256913631974582952183764
|
5 . 6 . . . . . 7
. 9 . 5 . . 3 . .
3 . . . . 2 . . .
. . . . 2 . . 7 .
. . . . . 1 . . 8
. . 9 6 . . 4 . .
. 4 . 2 . . . 1 .
6 . . 9 . 4 5 . .
. . . . 8 . 7 . 4
|
5 1 6 3 4 9 8 2 7
2 9 8 5 1 7 3 4 6
3 7 4 8 6 2 1 9 5
1 8 3 4 2 5 6 7 9
4 6 5 7 9 1 2 3 8
7 2 9 6 3 8 4 5 1
8 4 7 2 5 6 9 1 3
6 3 1 9 7 4 5 8 2
9 5 2 1 8 3 7 6 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8294_hard
|
516349827298517346374862195183425679465791238729638451847256913631974582952183764 #1 Extreme (26842) bf
Brute Force: r5c3=5
Hidden Single: r9c2=5
Forcing Net Contradiction in r5c1 => r5c5<>7
r5c5=7 (r5c5<>9 r4c6=9 r4c6<>5 r4c9=5 r6c8<>5) (r6c5<>7) (r6c6<>7) r5c4<>7 r3c4=7 r2c6<>7 r7c6=7 r7c6<>5 r7c5=5 r6c5<>5 r6c5=3 r6c8<>3 r6c8=2 (r6c2<>2) (r6c9<>2) r5c7<>2 r1c7=2 (r1c2<>2) r2c9<>2 r8c9=2 r8c2<>2 r5c2=2 r5c1<>2
r5c5=7 (r5c4<>7) (r6c5<>7) (r6c6<>7) r5c4<>7 r3c4=7 r2c6<>7 r7c6=7 r7c6<>5 r7c5=5 r6c5<>5 r6c5=3 r5c4<>3 r5c4=4 r5c1<>4
r5c5=7 r5c1<>7
Brute Force: r5c2=6
Hidden Triple: 5,6,9 in r4c679 => r4c69<>3, r4c6<>8, r4c79<>1
Hidden Single: r6c9=1
Locked Candidates Type 1 (Pointing): 3 in b6 => r89c8<>3
Empty Rectangle: 2 in b1 (r28c9) => r8c2<>2
Skyscraper: 2 in r5c7,r6c2 (connected by r1c27) => r5c1,r6c8<>2
Grouped Discontinuous Nice Loop: 2 r2c3 -2- r2c9 -6- r23c8 =6= r9c8 =9= r9c1 =2= r89c3 -2- r2c3 => r2c3<>2
Locked Candidates Type 2 (Claiming): 2 in c3 => r9c1<>2
Grouped Discontinuous Nice Loop: 4 r3c4 -4- r4c4 =4= r4c13 -4- r5c1 -7- r5c4 =7= r3c4 => r3c4<>4
Grouped Discontinuous Nice Loop: 3 r8c5 -3- r8c9 -2- r8c3 =2= r9c3 =3= r9c46 -3- r8c5 => r8c5<>3
Almost Locked Set XZ-Rule: A=r8c8 {28}, B=r457c7 {2689}, X=8, Z=2 => r5c8<>2
Hidden Single: r5c7=2
2-String Kite: 9 in r1c6,r5c8 (connected by r4c6,r5c5) => r1c8<>9
Forcing Chain Contradiction in r2c6 => r2c5<>7
r2c5=7 r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r2c6<>6
r2c5=7 r2c6<>7
r2c5=7 r3c4<>7 r5c4=7 r5c1<>7 r5c1=4 r4c13<>4 r4c4=4 r4c4<>8 r6c6=8 r2c6<>8
Forcing Chain Contradiction in r2c6 => r3c5<>7
r3c5=7 r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r2c6<>6
r3c5=7 r2c6<>7
r3c5=7 r3c4<>7 r5c4=7 r5c1<>7 r5c1=4 r4c13<>4 r4c4=4 r4c4<>8 r6c6=8 r2c6<>8
Turbot Fish: 7 r2c6 =7= r3c4 -7- r5c4 =7= r5c1 => r2c1<>7
Forcing Chain Contradiction in c2 => r2c6<>6
r2c6=6 r2c6<>7 r2c3=7 r3c2<>7
r2c6=6 r2c6<>7 r3c4=7 r5c4<>7 r5c1=7 r6c2<>7
r2c6=6 r9c6<>6 r9c6=3 r9c4<>3 r9c4=1 r8c5<>1 r8c5=7 r8c2<>7
Locked Candidates Type 1 (Pointing): 6 in b2 => r7c5<>6
Grouped Continuous Nice Loop: 3/8 8= r4c4 =4= r4c13 -4- r5c1 -7- r5c4 =7= r3c4 -7- r2c6 -8- r6c6 =8= r4c4 =4 => r4c4<>3, r1c6<>8
Locked Candidates Type 2 (Claiming): 3 in r4 => r6c2<>3
Grouped Discontinuous Nice Loop: 6 r3c9 -6- r23c8 =6= r9c8 -6- r9c6 -3- r1c6 -9- r4c6 -5- r4c9 =5= r3c9 => r3c9<>6
AIC: 9 9- r1c6 =9= r4c6 =5= r4c9 -5- r3c9 -9 => r1c7,r3c5<>9
Forcing Chain Contradiction in c2 => r8c5=7
r8c5<>7 r8c5=1 r2c5<>1 r2c13=1 r1c2<>1
r8c5<>7 r8c5=1 r2c5<>1 r2c13=1 r3c2<>1
r8c5<>7 r8c5=1 r9c4<>1 r9c4=3 r9c6<>3 r9c6=6 r9c8<>6 r23c8=6 r2c9<>6 r2c9=2 r8c9<>2 r8c9=3 r8c2<>3 r4c2=3 r4c2<>1
r8c5<>7 r8c5=1 r8c2<>1
Hidden Single: r9c4=1
Naked Single: r9c1=9
Naked Pair: 7,8 in r2c6,r3c4 => r1c4<>8
Naked Pair: 3,5 in r6c58 => r6c6<>3, r6c6<>5
Naked Pair: 3,5 in r67c5 => r15c5<>3
Hidden Triple: 3,5,9 in r356c8 => r3c8<>4, r3c8<>6, r3c8<>8
Naked Pair: 5,9 in r3c89 => r3c7<>9
Skyscraper: 7 in r5c4,r6c2 (connected by r3c24) => r5c1,r6c6<>7
Naked Single: r5c1=4
Naked Single: r6c6=8
Naked Single: r5c5=9
Naked Single: r2c6=7
Naked Single: r4c4=4
Naked Single: r4c6=5
Naked Single: r5c8=3
Full House: r5c4=7
Full House: r6c5=3
Naked Single: r3c4=8
Full House: r1c4=3
Naked Single: r6c8=5
Naked Single: r7c5=5
Naked Single: r1c6=9
Naked Single: r3c8=9
Naked Single: r3c9=5
Uniqueness Test 3: 6/9 in r4c79,r7c79 => r7c6<>3
Naked Single: r7c6=6
Full House: r9c6=3
Naked Single: r9c3=2
Full House: r9c8=6
XY-Chain: 1 1- r3c2 -7- r6c2 -2- r6c1 -7- r7c1 -8- r7c7 -9- r4c7 -6- r3c7 -1 => r3c35<>1
XY-Wing: 4/6/1 in r13c5,r3c7 => r1c7<>1
Naked Single: r1c7=8
Naked Single: r7c7=9
Naked Single: r4c7=6
Full House: r3c7=1
Full House: r4c9=9
Naked Single: r7c9=3
Naked Single: r3c2=7
Naked Single: r8c9=2
Full House: r2c9=6
Full House: r8c8=8
Naked Single: r3c3=4
Full House: r3c5=6
Naked Single: r6c2=2
Full House: r6c1=7
Naked Single: r1c2=1
Naked Single: r7c1=8
Full House: r7c3=7
Naked Single: r1c5=4
Full House: r1c8=2
Full House: r2c5=1
Full House: r2c8=4
Naked Single: r2c3=8
Full House: r2c1=2
Full House: r4c1=1
Naked Single: r8c2=3
Full House: r4c2=8
Full House: r4c3=3
Full House: r8c3=1
|
sudoku_normal_hard_125
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
8...23....3...6.9...25..3..3.7.6.5..1...359766..7...43.8.6...394..3...1...3..76..
|
816923457534876192972541368397468521148235976625719843781654239469382715253197684
|
8 . . . 2 3 . . .
. 3 . . . 6 . 9 .
. . 2 5 . . 3 . .
3 . 7 . 6 . 5 . .
1 . . . 3 5 9 7 6
6 . . 7 . . . 4 3
. 8 . 6 . . . 3 9
4 . . 3 . . . 1 .
. . 3 . . 7 6 . .
|
8 1 6 9 2 3 4 5 7
5 3 4 8 7 6 1 9 2
9 7 2 5 4 1 3 6 8
3 9 7 4 6 8 5 2 1
1 4 8 2 3 5 9 7 6
6 2 5 7 1 9 8 4 3
7 8 1 6 5 4 2 3 9
4 6 9 3 8 2 7 1 5
2 5 3 1 9 7 6 8 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7441_hard
|
816923457534876192972541368397468521148235976625719843781654239469382715253197684 #1 Extreme (42092) bf
Brute Force: r5c7=9
Hidden Single: r5c8=7
Locked Candidates Type 2 (Claiming): 3 in r5 => r4c4,r6c5<>3
Forcing Net Contradiction in c4 => r9c9<>2
r9c9=2 (r9c1<>2) (r9c8<>2 r4c8=2 r4c2<>2) (r9c2<>2) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r5c2<>2) r6c2<>2 r8c2=2 r8c2<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r8c3<>9 r1c3=9 r1c4<>9
r9c9=2 (r9c8<>2 r4c8=2 r4c2<>2) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r4c4<>9
r9c9=2 (r9c8<>2 r4c8=2 r4c8<>3 r7c8=3 r8c9<>3) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 r5c2<>2 r5c4=2 r5c4<>3 r5c5=3 r8c5<>3 r8c4=3 r8c4<>9
r9c9=2 (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r9c4<>9
Brute Force: r5c5=3
Hidden Pair: 3,6 in r78c4 => r7c4<>1, r78c4<>2, r7c4<>4, r8c4<>8, r8c4<>9
Forcing Chain Verity => r4c6<>2
r8c2=2 r5c2<>2 r5c4=2 r4c6<>2
r8c6=2 r4c6<>2
r8c7=2 r79c8<>2 r4c8=2 r4c6<>2
r8c9=2 r79c8<>2 r4c8=2 r4c6<>2
Forcing Net Contradiction in r1 => r8c2<>2
r8c2=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r9c1<>2) r8c2<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r8c3<>9 r1c3=9
r8c2=2 (r4c2<>2) r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r1c2<>9 r1c4=9
Forcing Net Contradiction in r3 => r4c1<>2
r4c1=2 r5c2<>2 r5c2=4 r3c2<>4
r4c1=2 (r4c8<>2) (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 r9c5<>4 r9c9=4 r9c9<>5) (r9c2<>1 r7c3=1 r7c3<>6) r9c8<>2 r7c8=2 r7c8<>3 r7c4=3 (r8c4<>3 r8c9=3 r8c9<>5) r7c4<>6 r7c1=6 r7c1<>7 r7c7=7 (r1c7<>7) (r8c7<>7) r8c9<>7 r8c2=7 r1c2<>7 r1c9=7 r1c9<>5 r2c9=5 r2c1<>5 r2c1=7 r2c5<>7 r3c5=7 r3c5<>4
r4c1=2 (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c8<>2 r7c8=2 r7c6<>2) r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 r3c6<>4
r4c1=2 (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c8<>2 r7c8=2 r7c6<>2) r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 (r9c4<>4) r9c5<>4 r9c9=4 r3c9<>4
Forcing Net Verity => r7c1<>6
r3c1=6 r7c1<>6
r3c1=7 (r2c1<>7 r2c1=5 r2c9<>5) r7c1<>7 r7c7=7 (r1c7<>7 r1c9=7 r1c9<>5) r7c7<>4 r9c9=4 r9c9<>5 r8c9=5 r8c9<>3 r8c4=3 r7c4<>3 r7c4=6 r7c1<>6
r3c1=9 r4c1<>9 r4c1=3 r4c8<>3 r7c8=3 r7c4<>3 r7c4=6 r7c1<>6
Forcing Net Contradiction in r1 => r6c1<>2
r6c1=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r6c1<>3 r6c9=3 r4c9<>3 r4c1=3 r4c1<>9) (r6c1<>9) r6c1<>6 r3c1=6 r3c1<>9 r9c1=9 r8c3<>9 r1c3=9
r6c1=2 (r4c2<>2) r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r1c2<>9 r1c4=9
Locked Candidates Type 1 (Pointing): 2 in b4 => r9c2<>2
Brute Force: r6c1=6
Hidden Single: r6c9=3
Hidden Single: r4c1=3
Hidden Single: r7c8=3
Naked Single: r7c4=6
Naked Single: r8c4=3
Empty Rectangle: 9 in b2 (r39c1) => r9c4<>9
Almost Locked Set XZ-Rule: A=r7c3 {15}, B=r4569c2 {12459}, X=1, Z=5 => r8c2<>5
Finned Franken Swordfish: 9 c34b8 r168 fr4c4 fr9c5 => r6c5<>9
Forcing Chain Contradiction in r9c2 => r1c2<>5
r1c2=5 r6c2<>5 r6c3=5 r7c3<>5 r7c3=1 r9c2<>1
r1c2=5 r9c2<>5
r1c2=5 r6c2<>5 r6c3=5 r6c3<>9 r46c2=9 r9c2<>9
Forcing Chain Contradiction in r6 => r1c7<>7
r1c7=7 r78c7<>7 r8c9=7 r8c9<>5 r9c89=5 r9c2<>5 r6c2=5 r6c2<>2
r1c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r1c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Forcing Chain Contradiction in r6 => r1c9<>5
r1c9=5 r1c8<>5 r9c8=5 r9c2<>5 r6c2=5 r6c2<>2
r1c9=5 r1c9<>7 r1c2=7 r8c2<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r1c9=5 r1c8<>5 r9c8=5 r9c8<>2 r4c8=2 r6c7<>2
Forcing Chain Contradiction in r1 => r1c2<>9
r1c2=9 r1c2<>6
r1c2=9 r3c1<>9 r3c1=7 r7c1<>7 r8c2=7 r8c2<>6 r8c3=6 r1c3<>6
r1c2=9 r3c1<>9 r3c1=7 r2c1<>7 r2c1=5 r2c9<>5 r1c8=5 r1c8<>6
Forcing Chain Contradiction in r6 => r2c7<>7
r2c7=7 r78c7<>7 r8c9=7 r8c9<>5 r9c89=5 r9c2<>5 r6c2=5 r6c2<>2
r2c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r2c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Locked Candidates Type 1 (Pointing): 7 in b3 => r8c9<>7
Forcing Chain Contradiction in r6 => r7c1<>5
r7c1=5 r9c2<>5 r6c2=5 r6c2<>2
r7c1=5 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r7c1=5 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Skyscraper: 5 in r1c8,r2c1 (connected by r9c18) => r1c3,r2c9<>5
Hidden Single: r1c8=5
Hidden Single: r3c8=6
Discontinuous Nice Loop: 8 r8c9 -8- r9c8 -2- r9c1 =2= r7c1 =7= r7c7 =4= r9c9 =5= r8c9 => r8c9<>8
Discontinuous Nice Loop: 8 r9c9 -8- r9c8 -2- r9c1 =2= r7c1 =7= r7c7 =4= r9c9 => r9c9<>8
Forcing Chain Contradiction in r6 => r8c9=5
r8c9<>5 r9c9=5 r9c2<>5 r6c2=5 r6c2<>2
r8c9<>5 r9c9=5 r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r8c9<>5 r8c9=2 r2c9<>2 r2c7=2 r6c7<>2
Naked Single: r9c9=4
Naked Pair: 2,7 in r7c17 => r7c6<>2
Discontinuous Nice Loop: 7 r1c2 -7- r1c9 -1- r4c9 =1= r6c7 -1- r6c5 -8- r8c5 -9- r8c3 -6- r8c2 =6= r1c2 => r1c2<>7
Hidden Single: r1c9=7
W-Wing: 8/1 in r3c9,r6c5 connected by 1 in r4c9,r6c7 => r3c5<>8
Almost Locked Set XZ-Rule: A=r4569c2 {12459}, B=r8c56,r9c4 {1289}, X=1, Z=9 => r8c2<>9
Almost Locked Set XY-Wing: A=r2c13479 {124578}, B=r689c5 {1589}, C=r379c1 {2579}, X,Y=5,7, Z=1,8 => r2c5<>1, r2c5<>8
AIC: 8 8- r2c4 =8= r3c6 -8- r3c9 -1- r4c9 =1= r6c7 -1- r6c5 -8 => r45c4<>8
Hidden Single: r5c3=8
Locked Candidates Type 1 (Pointing): 4 in b4 => r13c2<>4
Locked Candidates Type 2 (Claiming): 4 in r3 => r12c4,r2c5<>4
Naked Single: r2c5=7
Naked Single: r2c1=5
Locked Candidates Type 2 (Claiming): 4 in c4 => r4c6<>4
Hidden Pair: 1,5 in r7c3,r9c2 => r9c2<>9
Turbot Fish: 8 r2c4 =8= r9c4 -8- r9c8 =8= r8c7 => r2c7<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r4c9<>8
2-String Kite: 8 in r4c6,r8c7 (connected by r4c8,r6c7) => r8c6<>8
Uniqueness Test 4: 2/4 in r4c24,r5c24 => r4c24<>2
Locked Candidates Type 2 (Claiming): 2 in r4 => r6c7<>2
Naked Pair: 1,8 in r6c57 => r6c6<>1, r6c6<>8
Naked Pair: 2,9 in r68c6 => r34c6<>9
Naked Pair: 1,8 in r4c6,r6c5 => r4c4<>1
X-Wing: 8 r68 c57 => r9c5<>8
Skyscraper: 9 in r1c3,r4c2 (connected by r14c4) => r3c2,r6c3<>9
Naked Single: r6c3=5
Naked Single: r7c3=1
Naked Single: r2c3=4
Naked Single: r7c6=4
Naked Single: r9c2=5
Naked Single: r7c5=5
Hidden Single: r1c7=4
Hidden Single: r3c5=4
Hidden Single: r3c1=9
Naked Single: r1c3=6
Full House: r8c3=9
Naked Single: r9c1=2
Full House: r7c1=7
Full House: r7c7=2
Full House: r8c2=6
Naked Single: r1c2=1
Full House: r1c4=9
Full House: r3c2=7
Naked Single: r8c5=8
Naked Single: r8c6=2
Full House: r8c7=7
Full House: r9c8=8
Full House: r4c8=2
Naked Single: r2c7=1
Full House: r6c7=8
Full House: r4c9=1
Naked Single: r4c4=4
Naked Single: r6c5=1
Full House: r9c5=9
Full House: r9c4=1
Naked Single: r6c6=9
Full House: r6c2=2
Naked Single: r2c4=8
Full House: r5c4=2
Full House: r4c6=8
Full House: r4c2=9
Full House: r5c2=4
Full House: r2c9=2
Full House: r3c9=8
Full House: r3c6=1
|
sudoku_normal_extremely_hard_125
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
8...23....3...6.9...25..3....7.6.5..1....5..6...7...4..8......94......1...3..76..
|
816923457534876192972541368397468521148235976625719843781654239469382715253197684
|
8 . . . 2 3 . . .
. 3 . . . 6 . 9 .
. . 2 5 . . 3 . .
. . 7 . 6 . 5 . .
1 . . . . 5 . . 6
. . . 7 . . . 4 .
. 8 . . . . . . 9
4 . . . . . . 1 .
. . 3 . . 7 6 . .
|
8 1 6 9 2 3 4 5 7
5 3 4 8 7 6 1 9 2
9 7 2 5 4 1 3 6 8
3 9 7 4 6 8 5 2 1
1 4 8 2 3 5 9 7 6
6 2 5 7 1 9 8 4 3
7 8 1 6 5 4 2 3 9
4 6 9 3 8 2 7 1 5
2 5 3 1 9 7 6 8 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7441_hard
|
816923457534876192972541368397468521148235976625719843781654239469382715253197684 #1 Extreme (42092) bf
Brute Force: r5c7=9
Hidden Single: r5c8=7
Locked Candidates Type 2 (Claiming): 3 in r5 => r4c4,r6c5<>3
Forcing Net Contradiction in c4 => r9c9<>2
r9c9=2 (r9c1<>2) (r9c8<>2 r4c8=2 r4c2<>2) (r9c2<>2) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r5c2<>2) r6c2<>2 r8c2=2 r8c2<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r8c3<>9 r1c3=9 r1c4<>9
r9c9=2 (r9c8<>2 r4c8=2 r4c2<>2) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r4c4<>9
r9c9=2 (r9c8<>2 r4c8=2 r4c8<>3 r7c8=3 r8c9<>3) (r9c8<>2 r4c8=2 r4c1<>2) (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r6c1=2 r5c2<>2 r5c4=2 r5c4<>3 r5c5=3 r8c5<>3 r8c4=3 r8c4<>9
r9c9=2 (r9c1<>2) r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r9c4<>9
Brute Force: r5c5=3
Hidden Pair: 3,6 in r78c4 => r7c4<>1, r78c4<>2, r7c4<>4, r8c4<>8, r8c4<>9
Forcing Chain Verity => r4c6<>2
r8c2=2 r5c2<>2 r5c4=2 r4c6<>2
r8c6=2 r4c6<>2
r8c7=2 r79c8<>2 r4c8=2 r4c6<>2
r8c9=2 r79c8<>2 r4c8=2 r4c6<>2
Forcing Net Contradiction in r1 => r8c2<>2
r8c2=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r9c1<>2) r8c2<>7 r7c1=7 r2c1<>7 r2c1=5 r9c1<>5 r9c1=9 r8c3<>9 r1c3=9
r8c2=2 (r4c2<>2) r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r1c2<>9 r1c4=9
Forcing Net Contradiction in r3 => r4c1<>2
r4c1=2 r5c2<>2 r5c2=4 r3c2<>4
r4c1=2 (r4c8<>2) (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 r9c5<>4 r9c9=4 r9c9<>5) (r9c2<>1 r7c3=1 r7c3<>6) r9c8<>2 r7c8=2 r7c8<>3 r7c4=3 (r8c4<>3 r8c9=3 r8c9<>5) r7c4<>6 r7c1=6 r7c1<>7 r7c7=7 (r1c7<>7) (r8c7<>7) r8c9<>7 r8c2=7 r1c2<>7 r1c9=7 r1c9<>5 r2c9=5 r2c1<>5 r2c1=7 r2c5<>7 r3c5=7 r3c5<>4
r4c1=2 (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c8<>2 r7c8=2 r7c6<>2) r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 r3c6<>4
r4c1=2 (r4c2<>2) (r5c2<>2) r6c2<>2 r9c2=2 (r9c8<>2 r7c8=2 r7c6<>2) r9c2<>1 r7c3=1 r7c6<>1 r7c6=4 (r9c4<>4) r9c5<>4 r9c9=4 r3c9<>4
Forcing Net Verity => r7c1<>6
r3c1=6 r7c1<>6
r3c1=7 (r2c1<>7 r2c1=5 r2c9<>5) r7c1<>7 r7c7=7 (r1c7<>7 r1c9=7 r1c9<>5) r7c7<>4 r9c9=4 r9c9<>5 r8c9=5 r8c9<>3 r8c4=3 r7c4<>3 r7c4=6 r7c1<>6
r3c1=9 r4c1<>9 r4c1=3 r4c8<>3 r7c8=3 r7c4<>3 r7c4=6 r7c1<>6
Forcing Net Contradiction in r1 => r6c1<>2
r6c1=2 (r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r6c3<>9) (r6c1<>3 r6c9=3 r4c9<>3 r4c1=3 r4c1<>9) (r6c1<>9) r6c1<>6 r3c1=6 r3c1<>9 r9c1=9 r8c3<>9 r1c3=9
r6c1=2 (r4c2<>2) r5c2<>2 r5c2=4 r4c2<>4 r4c2=9 r1c2<>9 r1c4=9
Locked Candidates Type 1 (Pointing): 2 in b4 => r9c2<>2
Brute Force: r6c1=6
Hidden Single: r6c9=3
Hidden Single: r4c1=3
Hidden Single: r7c8=3
Naked Single: r7c4=6
Naked Single: r8c4=3
Empty Rectangle: 9 in b2 (r39c1) => r9c4<>9
Almost Locked Set XZ-Rule: A=r7c3 {15}, B=r4569c2 {12459}, X=1, Z=5 => r8c2<>5
Finned Franken Swordfish: 9 c34b8 r168 fr4c4 fr9c5 => r6c5<>9
Forcing Chain Contradiction in r9c2 => r1c2<>5
r1c2=5 r6c2<>5 r6c3=5 r7c3<>5 r7c3=1 r9c2<>1
r1c2=5 r9c2<>5
r1c2=5 r6c2<>5 r6c3=5 r6c3<>9 r46c2=9 r9c2<>9
Forcing Chain Contradiction in r6 => r1c7<>7
r1c7=7 r78c7<>7 r8c9=7 r8c9<>5 r9c89=5 r9c2<>5 r6c2=5 r6c2<>2
r1c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r1c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Forcing Chain Contradiction in r6 => r1c9<>5
r1c9=5 r1c8<>5 r9c8=5 r9c2<>5 r6c2=5 r6c2<>2
r1c9=5 r1c9<>7 r1c2=7 r8c2<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r1c9=5 r1c8<>5 r9c8=5 r9c8<>2 r4c8=2 r6c7<>2
Forcing Chain Contradiction in r1 => r1c2<>9
r1c2=9 r1c2<>6
r1c2=9 r3c1<>9 r3c1=7 r7c1<>7 r8c2=7 r8c2<>6 r8c3=6 r1c3<>6
r1c2=9 r3c1<>9 r3c1=7 r2c1<>7 r2c1=5 r2c9<>5 r1c8=5 r1c8<>6
Forcing Chain Contradiction in r6 => r2c7<>7
r2c7=7 r78c7<>7 r8c9=7 r8c9<>5 r9c89=5 r9c2<>5 r6c2=5 r6c2<>2
r2c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r2c7=7 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Locked Candidates Type 1 (Pointing): 7 in b3 => r8c9<>7
Forcing Chain Contradiction in r6 => r7c1<>5
r7c1=5 r9c2<>5 r6c2=5 r6c2<>2
r7c1=5 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r7c1=5 r7c1<>2 r9c1=2 r9c8<>2 r4c8=2 r6c7<>2
Skyscraper: 5 in r1c8,r2c1 (connected by r9c18) => r1c3,r2c9<>5
Hidden Single: r1c8=5
Hidden Single: r3c8=6
Discontinuous Nice Loop: 8 r8c9 -8- r9c8 -2- r9c1 =2= r7c1 =7= r7c7 =4= r9c9 =5= r8c9 => r8c9<>8
Discontinuous Nice Loop: 8 r9c9 -8- r9c8 -2- r9c1 =2= r7c1 =7= r7c7 =4= r9c9 => r9c9<>8
Forcing Chain Contradiction in r6 => r8c9=5
r8c9<>5 r9c9=5 r9c2<>5 r6c2=5 r6c2<>2
r8c9<>5 r9c9=5 r9c9<>4 r7c7=4 r7c7<>7 r7c1=7 r7c1<>2 r9c1=2 r9c4<>2 r45c4=2 r6c6<>2
r8c9<>5 r8c9=2 r2c9<>2 r2c7=2 r6c7<>2
Naked Single: r9c9=4
Naked Pair: 2,7 in r7c17 => r7c6<>2
Discontinuous Nice Loop: 7 r1c2 -7- r1c9 -1- r4c9 =1= r6c7 -1- r6c5 -8- r8c5 -9- r8c3 -6- r8c2 =6= r1c2 => r1c2<>7
Hidden Single: r1c9=7
W-Wing: 8/1 in r3c9,r6c5 connected by 1 in r4c9,r6c7 => r3c5<>8
Almost Locked Set XZ-Rule: A=r4569c2 {12459}, B=r8c56,r9c4 {1289}, X=1, Z=9 => r8c2<>9
Almost Locked Set XY-Wing: A=r2c13479 {124578}, B=r689c5 {1589}, C=r379c1 {2579}, X,Y=5,7, Z=1,8 => r2c5<>1, r2c5<>8
AIC: 8 8- r2c4 =8= r3c6 -8- r3c9 -1- r4c9 =1= r6c7 -1- r6c5 -8 => r45c4<>8
Hidden Single: r5c3=8
Locked Candidates Type 1 (Pointing): 4 in b4 => r13c2<>4
Locked Candidates Type 2 (Claiming): 4 in r3 => r12c4,r2c5<>4
Naked Single: r2c5=7
Naked Single: r2c1=5
Locked Candidates Type 2 (Claiming): 4 in c4 => r4c6<>4
Hidden Pair: 1,5 in r7c3,r9c2 => r9c2<>9
Turbot Fish: 8 r2c4 =8= r9c4 -8- r9c8 =8= r8c7 => r2c7<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r4c9<>8
2-String Kite: 8 in r4c6,r8c7 (connected by r4c8,r6c7) => r8c6<>8
Uniqueness Test 4: 2/4 in r4c24,r5c24 => r4c24<>2
Locked Candidates Type 2 (Claiming): 2 in r4 => r6c7<>2
Naked Pair: 1,8 in r6c57 => r6c6<>1, r6c6<>8
Naked Pair: 2,9 in r68c6 => r34c6<>9
Naked Pair: 1,8 in r4c6,r6c5 => r4c4<>1
X-Wing: 8 r68 c57 => r9c5<>8
Skyscraper: 9 in r1c3,r4c2 (connected by r14c4) => r3c2,r6c3<>9
Naked Single: r6c3=5
Naked Single: r7c3=1
Naked Single: r2c3=4
Naked Single: r7c6=4
Naked Single: r9c2=5
Naked Single: r7c5=5
Hidden Single: r1c7=4
Hidden Single: r3c5=4
Hidden Single: r3c1=9
Naked Single: r1c3=6
Full House: r8c3=9
Naked Single: r9c1=2
Full House: r7c1=7
Full House: r7c7=2
Full House: r8c2=6
Naked Single: r1c2=1
Full House: r1c4=9
Full House: r3c2=7
Naked Single: r8c5=8
Naked Single: r8c6=2
Full House: r8c7=7
Full House: r9c8=8
Full House: r4c8=2
Naked Single: r2c7=1
Full House: r6c7=8
Full House: r4c9=1
Naked Single: r4c4=4
Naked Single: r6c5=1
Full House: r9c5=9
Full House: r9c4=1
Naked Single: r6c6=9
Full House: r6c2=2
Naked Single: r2c4=8
Full House: r5c4=2
Full House: r4c6=8
Full House: r4c2=9
Full House: r5c2=4
Full House: r2c9=2
Full House: r3c9=8
Full House: r3c6=1
|
sudoku_normal_hard_126
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..6..9.2..4.36.5..1..........8..5..23...468...6.1.87..6......89..5..72......8....
|
586479123249361578173852946718935462352746891964128735627514389835697214491283657
|
. . 6 . . 9 . 2 .
. 4 . 3 6 . 5 . .
1 . . . . . . . .
. . 8 . . 5 . . 2
3 . . . 4 6 8 . .
. 6 . 1 . 8 7 . .
6 . . . . . . 8 9
. . 5 . . 7 2 . .
. . . . 8 . . . .
|
5 8 6 4 7 9 1 2 3
2 4 9 3 6 1 5 7 8
1 7 3 8 5 2 9 4 6
7 1 8 9 3 5 4 6 2
3 5 2 7 4 6 8 9 1
9 6 4 1 2 8 7 3 5
6 2 7 5 1 4 3 8 9
8 3 5 6 9 7 2 1 4
4 9 1 2 8 3 6 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4223_hard
|
586479123249361578173852946718935462352746891964128735627514389835697214491283657 #1 Extreme (31346) bf
Locked Candidates Type 1 (Pointing): 5 in b9 => r9c4<>5
Locked Candidates Type 1 (Pointing): 7 in b9 => r9c123<>7
Hidden Pair: 5,7 in r9c89 => r9c89<>1, r9c89<>3, r9c89<>4, r9c89<>6
Brute Force: r5c7=8
Hidden Single: r6c6=8
Locked Candidates Type 1 (Pointing): 3 in b5 => r78c5<>3
Forcing Net Contradiction in r6c9 => r2c9<>1
r2c9=1 (r1c9<>1 r1c5=1 r8c5<>1) (r8c9<>1) r2c9<>8 r2c1=8 r8c1<>8 r8c2=8 (r8c2<>3) r8c2<>1 r8c8=1 r8c8<>3 r8c9=3 r6c9<>3
r2c9=1 (r2c9<>8 r2c1=8 r8c1<>8) (r1c7<>1) r1c9<>1 r1c5=1 r8c5<>1 r8c5=9 r8c1<>9 r8c1=4 (r7c3<>4) r9c3<>4 r6c3=4 r6c9<>4
r2c9=1 (r5c9<>1) r2c6<>1 r2c6=2 r5c6<>2 r5c6=6 r5c9<>6 r5c9=5 r6c9<>5
Forcing Net Contradiction in r4c7 => r3c9<>3
r3c9=3 (r6c9<>3) (r8c9<>3) (r1c7<>3) r1c9<>3 r1c2=3 r8c2<>3 r8c8=3 (r8c8<>6) (r4c8<>3) r6c8<>3 r6c5=3 r4c5<>3 r4c7=3 (r4c7<>6) (r4c7<>6) r4c7<>9 r3c7=9 (r3c7<>6) r3c7<>6 r9c7=6 r8c9<>6 r8c4=6 r4c4<>6 r4c8=6 r3c8<>6 r3c9=6 r3c9<>3
Brute Force: r5c6=6
Forcing Net Contradiction in b4 => r1c4<>7
r1c4=7 (r4c4<>7 r4c4=9 r6c5<>9 r8c5=9 r8c5<>1) (r4c4<>7 r4c4=9 r4c7<>9 r3c7=9 r2c8<>9) (r1c1<>7) (r1c5<>7) r3c5<>7 r4c5=7 (r4c2<>7 r4c2=1 r8c2<>1) r4c1<>7 r2c1=7 r2c8<>7 r2c8=1 r8c8<>1 r8c9=1 r5c9<>1 r5c9=5 r5c2<>5
r1c4=7 (r1c1<>7) (r3c5<>7 r4c5=7 r4c1<>7 r4c1=4 r8c1<>4) r4c4<>7 r4c4=9 (r4c5<>9) r6c5<>9 r8c5=9 r8c1<>9 r8c1=8 r1c1<>8 r1c1=5 r6c1<>5
Forcing Net Contradiction in r2c3 => r3c3<>9
r3c3=9 (r6c3<>9) r3c7<>9 r4c7=9 (r4c1<>9) r4c4<>9 r4c4=7 r4c1<>7 r4c1=4 r6c3<>4 r6c3=2 r2c3<>2
r3c3=9 r3c7<>9 r4c7=9 r4c4<>9 r4c4=7 r4c1<>7 r12c1=7 r2c3<>7
r3c3=9 r2c3<>9
Forcing Net Contradiction in r1c1 => r3c9<>7
r3c9=7 (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) (r2c8<>7) (r3c4<>7) r3c5<>7 r1c5=7 r1c5<>1 r2c6=1 r2c8<>1 r2c8=9 r5c8<>9 r5c8=5 (r6c8<>5) r6c9<>5 r6c1=5 r1c1<>5
r3c9=7 (r3c4<>7) r3c5<>7 r1c5=7 r1c1<>7
r3c9=7 (r3c9<>6 r8c9=6 r8c9<>3) (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r4c8<>1) (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) (r3c4<>7) r3c5<>7 r1c5=7 r1c5<>1 r2c6=1 r2c8<>1 r8c8=1 r8c8<>3 r8c2=3 r8c2<>8 r8c1=8 r1c1<>8
Forcing Net Contradiction in b2 => r3c9<>8
r3c9=8 (r3c9<>6 r8c9=6 r8c9<>1) (r3c9<>6 r8c9=6 r8c9<>3) r2c9<>8 r2c1=8 r8c1<>8 r8c2=8 (r8c2<>1) r8c2<>3 r8c8=3 r8c8<>1 r8c5=1 r1c5<>1
r3c9=8 (r3c9<>6 r8c9=6 r8c9<>3) r2c9<>8 (r2c9=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r4c8<>1) (r2c9=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) r2c1=8 r8c1<>8 r8c2=8 r8c2<>3 r8c8=3 r8c8<>1 r2c8=1 r2c6<>1
Forcing Chain Contradiction in r1c4 => r3c2<>2
r3c2=2 r3c6<>2 r3c6=4 r1c4<>4
r3c2=2 r3c2<>5 r1c12=5 r1c4<>5
r3c2=2 r3c2<>8 r3c4=8 r1c4<>8
Forcing Net Contradiction in b1 => r3c4<>7
r3c4=7 (r3c4<>8 r3c2=8 r8c2<>8) (r3c5<>7 r4c5=7 r4c2<>7 r4c2=1 r8c2<>1) r4c4<>7 r4c4=9 (r4c5<>9) r6c5<>9 r8c5=9 r8c2<>9 r8c2=3 r1c2<>3
r3c4=7 r3c4<>8 r3c2=8 r3c2<>3
r3c4=7 (r3c4<>2) (r3c4<>4) r3c4<>8 (r3c2=8 r3c2<>5 r3c5=5 r3c5<>2) r1c4=8 r1c4<>4 r3c6=4 r3c6<>2 r3c3=2 r3c3<>3
Locked Candidates Type 1 (Pointing): 7 in b2 => r4c5<>7
Forcing Net Contradiction in r8 => r2c6=1
r2c6<>1 r2c8=1 (r2c8<>7) (r1c7<>1) r1c9<>1 r1c5=1 r1c5<>7 r3c5=7 r3c8<>7 r9c8=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 (r4c7<>1) r4c8<>1 r4c2=1 r8c2<>1
r2c6<>1 r2c8=1 (r1c7<>1) r1c9<>1 r1c5=1 r8c5<>1
r2c6<>1 r2c8=1 r8c8<>1
r2c6<>1 r2c8=1 (r2c8<>7) (r1c7<>1) r1c9<>1 r1c5=1 r1c5<>7 r3c5=7 r3c8<>7 r9c8=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r8c9<>1
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c3<>2
Grouped Discontinuous Nice Loop: 7 r1c9 -7- r1c5 -5- r1c12 =5= r3c2 =9= r2c13 -9- r2c8 -7- r1c9 => r1c9<>7
Grouped Discontinuous Nice Loop: 7 r2c3 -7- r2c8 -9- r3c7 =9= r4c7 -9- r4c4 -7- r4c1 =7= r12c1 -7- r2c3 => r2c3<>7
Grouped Discontinuous Nice Loop: 3 r3c7 -3- r3c3 -7- r12c1 =7= r4c1 -7- r4c4 -9- r4c7 =9= r3c7 => r3c7<>3
Almost Locked Set XZ-Rule: A=r5c89 {159}, B=r29c8 {579}, X=9, Z=5 => r6c8<>5
Almost Locked Set XZ-Rule: A=r45c4 {279}, B=r79c6,r89c4 {23469}, X=9, Z=2 => r7c4<>2
Forcing Chain Contradiction in r1c1 => r2c9=8
r2c9<>8 r2c9=7 r9c9<>7 r9c9=5 r6c9<>5 r6c1=5 r1c1<>5
r2c9<>8 r2c9=7 r2c8<>7 r2c8=9 r2c13<>9 r3c2=9 r3c2<>5 r1c12=5 r1c5<>5 r1c5=7 r1c1<>7
r2c9<>8 r2c1=8 r1c1<>8
Hidden Single: r9c9=7
Naked Single: r9c8=5
Forcing Chain Verity => r1c2<>3
r1c7=3 r1c2<>3
r4c7=3 r4c5<>3 r4c5=9 r4c4<>9 r4c4=7 r4c1<>7 r12c1=7 r3c3<>7 r3c3=3 r1c2<>3
r7c7=3 r8c89<>3 r8c2=3 r1c2<>3
r9c7=3 r8c89<>3 r8c2=3 r1c2<>3
Locked Candidates Type 1 (Pointing): 3 in b1 => r3c8<>3
Naked Triple: 5,7,8 in r1c125 => r1c4<>5, r1c4<>8
Naked Single: r1c4=4
Naked Single: r3c6=2
Naked Single: r7c4=5
Naked Single: r3c4=8
Finned X-Wing: 2 c24 r59 fr7c2 => r9c13<>2
AIC: 9 9- r2c3 -2- r2c1 =2= r6c1 =5= r6c9 -5- r5c9 -1- r5c8 -9- r4c7 =9= r3c7 -9 => r2c8,r3c2<>9
Naked Single: r2c8=7
Discontinuous Nice Loop: 9 r5c3 -9- r5c8 -1- r5c9 -5- r5c2 =5= r6c1 =2= r2c1 =9= r2c3 -9- r5c3 => r5c3<>9
Discontinuous Nice Loop: 2 r6c1 -2- r6c5 =2= r5c4 =7= r4c4 -7- r4c1 =7= r1c1 =5= r6c1 => r6c1<>2
Hidden Single: r2c1=2
Full House: r2c3=9
Discontinuous Nice Loop: 4 r6c1 -4- r6c3 -2- r6c5 =2= r5c4 =7= r4c4 -7- r4c1 =7= r1c1 =5= r6c1 => r6c1<>4
AIC: 9 9- r8c5 -1- r7c5 -2- r6c5 =2= r6c3 =4= r4c1 -4- r9c1 -9 => r8c12,r9c4<>9
Discontinuous Nice Loop: 4 r4c8 -4- r4c1 =4= r6c3 =2= r6c5 -2- r7c5 =2= r9c4 =6= r9c7 -6- r4c7 =6= r4c8 => r4c8<>4
Empty Rectangle: 4 in b9 (r4c17) => r8c1<>4
Naked Single: r8c1=8
Hidden Single: r1c2=8
Locked Candidates Type 2 (Claiming): 4 in r8 => r79c7<>4
Naked Pair: 1,3 in r17c7 => r49c7<>1, r49c7<>3
Naked Single: r9c7=6
Naked Single: r9c4=2
Naked Single: r7c5=1
Naked Single: r7c7=3
Naked Single: r8c5=9
Naked Single: r1c7=1
Naked Single: r7c6=4
Full House: r9c6=3
Full House: r8c4=6
Naked Single: r4c5=3
Naked Single: r1c9=3
Naked Single: r6c5=2
Naked Single: r6c3=4
Naked Single: r6c9=5
Naked Single: r9c3=1
Naked Single: r5c9=1
Naked Single: r6c1=9
Full House: r6c8=3
Naked Single: r8c2=3
Naked Single: r9c2=9
Full House: r9c1=4
Naked Single: r5c8=9
Naked Single: r8c9=4
Full House: r3c9=6
Full House: r8c8=1
Naked Single: r4c1=7
Full House: r1c1=5
Full House: r1c5=7
Full House: r3c5=5
Naked Single: r4c7=4
Full House: r4c8=6
Full House: r3c8=4
Full House: r3c7=9
Naked Single: r5c4=7
Full House: r4c4=9
Full House: r4c2=1
Naked Single: r5c3=2
Full House: r5c2=5
Naked Single: r3c2=7
Full House: r3c3=3
Full House: r7c3=7
Full House: r7c2=2
|
sudoku_normal_extremely_hard_126
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..6..9.2..4.36.5..1..........8..5..23...4.....6.1..7..6......89..5..72......8....
|
586479123249361578173852946718935462352746891964128735627514389835697214491283657
|
. . 6 . . 9 . 2 .
. 4 . 3 6 . 5 . .
1 . . . . . . . .
. . 8 . . 5 . . 2
3 . . . 4 . . . .
. 6 . 1 . . 7 . .
6 . . . . . . 8 9
. . 5 . . 7 2 . .
. . . . 8 . . . .
|
5 8 6 4 7 9 1 2 3
2 4 9 3 6 1 5 7 8
1 7 3 8 5 2 9 4 6
7 1 8 9 3 5 4 6 2
3 5 2 7 4 6 8 9 1
9 6 4 1 2 8 7 3 5
6 2 7 5 1 4 3 8 9
8 3 5 6 9 7 2 1 4
4 9 1 2 8 3 6 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4223_hard
|
586479123249361578173852946718935462352746891964128735627514389835697214491283657 #1 Extreme (31346) bf
Locked Candidates Type 1 (Pointing): 5 in b9 => r9c4<>5
Locked Candidates Type 1 (Pointing): 7 in b9 => r9c123<>7
Hidden Pair: 5,7 in r9c89 => r9c89<>1, r9c89<>3, r9c89<>4, r9c89<>6
Brute Force: r5c7=8
Hidden Single: r6c6=8
Locked Candidates Type 1 (Pointing): 3 in b5 => r78c5<>3
Forcing Net Contradiction in r6c9 => r2c9<>1
r2c9=1 (r1c9<>1 r1c5=1 r8c5<>1) (r8c9<>1) r2c9<>8 r2c1=8 r8c1<>8 r8c2=8 (r8c2<>3) r8c2<>1 r8c8=1 r8c8<>3 r8c9=3 r6c9<>3
r2c9=1 (r2c9<>8 r2c1=8 r8c1<>8) (r1c7<>1) r1c9<>1 r1c5=1 r8c5<>1 r8c5=9 r8c1<>9 r8c1=4 (r7c3<>4) r9c3<>4 r6c3=4 r6c9<>4
r2c9=1 (r5c9<>1) r2c6<>1 r2c6=2 r5c6<>2 r5c6=6 r5c9<>6 r5c9=5 r6c9<>5
Forcing Net Contradiction in r4c7 => r3c9<>3
r3c9=3 (r6c9<>3) (r8c9<>3) (r1c7<>3) r1c9<>3 r1c2=3 r8c2<>3 r8c8=3 (r8c8<>6) (r4c8<>3) r6c8<>3 r6c5=3 r4c5<>3 r4c7=3 (r4c7<>6) (r4c7<>6) r4c7<>9 r3c7=9 (r3c7<>6) r3c7<>6 r9c7=6 r8c9<>6 r8c4=6 r4c4<>6 r4c8=6 r3c8<>6 r3c9=6 r3c9<>3
Brute Force: r5c6=6
Forcing Net Contradiction in b4 => r1c4<>7
r1c4=7 (r4c4<>7 r4c4=9 r6c5<>9 r8c5=9 r8c5<>1) (r4c4<>7 r4c4=9 r4c7<>9 r3c7=9 r2c8<>9) (r1c1<>7) (r1c5<>7) r3c5<>7 r4c5=7 (r4c2<>7 r4c2=1 r8c2<>1) r4c1<>7 r2c1=7 r2c8<>7 r2c8=1 r8c8<>1 r8c9=1 r5c9<>1 r5c9=5 r5c2<>5
r1c4=7 (r1c1<>7) (r3c5<>7 r4c5=7 r4c1<>7 r4c1=4 r8c1<>4) r4c4<>7 r4c4=9 (r4c5<>9) r6c5<>9 r8c5=9 r8c1<>9 r8c1=8 r1c1<>8 r1c1=5 r6c1<>5
Forcing Net Contradiction in r2c3 => r3c3<>9
r3c3=9 (r6c3<>9) r3c7<>9 r4c7=9 (r4c1<>9) r4c4<>9 r4c4=7 r4c1<>7 r4c1=4 r6c3<>4 r6c3=2 r2c3<>2
r3c3=9 r3c7<>9 r4c7=9 r4c4<>9 r4c4=7 r4c1<>7 r12c1=7 r2c3<>7
r3c3=9 r2c3<>9
Forcing Net Contradiction in r1c1 => r3c9<>7
r3c9=7 (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) (r2c8<>7) (r3c4<>7) r3c5<>7 r1c5=7 r1c5<>1 r2c6=1 r2c8<>1 r2c8=9 r5c8<>9 r5c8=5 (r6c8<>5) r6c9<>5 r6c1=5 r1c1<>5
r3c9=7 (r3c4<>7) r3c5<>7 r1c5=7 r1c1<>7
r3c9=7 (r3c9<>6 r8c9=6 r8c9<>3) (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r4c8<>1) (r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) (r3c4<>7) r3c5<>7 r1c5=7 r1c5<>1 r2c6=1 r2c8<>1 r8c8=1 r8c8<>3 r8c2=3 r8c2<>8 r8c1=8 r1c1<>8
Forcing Net Contradiction in b2 => r3c9<>8
r3c9=8 (r3c9<>6 r8c9=6 r8c9<>1) (r3c9<>6 r8c9=6 r8c9<>3) r2c9<>8 r2c1=8 r8c1<>8 r8c2=8 (r8c2<>1) r8c2<>3 r8c8=3 r8c8<>1 r8c5=1 r1c5<>1
r3c9=8 (r3c9<>6 r8c9=6 r8c9<>3) r2c9<>8 (r2c9=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r4c8<>1) (r2c9=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r5c8<>1) r2c1=8 r8c1<>8 r8c2=8 r8c2<>3 r8c8=3 r8c8<>1 r2c8=1 r2c6<>1
Forcing Chain Contradiction in r1c4 => r3c2<>2
r3c2=2 r3c6<>2 r3c6=4 r1c4<>4
r3c2=2 r3c2<>5 r1c12=5 r1c4<>5
r3c2=2 r3c2<>8 r3c4=8 r1c4<>8
Forcing Net Contradiction in b1 => r3c4<>7
r3c4=7 (r3c4<>8 r3c2=8 r8c2<>8) (r3c5<>7 r4c5=7 r4c2<>7 r4c2=1 r8c2<>1) r4c4<>7 r4c4=9 (r4c5<>9) r6c5<>9 r8c5=9 r8c2<>9 r8c2=3 r1c2<>3
r3c4=7 r3c4<>8 r3c2=8 r3c2<>3
r3c4=7 (r3c4<>2) (r3c4<>4) r3c4<>8 (r3c2=8 r3c2<>5 r3c5=5 r3c5<>2) r1c4=8 r1c4<>4 r3c6=4 r3c6<>2 r3c3=2 r3c3<>3
Locked Candidates Type 1 (Pointing): 7 in b2 => r4c5<>7
Forcing Net Contradiction in r8 => r2c6=1
r2c6<>1 r2c8=1 (r2c8<>7) (r1c7<>1) r1c9<>1 r1c5=1 r1c5<>7 r3c5=7 r3c8<>7 r9c8=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 (r4c7<>1) r4c8<>1 r4c2=1 r8c2<>1
r2c6<>1 r2c8=1 (r1c7<>1) r1c9<>1 r1c5=1 r8c5<>1
r2c6<>1 r2c8=1 r8c8<>1
r2c6<>1 r2c8=1 (r2c8<>7) (r1c7<>1) r1c9<>1 r1c5=1 r1c5<>7 r3c5=7 r3c8<>7 r9c8=7 r9c9<>7 r9c9=5 r5c9<>5 r5c9=1 r8c9<>1
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c3<>2
Grouped Discontinuous Nice Loop: 7 r1c9 -7- r1c5 -5- r1c12 =5= r3c2 =9= r2c13 -9- r2c8 -7- r1c9 => r1c9<>7
Grouped Discontinuous Nice Loop: 7 r2c3 -7- r2c8 -9- r3c7 =9= r4c7 -9- r4c4 -7- r4c1 =7= r12c1 -7- r2c3 => r2c3<>7
Grouped Discontinuous Nice Loop: 3 r3c7 -3- r3c3 -7- r12c1 =7= r4c1 -7- r4c4 -9- r4c7 =9= r3c7 => r3c7<>3
Almost Locked Set XZ-Rule: A=r5c89 {159}, B=r29c8 {579}, X=9, Z=5 => r6c8<>5
Almost Locked Set XZ-Rule: A=r45c4 {279}, B=r79c6,r89c4 {23469}, X=9, Z=2 => r7c4<>2
Forcing Chain Contradiction in r1c1 => r2c9=8
r2c9<>8 r2c9=7 r9c9<>7 r9c9=5 r6c9<>5 r6c1=5 r1c1<>5
r2c9<>8 r2c9=7 r2c8<>7 r2c8=9 r2c13<>9 r3c2=9 r3c2<>5 r1c12=5 r1c5<>5 r1c5=7 r1c1<>7
r2c9<>8 r2c1=8 r1c1<>8
Hidden Single: r9c9=7
Naked Single: r9c8=5
Forcing Chain Verity => r1c2<>3
r1c7=3 r1c2<>3
r4c7=3 r4c5<>3 r4c5=9 r4c4<>9 r4c4=7 r4c1<>7 r12c1=7 r3c3<>7 r3c3=3 r1c2<>3
r7c7=3 r8c89<>3 r8c2=3 r1c2<>3
r9c7=3 r8c89<>3 r8c2=3 r1c2<>3
Locked Candidates Type 1 (Pointing): 3 in b1 => r3c8<>3
Naked Triple: 5,7,8 in r1c125 => r1c4<>5, r1c4<>8
Naked Single: r1c4=4
Naked Single: r3c6=2
Naked Single: r7c4=5
Naked Single: r3c4=8
Finned X-Wing: 2 c24 r59 fr7c2 => r9c13<>2
AIC: 9 9- r2c3 -2- r2c1 =2= r6c1 =5= r6c9 -5- r5c9 -1- r5c8 -9- r4c7 =9= r3c7 -9 => r2c8,r3c2<>9
Naked Single: r2c8=7
Discontinuous Nice Loop: 9 r5c3 -9- r5c8 -1- r5c9 -5- r5c2 =5= r6c1 =2= r2c1 =9= r2c3 -9- r5c3 => r5c3<>9
Discontinuous Nice Loop: 2 r6c1 -2- r6c5 =2= r5c4 =7= r4c4 -7- r4c1 =7= r1c1 =5= r6c1 => r6c1<>2
Hidden Single: r2c1=2
Full House: r2c3=9
Discontinuous Nice Loop: 4 r6c1 -4- r6c3 -2- r6c5 =2= r5c4 =7= r4c4 -7- r4c1 =7= r1c1 =5= r6c1 => r6c1<>4
AIC: 9 9- r8c5 -1- r7c5 -2- r6c5 =2= r6c3 =4= r4c1 -4- r9c1 -9 => r8c12,r9c4<>9
Discontinuous Nice Loop: 4 r4c8 -4- r4c1 =4= r6c3 =2= r6c5 -2- r7c5 =2= r9c4 =6= r9c7 -6- r4c7 =6= r4c8 => r4c8<>4
Empty Rectangle: 4 in b9 (r4c17) => r8c1<>4
Naked Single: r8c1=8
Hidden Single: r1c2=8
Locked Candidates Type 2 (Claiming): 4 in r8 => r79c7<>4
Naked Pair: 1,3 in r17c7 => r49c7<>1, r49c7<>3
Naked Single: r9c7=6
Naked Single: r9c4=2
Naked Single: r7c5=1
Naked Single: r7c7=3
Naked Single: r8c5=9
Naked Single: r1c7=1
Naked Single: r7c6=4
Full House: r9c6=3
Full House: r8c4=6
Naked Single: r4c5=3
Naked Single: r1c9=3
Naked Single: r6c5=2
Naked Single: r6c3=4
Naked Single: r6c9=5
Naked Single: r9c3=1
Naked Single: r5c9=1
Naked Single: r6c1=9
Full House: r6c8=3
Naked Single: r8c2=3
Naked Single: r9c2=9
Full House: r9c1=4
Naked Single: r5c8=9
Naked Single: r8c9=4
Full House: r3c9=6
Full House: r8c8=1
Naked Single: r4c1=7
Full House: r1c1=5
Full House: r1c5=7
Full House: r3c5=5
Naked Single: r4c7=4
Full House: r4c8=6
Full House: r3c8=4
Full House: r3c7=9
Naked Single: r5c4=7
Full House: r4c4=9
Full House: r4c2=1
Naked Single: r5c3=2
Full House: r5c2=5
Naked Single: r3c2=7
Full House: r3c3=3
Full House: r7c3=7
Full House: r7c2=2
|
sudoku_normal_hard_127
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
9.....4.7.7.42.89.4.8..7....4..691.2..6.7.349...1..76.....3.51.5.........2...8..4
|
912586437675423891438917625847369152156872349293145768789234516564791283321658974
|
9 . . . . . 4 . 7
. 7 . 4 2 . 8 9 .
4 . 8 . . 7 . . .
. 4 . . 6 9 1 . 2
. . 6 . 7 . 3 4 9
. . . 1 . . 7 6 .
. . . . 3 . 5 1 .
5 . . . . . . . .
. 2 . . . 8 . . 4
|
9 1 2 5 8 6 4 3 7
6 7 5 4 2 3 8 9 1
4 3 8 9 1 7 6 2 5
8 4 7 3 6 9 1 5 2
1 5 6 8 7 2 3 4 9
2 9 3 1 4 5 7 6 8
7 8 9 2 3 4 5 1 6
5 6 4 7 9 1 2 8 3
3 2 1 6 5 8 9 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8577_hard
|
912586437675423891438917625847369152156872349293145768789234516564791283321658974 #1 Extreme (28602) bf
Locked Candidates Type 1 (Pointing): 9 in b2 => r3c789<>9
Locked Candidates Type 1 (Pointing): 2 in b9 => r8c46<>2
Hidden Pair: 2,4 in r1c3,r3c1 => r1c3,r3c1<>1, r1c3,r3c1<>3, r1c3<>5, r3c1<>6
Brute Force: r5c8=4
Grouped Discontinuous Nice Loop: 7 r8c7 -7- r46c7 =7= r4c8 =8= r8c8 =2= r8c7 => r8c7<>7
Brute Force: r5c9=9
Naked Single: r6c7=7
Naked Single: r4c7=1
Hidden Single: r2c8=9
Forcing Chain Contradiction in r7c6 => r6c5<>5
r6c5=5 r5c6<>5 r5c6=2 r7c6<>2
r6c5=5 r6c5<>4 r6c6=4 r7c6<>4
r6c5=5 r6c9<>5 r6c9=8 r7c9<>8 r7c9=6 r7c6<>6
Forcing Chain Contradiction in r4 => r9c1<>7
r9c1=7 r4c1<>7 r4c3=7 r4c3<>5
r9c1=7 r7c13<>7 r7c4=7 r7c4<>2 r7c6=2 r5c6<>2 r5c6=5 r4c4<>5
r9c1=7 r9c8<>7 r8c8=7 r8c8<>8 r4c8=8 r4c8<>5
Forcing Net Contradiction in r8c7 => r1c5<>5
r1c5=5 (r9c5<>5 r9c4=5 r4c4<>5) r1c5<>8 r6c5=8 r6c9<>8 r6c9=5 r4c8<>5 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 r2c9<>5 r2c6=5 r1c5<>5
Forcing Chain Contradiction in r9c4 => r9c3<>9
r9c3=9 r7c23<>9 r7c4=9 r3c4<>9 r3c5=9 r3c5<>5 r9c5=5 r9c4<>5
r9c3=9 r9c7<>9 r9c7=6 r9c4<>6
r9c3=9 r9c7<>9 r8c7=9 r8c7<>2 r8c8=2 r8c8<>7 r9c8=7 r9c4<>7
r9c3=9 r9c4<>9
Forcing Net Contradiction in r7c6 => r7c1<>6
r7c1=6 (r7c1<>7 r4c1=7 r4c3<>7) r7c9<>6 r7c9=8 (r7c2<>8 r7c2=9 r6c2<>9) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 r4c3<>3 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 (r6c2<>5) r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r7c6<>2
r7c1=6 (r7c1<>7 r4c1=7 r4c3<>7) r7c9<>6 r7c9=8 (r7c2<>8 r7c2=9 r6c2<>9) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 (r6c6<>3) r4c3<>3 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 (r6c6<>5) (r6c2<>5) r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r6c6<>2 r6c6=4 r7c6<>4
r7c1=6 r7c6<>6
Forcing Net Contradiction in r7c1 => r2c9<>6
r2c9=6 (r7c9<>6 r7c9=8 r7c2<>8) r2c1<>6 r9c1=6 r7c2<>6 r7c2=9 r6c2<>9 r6c3=9 r6c3<>2 r1c3=2 r3c1<>2 r3c1=4 r7c1<>4
r2c9=6 (r2c1<>6 r9c1=6 r7c2<>6 r7c2=9 r6c2<>9) r7c9<>6 r7c9=8 (r8c8<>8 r4c8=8 r4c1<>8) (r6c9<>8 r6c9=5 r6c2<>5) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 r4c1<>3 r4c1=7 r7c1<>7
r2c9=6 r7c9<>6 r7c9=8 r7c1<>8
Finned Franken Swordfish: 6 r29b3 c147 fr2c6 fr3c9 => r3c4<>6
Forcing Chain Verity => r7c6<>6
r7c2=6 r7c6<>6
r8c2=6 r8c2<>8 r7c12=8 r7c9<>8 r7c9=6 r7c6<>6
r9c1=6 r2c1<>6 r2c6=6 r7c6<>6
Forcing Net Contradiction in r8c7 => r1c3=2
r1c3<>2 (r6c3=2 r6c3<>9 r6c2=9 r6c2<>5) (r6c3=2 r6c3<>5) r1c3=4 r3c1<>4 r7c1=4 r7c6<>4 r7c6=2 r5c6<>2 r5c6=5 r5c2<>5 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r7c6<>2 r7c6=4 r7c1<>4 r3c1=4 r1c3<>4 r1c3=2
Naked Single: r3c1=4
Hidden Single: r1c7=4
Locked Candidates Type 1 (Pointing): 6 in b3 => r3c2<>6
Almost Locked Set XZ-Rule: A=r6c2359 {34589}, B=r47c1 {378}, X=3, Z=8 => r6c1<>8
Forcing Chain Verity => r3c7=6
r4c1=8 r4c8<>8 r8c8=8 r8c8<>2 r8c7=2 r3c7<>2 r3c7=6
r5c1=8 r5c1<>1 r5c2=1 r13c2<>1 r2c13=1 r2c9<>1 r3c9=1 r3c9<>6 r3c7=6
r7c1=8 r7c9<>8 r7c9=6 r3c9<>6 r3c7=6
Naked Single: r9c7=9
Full House: r8c7=2
Hidden Single: r3c8=2
Skyscraper: 6 in r2c6,r9c4 (connected by r29c1) => r1c4,r8c6<>6
Almost Locked Set XY-Wing: A=r1c458 {1358}, B=r57c6 {245}, C=r389c5 {1459}, X,Y=1,4, Z=5 => r1c6<>5
Finned Franken Swordfish: 5 c36b6 r246 fr5c6 => r4c4<>5
XY-Wing: 5/8/3 in r14c8,r4c4 => r1c4<>3
XY-Wing: 1/8/5 in r1c45,r9c5 => r3c5,r9c4<>5
Hidden Single: r9c5=5
Locked Candidates Type 1 (Pointing): 1 in b8 => r8c23<>1
AIC: 5 5- r1c4 -8- r1c5 =8= r6c5 =4= r6c6 -4- r7c6 -2- r5c6 -5 => r2c6,r5c4<>5
Skyscraper: 5 in r2c9,r4c8 (connected by r24c3) => r1c8,r6c9<>5
Naked Single: r1c8=3
Naked Single: r6c9=8
Full House: r4c8=5
Naked Single: r9c8=7
Full House: r8c8=8
Naked Single: r6c5=4
Naked Single: r7c9=6
Full House: r8c9=3
Naked Single: r9c4=6
Hidden Single: r1c5=8
Naked Single: r1c4=5
Hidden Single: r8c2=6
Naked Single: r1c2=1
Full House: r1c6=6
Hidden Single: r2c1=6
Hidden Single: r9c3=1
Full House: r9c1=3
Naked Single: r6c1=2
Hidden Single: r5c1=1
Skyscraper: 3 in r2c6,r4c4 (connected by r24c3) => r3c4,r6c6<>3
Naked Single: r3c4=9
Naked Single: r6c6=5
Naked Single: r3c5=1
Full House: r2c6=3
Full House: r8c5=9
Naked Single: r8c4=7
Naked Single: r5c6=2
Naked Single: r3c9=5
Full House: r2c9=1
Full House: r2c3=5
Full House: r3c2=3
Naked Single: r7c4=2
Naked Single: r8c3=4
Full House: r8c6=1
Full House: r7c6=4
Naked Single: r5c4=8
Full House: r4c4=3
Full House: r5c2=5
Naked Single: r6c2=9
Full House: r6c3=3
Full House: r7c2=8
Naked Single: r4c3=7
Full House: r4c1=8
Full House: r7c1=7
Full House: r7c3=9
|
sudoku_normal_extremely_hard_127
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
9.......7.7.42.8....8..7....4..69..2..6.7.3.....1...6.....3.51.5.........2...8..4
|
912586437675423891438917625847369152156872349293145768789234516564791283321658974
|
9 . . . . . . . 7
. 7 . 4 2 . 8 . .
. . 8 . . 7 . . .
. 4 . . 6 9 . . 2
. . 6 . 7 . 3 . .
. . . 1 . . . 6 .
. . . . 3 . 5 1 .
5 . . . . . . . .
. 2 . . . 8 . . 4
|
9 1 2 5 8 6 4 3 7
6 7 5 4 2 3 8 9 1
4 3 8 9 1 7 6 2 5
8 4 7 3 6 9 1 5 2
1 5 6 8 7 2 3 4 9
2 9 3 1 4 5 7 6 8
7 8 9 2 3 4 5 1 6
5 6 4 7 9 1 2 8 3
3 2 1 6 5 8 9 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8577_hard
|
912586437675423891438917625847369152156872349293145768789234516564791283321658974 #1 Extreme (28602) bf
Locked Candidates Type 1 (Pointing): 9 in b2 => r3c789<>9
Locked Candidates Type 1 (Pointing): 2 in b9 => r8c46<>2
Hidden Pair: 2,4 in r1c3,r3c1 => r1c3,r3c1<>1, r1c3,r3c1<>3, r1c3<>5, r3c1<>6
Brute Force: r5c8=4
Grouped Discontinuous Nice Loop: 7 r8c7 -7- r46c7 =7= r4c8 =8= r8c8 =2= r8c7 => r8c7<>7
Brute Force: r5c9=9
Naked Single: r6c7=7
Naked Single: r4c7=1
Hidden Single: r2c8=9
Forcing Chain Contradiction in r7c6 => r6c5<>5
r6c5=5 r5c6<>5 r5c6=2 r7c6<>2
r6c5=5 r6c5<>4 r6c6=4 r7c6<>4
r6c5=5 r6c9<>5 r6c9=8 r7c9<>8 r7c9=6 r7c6<>6
Forcing Chain Contradiction in r4 => r9c1<>7
r9c1=7 r4c1<>7 r4c3=7 r4c3<>5
r9c1=7 r7c13<>7 r7c4=7 r7c4<>2 r7c6=2 r5c6<>2 r5c6=5 r4c4<>5
r9c1=7 r9c8<>7 r8c8=7 r8c8<>8 r4c8=8 r4c8<>5
Forcing Net Contradiction in r8c7 => r1c5<>5
r1c5=5 (r9c5<>5 r9c4=5 r4c4<>5) r1c5<>8 r6c5=8 r6c9<>8 r6c9=5 r4c8<>5 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 r2c9<>5 r2c6=5 r1c5<>5
Forcing Chain Contradiction in r9c4 => r9c3<>9
r9c3=9 r7c23<>9 r7c4=9 r3c4<>9 r3c5=9 r3c5<>5 r9c5=5 r9c4<>5
r9c3=9 r9c7<>9 r9c7=6 r9c4<>6
r9c3=9 r9c7<>9 r8c7=9 r8c7<>2 r8c8=2 r8c8<>7 r9c8=7 r9c4<>7
r9c3=9 r9c4<>9
Forcing Net Contradiction in r7c6 => r7c1<>6
r7c1=6 (r7c1<>7 r4c1=7 r4c3<>7) r7c9<>6 r7c9=8 (r7c2<>8 r7c2=9 r6c2<>9) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 r4c3<>3 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 (r6c2<>5) r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r7c6<>2
r7c1=6 (r7c1<>7 r4c1=7 r4c3<>7) r7c9<>6 r7c9=8 (r7c2<>8 r7c2=9 r6c2<>9) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 (r6c6<>3) r4c3<>3 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 (r6c6<>5) (r6c2<>5) r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r6c6<>2 r6c6=4 r7c6<>4
r7c1=6 r7c6<>6
Forcing Net Contradiction in r7c1 => r2c9<>6
r2c9=6 (r7c9<>6 r7c9=8 r7c2<>8) r2c1<>6 r9c1=6 r7c2<>6 r7c2=9 r6c2<>9 r6c3=9 r6c3<>2 r1c3=2 r3c1<>2 r3c1=4 r7c1<>4
r2c9=6 (r2c1<>6 r9c1=6 r7c2<>6 r7c2=9 r6c2<>9) r7c9<>6 r7c9=8 (r8c8<>8 r4c8=8 r4c1<>8) (r6c9<>8 r6c9=5 r6c2<>5) (r8c8<>8) r8c9<>8 r8c2=8 r6c2<>8 r6c2=3 r4c1<>3 r4c1=7 r7c1<>7
r2c9=6 r7c9<>6 r7c9=8 r7c1<>8
Finned Franken Swordfish: 6 r29b3 c147 fr2c6 fr3c9 => r3c4<>6
Forcing Chain Verity => r7c6<>6
r7c2=6 r7c6<>6
r8c2=6 r8c2<>8 r7c12=8 r7c9<>8 r7c9=6 r7c6<>6
r9c1=6 r2c1<>6 r2c6=6 r7c6<>6
Forcing Net Contradiction in r8c7 => r1c3=2
r1c3<>2 (r6c3=2 r6c3<>9 r6c2=9 r6c2<>5) (r6c3=2 r6c3<>5) r1c3=4 r3c1<>4 r7c1=4 r7c6<>4 r7c6=2 r5c6<>2 r5c6=5 r5c2<>5 r4c3=5 (r2c3<>5) r4c8<>5 r6c9=5 r2c9<>5 r2c6=5 r5c6<>5 r5c6=2 r7c6<>2 r7c6=4 r7c1<>4 r3c1=4 r1c3<>4 r1c3=2
Naked Single: r3c1=4
Hidden Single: r1c7=4
Locked Candidates Type 1 (Pointing): 6 in b3 => r3c2<>6
Almost Locked Set XZ-Rule: A=r6c2359 {34589}, B=r47c1 {378}, X=3, Z=8 => r6c1<>8
Forcing Chain Verity => r3c7=6
r4c1=8 r4c8<>8 r8c8=8 r8c8<>2 r8c7=2 r3c7<>2 r3c7=6
r5c1=8 r5c1<>1 r5c2=1 r13c2<>1 r2c13=1 r2c9<>1 r3c9=1 r3c9<>6 r3c7=6
r7c1=8 r7c9<>8 r7c9=6 r3c9<>6 r3c7=6
Naked Single: r9c7=9
Full House: r8c7=2
Hidden Single: r3c8=2
Skyscraper: 6 in r2c6,r9c4 (connected by r29c1) => r1c4,r8c6<>6
Almost Locked Set XY-Wing: A=r1c458 {1358}, B=r57c6 {245}, C=r389c5 {1459}, X,Y=1,4, Z=5 => r1c6<>5
Finned Franken Swordfish: 5 c36b6 r246 fr5c6 => r4c4<>5
XY-Wing: 5/8/3 in r14c8,r4c4 => r1c4<>3
XY-Wing: 1/8/5 in r1c45,r9c5 => r3c5,r9c4<>5
Hidden Single: r9c5=5
Locked Candidates Type 1 (Pointing): 1 in b8 => r8c23<>1
AIC: 5 5- r1c4 -8- r1c5 =8= r6c5 =4= r6c6 -4- r7c6 -2- r5c6 -5 => r2c6,r5c4<>5
Skyscraper: 5 in r2c9,r4c8 (connected by r24c3) => r1c8,r6c9<>5
Naked Single: r1c8=3
Naked Single: r6c9=8
Full House: r4c8=5
Naked Single: r9c8=7
Full House: r8c8=8
Naked Single: r6c5=4
Naked Single: r7c9=6
Full House: r8c9=3
Naked Single: r9c4=6
Hidden Single: r1c5=8
Naked Single: r1c4=5
Hidden Single: r8c2=6
Naked Single: r1c2=1
Full House: r1c6=6
Hidden Single: r2c1=6
Hidden Single: r9c3=1
Full House: r9c1=3
Naked Single: r6c1=2
Hidden Single: r5c1=1
Skyscraper: 3 in r2c6,r4c4 (connected by r24c3) => r3c4,r6c6<>3
Naked Single: r3c4=9
Naked Single: r6c6=5
Naked Single: r3c5=1
Full House: r2c6=3
Full House: r8c5=9
Naked Single: r8c4=7
Naked Single: r5c6=2
Naked Single: r3c9=5
Full House: r2c9=1
Full House: r2c3=5
Full House: r3c2=3
Naked Single: r7c4=2
Naked Single: r8c3=4
Full House: r8c6=1
Full House: r7c6=4
Naked Single: r5c4=8
Full House: r4c4=3
Full House: r5c2=5
Naked Single: r6c2=9
Full House: r6c3=3
Full House: r7c2=8
Naked Single: r4c3=7
Full House: r4c1=8
Full House: r7c1=7
Full House: r7c3=9
|
sudoku_normal_hard_128
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.7.9..6.2..3.6579.9.6.27.8...7.9.8166..7..923.9...6547.6..7.2.97....9.6.4.96...7.
|
874913652213865794956427381347592816685741923192386547568174239731259468429638175
|
. 7 . 9 . . 6 . 2
. . 3 . 6 5 7 9 .
9 . 6 . 2 7 . 8 .
. . 7 . 9 . 8 1 6
6 . . 7 . . 9 2 3
. 9 . . . 6 5 4 7
. 6 . . 7 . 2 . 9
7 . . . . 9 . 6 .
4 . 9 6 . . . 7 .
|
8 7 4 9 1 3 6 5 2
2 1 3 8 6 5 7 9 4
9 5 6 4 2 7 3 8 1
3 4 7 5 9 2 8 1 6
6 8 5 7 4 1 9 2 3
1 9 2 3 8 6 5 4 7
5 6 8 1 7 4 2 3 9
7 3 1 2 5 9 4 6 8
4 2 9 6 3 8 1 7 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4702_hard
|
874913652213865794956427381347592816685741923192386547568174239731259468429638175 #1 Extreme (36012) bf
Hidden Single: r3c6=7
Hidden Single: r9c3=9
Hidden Single: r4c9=6
Hidden Single: r8c1=7
Hidden Single: r2c5=6
Hidden Single: r7c2=6
Hidden Single: r6c6=6
Finned Swordfish: 2 r249 c126 fr4c4 => r5c6<>2
Grouped Discontinuous Nice Loop: 1/5 r3c1 =9= r3c7 -9- r5c7 =9= r5c8 =2= r5c23 -2- r46c1 =2= r2c1 =9= r3c1 => r3c1<>1, r3c1<>5
Naked Single: r3c1=9
Hidden Pair: 7,9 in r2c78 => r2c7<>1, r2c78<>4
Brute Force: r5c7=9
Naked Single: r2c7=7
Naked Single: r2c8=9
Hidden Single: r9c8=7
Finned Swordfish: 5 r359 c259 fr5c3 => r4c2<>5
Brute Force: r5c8=2
Brute Force: r5c9=3
Naked Single: r6c8=4
Full House: r4c7=8
Locked Candidates Type 1 (Pointing): 4 in b9 => r8c45<>4
X-Wing: 4 c35 r15 => r15c6,r5c2<>4
2-String Kite: 3 in r3c4,r7c8 (connected by r1c8,r3c7) => r7c4<>3
Almost Locked Set XY-Wing: A=r15c6 {138}, B=r7c8,r9c7 {135}, C=r1c8 {35}, X,Y=3,5, Z=1 => r9c6<>1
Forcing Net Contradiction in b5 => r4c2<>3
r4c2=3 (r4c2<>4) (r4c6<>3) (r4c1<>3) r6c1<>3 r7c1=3 (r7c6<>3) r7c8<>3 r1c8=3 r1c6<>3 r9c6=3 r9c6<>2 r4c6=2 r4c6<>4 r4c4=4 r4c4<>5
r4c2=3 (r4c6<>3) (r4c1<>3) r6c1<>3 r7c1=3 (r7c6<>3) r7c8<>3 (r7c8=5 r9c9<>5) r1c8=3 r1c6<>3 r9c6=3 r9c6<>2 r9c2=2 r9c2<>5 r9c5=5 r5c5<>5
Locked Candidates Type 1 (Pointing): 3 in b4 => r7c1<>3
Discontinuous Nice Loop: 2 r4c4 -2- r4c2 -4- r5c3 =4= r5c5 =5= r4c4 => r4c4<>2
X-Wing: 2 c34 r68 => r6c1,r8c2<>2
Almost Locked Set XZ-Rule: A=r7c13 {158}, B=r7c8,r9c7 {135}, X=5, Z=1 => r9c2<>1
Forcing Chain Contradiction in c3 => r1c1<>5
r1c1=5 r1c3<>5
r1c1=5 r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r4c6=4 r4c2<>4 r5c3=4 r5c3<>5
r1c1=5 r1c8<>5 r7c8=5 r7c3<>5
r1c1=5 r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r4c6=4 r4c6<>2 r9c6=2 r9c2<>2 r8c3=2 r8c3<>5
Multi Colors 1: 5 (r1c3,r3c9,r7c8) / (r1c8,r3c2), (r4c1,r5c5) / (r4c4,r7c1) => r5c2<>5
Naked Pair: 1,8 in r5c26 => r5c35<>1, r5c35<>8
Discontinuous Nice Loop: 5 r8c3 -5- r5c3 -4- r4c2 -2- r9c2 =2= r8c3 => r8c3<>5
Finned Swordfish: 5 r389 c249 fr8c5 fr9c5 => r7c4<>5
Skyscraper: 5 in r7c1,r8c4 (connected by r4c14) => r8c2<>5
Discontinuous Nice Loop: 3 r8c7 -3- r8c2 =3= r9c2 =5= r3c2 -5- r3c9 =5= r1c8 =3= r7c8 -3- r8c7 => r8c7<>3
Forcing Chain Contradiction in r4c4 => r1c8=5
r1c8<>5 r1c8=3 r3c7<>3 r3c4=3 r4c4<>3
r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r7c4=4 r4c4<>4
r1c8<>5 r1c3=5 r5c3<>5 r5c5=5 r4c4<>5
Full House: r7c8=3
Naked Single: r9c7=1
Naked Single: r8c7=4
Full House: r3c7=3
Hidden Single: r3c2=5
Naked Triple: 1,4,8 in r237c4 => r4c4<>4, r68c4<>1, r68c4<>8
Hidden Pair: 1,8 in r5c6,r6c5 => r6c5<>3
Uniqueness Test 1: 1/4 in r2c49,r3c49 => r2c4<>1, r2c4<>4
Naked Single: r2c4=8
Sashimi X-Wing: 8 r57 c26 fr7c1 fr7c3 => r89c2<>8
Hidden Single: r5c2=8
Naked Single: r5c6=1
Naked Single: r1c6=3
Naked Single: r6c5=8
Locked Candidates Type 1 (Pointing): 3 in b5 => r8c4<>3
Naked Pair: 2,4 in r4c26 => r4c1<>2
Hidden Single: r2c1=2
Skyscraper: 1 in r1c5,r2c2 (connected by r8c25) => r1c13<>1
Naked Single: r1c1=8
Naked Single: r1c3=4
Full House: r1c5=1
Full House: r2c2=1
Full House: r3c4=4
Full House: r2c9=4
Full House: r3c9=1
Naked Single: r5c3=5
Full House: r5c5=4
Naked Single: r8c2=3
Naked Single: r7c4=1
Naked Single: r4c1=3
Naked Single: r4c6=2
Naked Single: r8c5=5
Full House: r9c5=3
Naked Single: r9c2=2
Full House: r4c2=4
Full House: r4c4=5
Full House: r6c4=3
Full House: r8c4=2
Naked Single: r7c1=5
Full House: r6c1=1
Full House: r6c3=2
Naked Single: r7c3=8
Full House: r7c6=4
Full House: r9c6=8
Full House: r8c3=1
Full House: r8c9=8
Full House: r9c9=5
|
sudoku_normal_extremely_hard_128
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.7.9..6.2..3..5.....6.2..8...7.9..1.6..7......9....5.7....7.2.9.....9.6.4..6.....
|
874913652213865794956427381347592816685741923192386547568174239731259468429638175
|
. 7 . 9 . . 6 . 2
. . 3 . . 5 . . .
. . 6 . 2 . . 8 .
. . 7 . 9 . . 1 .
6 . . 7 . . . . .
. 9 . . . . 5 . 7
. . . . 7 . 2 . 9
. . . . . 9 . 6 .
4 . . 6 . . . . .
|
8 7 4 9 1 3 6 5 2
2 1 3 8 6 5 7 9 4
9 5 6 4 2 7 3 8 1
3 4 7 5 9 2 8 1 6
6 8 5 7 4 1 9 2 3
1 9 2 3 8 6 5 4 7
5 6 8 1 7 4 2 3 9
7 3 1 2 5 9 4 6 8
4 2 9 6 3 8 1 7 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4702_hard
|
874913652213865794956427381347592816685741923192386547568174239731259468429638175 #1 Extreme (36012) bf
Hidden Single: r3c6=7
Hidden Single: r9c3=9
Hidden Single: r4c9=6
Hidden Single: r8c1=7
Hidden Single: r2c5=6
Hidden Single: r7c2=6
Hidden Single: r6c6=6
Finned Swordfish: 2 r249 c126 fr4c4 => r5c6<>2
Grouped Discontinuous Nice Loop: 1/5 r3c1 =9= r3c7 -9- r5c7 =9= r5c8 =2= r5c23 -2- r46c1 =2= r2c1 =9= r3c1 => r3c1<>1, r3c1<>5
Naked Single: r3c1=9
Hidden Pair: 7,9 in r2c78 => r2c7<>1, r2c78<>4
Brute Force: r5c7=9
Naked Single: r2c7=7
Naked Single: r2c8=9
Hidden Single: r9c8=7
Finned Swordfish: 5 r359 c259 fr5c3 => r4c2<>5
Brute Force: r5c8=2
Brute Force: r5c9=3
Naked Single: r6c8=4
Full House: r4c7=8
Locked Candidates Type 1 (Pointing): 4 in b9 => r8c45<>4
X-Wing: 4 c35 r15 => r15c6,r5c2<>4
2-String Kite: 3 in r3c4,r7c8 (connected by r1c8,r3c7) => r7c4<>3
Almost Locked Set XY-Wing: A=r15c6 {138}, B=r7c8,r9c7 {135}, C=r1c8 {35}, X,Y=3,5, Z=1 => r9c6<>1
Forcing Net Contradiction in b5 => r4c2<>3
r4c2=3 (r4c2<>4) (r4c6<>3) (r4c1<>3) r6c1<>3 r7c1=3 (r7c6<>3) r7c8<>3 r1c8=3 r1c6<>3 r9c6=3 r9c6<>2 r4c6=2 r4c6<>4 r4c4=4 r4c4<>5
r4c2=3 (r4c6<>3) (r4c1<>3) r6c1<>3 r7c1=3 (r7c6<>3) r7c8<>3 (r7c8=5 r9c9<>5) r1c8=3 r1c6<>3 r9c6=3 r9c6<>2 r9c2=2 r9c2<>5 r9c5=5 r5c5<>5
Locked Candidates Type 1 (Pointing): 3 in b4 => r7c1<>3
Discontinuous Nice Loop: 2 r4c4 -2- r4c2 -4- r5c3 =4= r5c5 =5= r4c4 => r4c4<>2
X-Wing: 2 c34 r68 => r6c1,r8c2<>2
Almost Locked Set XZ-Rule: A=r7c13 {158}, B=r7c8,r9c7 {135}, X=5, Z=1 => r9c2<>1
Forcing Chain Contradiction in c3 => r1c1<>5
r1c1=5 r1c3<>5
r1c1=5 r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r4c6=4 r4c2<>4 r5c3=4 r5c3<>5
r1c1=5 r1c8<>5 r7c8=5 r7c3<>5
r1c1=5 r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r4c6=4 r4c6<>2 r9c6=2 r9c2<>2 r8c3=2 r8c3<>5
Multi Colors 1: 5 (r1c3,r3c9,r7c8) / (r1c8,r3c2), (r4c1,r5c5) / (r4c4,r7c1) => r5c2<>5
Naked Pair: 1,8 in r5c26 => r5c35<>1, r5c35<>8
Discontinuous Nice Loop: 5 r8c3 -5- r5c3 -4- r4c2 -2- r9c2 =2= r8c3 => r8c3<>5
Finned Swordfish: 5 r389 c249 fr8c5 fr9c5 => r7c4<>5
Skyscraper: 5 in r7c1,r8c4 (connected by r4c14) => r8c2<>5
Discontinuous Nice Loop: 3 r8c7 -3- r8c2 =3= r9c2 =5= r3c2 -5- r3c9 =5= r1c8 =3= r7c8 -3- r8c7 => r8c7<>3
Forcing Chain Contradiction in r4c4 => r1c8=5
r1c8<>5 r1c8=3 r3c7<>3 r3c4=3 r4c4<>3
r1c8<>5 r1c8=3 r7c8<>3 r7c6=3 r7c6<>4 r7c4=4 r4c4<>4
r1c8<>5 r1c3=5 r5c3<>5 r5c5=5 r4c4<>5
Full House: r7c8=3
Naked Single: r9c7=1
Naked Single: r8c7=4
Full House: r3c7=3
Hidden Single: r3c2=5
Naked Triple: 1,4,8 in r237c4 => r4c4<>4, r68c4<>1, r68c4<>8
Hidden Pair: 1,8 in r5c6,r6c5 => r6c5<>3
Uniqueness Test 1: 1/4 in r2c49,r3c49 => r2c4<>1, r2c4<>4
Naked Single: r2c4=8
Sashimi X-Wing: 8 r57 c26 fr7c1 fr7c3 => r89c2<>8
Hidden Single: r5c2=8
Naked Single: r5c6=1
Naked Single: r1c6=3
Naked Single: r6c5=8
Locked Candidates Type 1 (Pointing): 3 in b5 => r8c4<>3
Naked Pair: 2,4 in r4c26 => r4c1<>2
Hidden Single: r2c1=2
Skyscraper: 1 in r1c5,r2c2 (connected by r8c25) => r1c13<>1
Naked Single: r1c1=8
Naked Single: r1c3=4
Full House: r1c5=1
Full House: r2c2=1
Full House: r3c4=4
Full House: r2c9=4
Full House: r3c9=1
Naked Single: r5c3=5
Full House: r5c5=4
Naked Single: r8c2=3
Naked Single: r7c4=1
Naked Single: r4c1=3
Naked Single: r4c6=2
Naked Single: r8c5=5
Full House: r9c5=3
Naked Single: r9c2=2
Full House: r4c2=4
Full House: r4c4=5
Full House: r6c4=3
Full House: r8c4=2
Naked Single: r7c1=5
Full House: r6c1=1
Full House: r6c3=2
Naked Single: r7c3=8
Full House: r7c6=4
Full House: r9c6=8
Full House: r8c3=1
Full House: r8c9=8
Full House: r9c9=5
|
sudoku_normal_hard_129
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..5..23..21..7...59..5...2...2.1568.16.7..5.2.59.26.7.52...7..6..7.5..4..9.....5.
|
745192368216873495938564721372415689164789532859326174523947816687251943491638257
|
. . 5 . . 2 3 . .
2 1 . . 7 . . . 5
9 . . 5 . . . 2 .
. . 2 . 1 5 6 8 .
1 6 . 7 . . 5 . 2
. 5 9 . 2 6 . 7 .
5 2 . . . 7 . . 6
. . 7 . 5 . . 4 .
. 9 . . . . . 5 .
|
7 4 5 1 9 2 3 6 8
2 1 6 8 7 3 4 9 5
9 3 8 5 6 4 7 2 1
3 7 2 4 1 5 6 8 9
1 6 4 7 8 9 5 3 2
8 5 9 3 2 6 1 7 4
5 2 3 9 4 7 8 1 6
6 8 7 2 5 1 9 4 3
4 9 1 6 3 8 2 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3075_hard
|
745192368216873495938564721372415689164789532859326174523947816687251943491638257 #1 Extreme (23968) bf
Hidden Single: r4c3=2
Hidden Single: r4c7=6
Hidden Single: r5c4=7
Empty Rectangle: 5 in b5 (r59c8) => r9c6<>5
Brute Force: r5c7=5
Hidden Single: r1c3=5
Hidden Single: r4c6=5
Hidden Single: r9c8=5
Hidden Single: r6c2=5
Hidden Single: r8c5=5
Hidden Single: r3c8=2
Empty Rectangle: 3 in b5 (r57c8) => r7c4<>3
Finned Swordfish: 1 r368 c679 fr8c4 => r9c6<>1
Finned Franken Swordfish: 9 c67b6 r258 fr4c9 fr7c7 => r8c9<>9
Forcing Chain Contradiction in c4 => r1c1<>6
r1c1=6 r89c1<>6 r9c3=6 r9c3<>1 r7c3=1 r7c8<>1 r1c8=1 r1c4<>1
r1c1=6 r89c1<>6 r9c3=6 r9c3<>1 r7c3=1 r7c4<>1
r1c1=6 r8c1<>6 r8c4=6 r8c4<>1
r1c1=6 r8c1<>6 r8c4=6 r8c4<>2 r9c4=2 r9c4<>1
Locked Candidates Type 1 (Pointing): 6 in b1 => r9c3<>6
Forcing Chain Contradiction in c5 => r8c4<>3
r8c4=3 r46c4<>3 r5c56=3 r5c8<>3 r5c8=9 r4c9<>9 r1c9=9 r1c5<>9
r8c4=3 r46c4<>3 r5c56=3 r5c8<>3 r5c8=9 r5c5<>9
r8c4=3 r8c4<>2 r8c7=2 r8c7<>9 r7c78=9 r7c5<>9
Forcing Net Contradiction in r3c6 => r3c3<>4
r3c3=4 (r3c2<>4 r4c2=4 r6c1<>4 r9c1=4 r9c1<>6) r3c3<>6 r3c5=6 (r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c7<>1) (r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c9<>1) r9c5<>6 r9c4=6 r9c4<>2 r9c7=2 r8c7<>2 r8c4=2 r8c4<>1 r8c6=1 r3c6<>1
r3c3=4 (r3c3<>3) r3c3<>6 r2c3=6 r2c3<>3 r3c2=3 r3c6<>3
r3c3=4 r3c6<>4
r3c3=4 (r7c3<>4) (r7c3<>4) r3c3<>6 (r2c3=6 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r7c3<>8) r3c5=6 (r1c4<>6) r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r7c3<>1 r7c3=3 (r7c8<>3 r5c8=3 r5c5<>3 r9c5=3 r9c6<>3) r7c3<>1 r9c3=1 r9c3<>4 r9c1=4 r9c6<>4 r9c6=8 r3c6<>8
Forcing Net Contradiction in r2 => r5c3<>3
r5c3=3 r2c3<>3
r5c3=3 (r6c1<>3) (r4c1<>3) (r4c2<>3) r5c8<>3 r5c8=9 r4c9<>9 r4c4=9 r4c4<>3 r4c9=3 r6c9<>3 r6c4=3 r2c4<>3
r5c3=3 r5c8<>3 r5c8=9 (r2c8<>9) r4c9<>9 (r4c4=9 r2c4<>9) r1c9=9 r2c7<>9 r2c6=9 r2c6<>3
Forcing Net Verity => r4c2<>3
r4c4=3 r4c2<>3
r5c5=3 (r3c5<>3) r5c8<>3 (r5c8=9 r2c8<>9 r2c8=6 r2c3<>6 r3c3=6 r3c3<>3) r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>3 r3c2=3 r4c2<>3
r5c6=3 (r8c6<>3) r5c8<>3 (r5c8=9 r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r8c6<>9) r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r8c6<>1 r8c6=8 r8c2<>8 r8c2=3 r4c2<>3
r6c4=3 (r4c4<>3) (r5c5<>3) r5c6<>3 r5c8=3 r5c8<>9 r4c9=9 r4c4<>9 r4c4=4 r5c6<>4 r5c3=4 (r4c1<>4) (r9c3<>4 r9c1=4 r1c1<>4) (r5c5<>4) r5c3<>8 r6c1=8 r1c1<>8 r1c1=7 r4c1<>7 r4c1=3 r4c2<>3
Locked Candidates Type 1 (Pointing): 3 in b4 => r89c1<>3
Forcing Net Verity => r8c1=6
r3c2=3 r8c2<>3 r8c2=8 r8c1<>8 r8c1=6
r3c3=3 (r3c2<>3 r8c2=3 r8c9<>3) r3c3<>6 r3c5=6 (r1c4<>6) r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c9<>1 r8c9=8 r8c1<>8 r8c1=6
r3c5=3 (r9c5<>3) (r5c5<>3) (r7c5<>3) (r2c4<>3) r2c6<>3 r2c3=3 (r9c3<>3) r7c3<>3 r7c8=3 (r9c9<>3) r5c8<>3 r5c6=3 r9c6<>3 r9c4=3 r9c4<>2 r9c7=2 r8c7<>2 r8c4=2 r8c4<>6 r8c1=6
r3c6=3 (r3c2<>3 r8c2=3 r8c9<>3) r3c6<>1 r8c6=1 r8c9<>1 r8c9=8 r8c1<>8 r8c1=6
Forcing Chain Contradiction in b9 => r3c3<>3
r3c3=3 r3c3<>6 r3c5=6 r1c45<>6 r1c8=6 r1c8<>1 r7c8=1 r7c8<>3
r3c3=3 r3c2<>3 r8c2=3 r8c9<>3
r3c3=3 r3c3<>6 r3c5=6 r9c5<>6 r9c4=6 r9c4<>2 r9c7=2 r9c7<>7 r9c9=7 r9c9<>3
Forcing Net Contradiction in b9 => r1c9<>7
r1c9=7 (r1c1<>7 r4c1=7 r4c2<>7 r4c2=4 r5c3<>4 r5c3=8 r7c3<>8) (r1c1<>7 r4c1=7 r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) (r1c9<>9 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r3c7<>7) r3c9<>7 r3c2=7 r3c2<>3 r8c2=3 r7c3<>3 r7c5=3 r7c5<>8 r7c7=8
r1c9=7 (r1c9<>9 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r3c7<>7) r3c9<>7 r3c2=7 (r3c2<>3) r3c2<>3 r8c2=3 (r8c9<>3) r7c3<>3 r7c5=3 r3c5<>3 r3c6=3 r3c6<>1 r8c6=1 r8c9<>1 r8c9=8
Locked Candidates Type 1 (Pointing): 7 in b3 => r3c2<>7
Hidden Rectangle: 4/7 in r1c12,r4c12 => r1c1<>4
Forcing Net Verity => r3c6<>8
r2c4=3 r46c4<>3 r5c56=3 r5c8<>3 r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>8
r2c6=3 (r9c6<>3) (r3c5<>3) r3c6<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r9c6<>4 r9c6=8 r3c6<>8
r3c5=3 (r7c5<>3) (r2c4<>3) r2c6<>3 r2c3=3 r7c3<>3 r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>8
r3c6=3 r3c6<>8
Forcing Net Contradiction in c7 => r4c9<>3
r4c9=3 (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r2c4<>8) (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r5c6<>8 r5c3=8 r2c3<>8) (r5c8<>3 r5c8=9 r2c8<>9) r4c9<>9 (r4c4=9 r2c4<>9) r1c9=9 r2c7<>9 r2c6=9 r2c6<>8 r2c7=8
r4c9=3 (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r5c6<>8 r5c3=8 r7c3<>8) (r5c8<>3 r5c8=9 r5c5<>9) r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r7c5<>8 r7c7=8
Forcing Net Contradiction in c9 => r1c1=7
r1c1<>7 r1c1=8 r1c9<>8
r1c1<>7 (r1c2=7 r4c2<>7 r4c1=7 r4c1<>3 r4c4=3 r2c4<>3) r1c1=8 (r2c3<>8) (r6c1<>8 r6c4=8 r2c4<>8) (r1c2<>8) r3c2<>8 r8c2=8 r8c2<>3 r3c2=3 r2c3<>3 r2c6=3 r2c6<>8 r2c7=8 r3c9<>8
r1c1<>7 r1c1=8 (r1c2<>8) r3c2<>8 r8c2=8 r8c9<>8
r1c1<>7 (r1c2=7 r4c2<>7 r4c1=7 r4c1<>3 r4c4=3 r2c4<>3) r1c1=8 (r9c1<>8 r9c1=4 r9c6<>4) (r1c2<>8) r3c2<>8 r8c2=8 r8c2<>3 r3c2=3 r2c3<>3 r2c6=3 r9c6<>3 r9c6=8 r9c9<>8
Hidden Single: r4c2=7
Locked Candidates Type 2 (Claiming): 4 in c2 => r2c3<>4
Forcing Net Verity => r2c7=4
r4c4=3 (r5c6<>3 r5c8=3 r7c8<>3) r4c1<>3 (r6c1=3 r6c1<>8 r6c4=8 r8c4<>8) (r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) r4c1=4 (r5c3<>4 r5c3=8 r7c3<>8) r9c1<>4 r9c1=8 (r8c2<>8) r8c2<>8 r8c2=3 (r7c3<>3) (r3c2<>3) r7c3<>3 r7c5=3 r7c5<>8 r7c7=8 (r7c7<>1) (r8c7<>8) r8c9<>8 r8c6=8 r8c6<>1 r3c6=1 r3c6<>3 r3c5=3 r7c5<>3 r7c8=3 (r7c8<>9 r78c7=9 r2c7<>9) r5c8<>3 r5c8=9 (r5c5<>9) r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r7c7<>9 r7c7=8 (r7c7<>1) (r8c7<>8) r2c7<>8 r2c7=4
r4c4=4 (r2c4<>4) (r5c6<>4) (r4c9<>4 r4c9=9 r5c8<>9 r5c8=3 r6c9<>3) (r4c9<>4 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r7c4<>4) (r5c5<>4) r5c6<>4 r5c3=4 (r6c1<>4 r9c1=4 r9c6<>4) r7c3<>4 r7c5=4 r7c5<>3 r7c3=3 (r2c3<>3) r8c2<>3 r8c2=8 r9c1<>8 r6c1=8 r6c1<>3 r6c4=3 r2c4<>3 r2c6=3 r2c6<>4 r3c6=4 r2c6<>4 r2c7=4
r4c4=9 (r5c5<>9) r4c9<>9 (r4c9=4 r6c7<>4 r6c7=1 r7c7<>1) r1c9=9 (r2c7<>9) r1c5<>9 r7c5=9 r7c7<>9 r7c7=8 r2c7<>8 r2c7=4
Naked Single: r6c7=1
Locked Candidates Type 2 (Claiming): 9 in c7 => r7c8<>9
Hidden Rectangle: 7/8 in r3c79,r9c79 => r9c9<>8
Forcing Chain Contradiction in c6 => r1c4<>8
r1c4=8 r1c4<>1 r3c6=1 r3c6<>4
r1c4=8 r6c4<>8 r6c1=8 r5c3<>8 r5c3=4 r5c6<>4
r1c4=8 r6c4<>8 r6c1=8 r9c1<>8 r9c1=4 r9c6<>4
Forcing Chain Contradiction in c6 => r2c4<>3
r2c4=3 r46c4<>3 r5c56=3 r5c8<>3 r7c8=3 r7c8<>1 r1c8=1 r1c4<>1 r3c6=1 r3c6<>4
r2c4=3 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r46c1<>4 r5c3=4 r5c6<>4
r2c4=3 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r9c6<>4
2-String Kite: 3 in r2c6,r8c2 (connected by r2c3,r3c2) => r8c6<>3
Discontinuous Nice Loop: 3 r9c3 -3- r8c2 =3= r8c9 -3- r7c8 -1- r7c3 =1= r9c3 => r9c3<>3
Grouped Discontinuous Nice Loop: 1 r9c4 -1- r9c3 =1= r7c3 -1- r7c8 -3- r5c8 =3= r5c56 -3- r46c4 =3= r9c4 => r9c4<>1
Grouped Discontinuous Nice Loop: 4/8 r9c3 =1= r9c9 =7= r9c7 =2= r9c4 =3= r46c4 -3- r5c56 =3= r5c8 -3- r7c8 -1- r7c3 =1= r9c3 => r9c3<>4, r9c3<>8
Naked Single: r9c3=1
Empty Rectangle: 4 in b5 (r57c3) => r7c4<>4
Forcing Chain Contradiction in r7c4 => r3c7=7
r3c7<>7 r3c7=8 r789c7<>8 r8c9=8 r8c9<>1 r7c8=1 r7c4<>1
r3c7<>7 r3c9=7 r9c9<>7 r9c9=3 r9c456<>3 r7c5=3 r7c5<>4 r7c3=4 r5c3<>4 r5c3=8 r6c1<>8 r6c4=8 r7c4<>8
r3c7<>7 r3c7=8 r7c7<>8 r7c7=9 r7c4<>9
Hidden Single: r9c9=7
Locked Candidates Type 1 (Pointing): 8 in b3 => r8c9<>8
Locked Candidates Type 2 (Claiming): 3 in r9 => r7c5<>3
XY-Wing: 1/3/8 in r38c9,r8c2 => r3c2<>8
Hidden Rectangle: 2/8 in r8c47,r9c47 => r8c4<>8
XY-Chain: 4 4- r4c9 -9- r5c8 -3- r7c8 -1- r8c9 -3- r8c2 -8- r9c1 -4 => r4c1<>4
Naked Single: r4c1=3
Simple Colors Trap: 3 (r2c3,r6c9,r7c8,r8c2,r9c4) / (r2c6,r3c2,r5c8,r6c4,r7c3,r8c9) => r9c6<>3
Naked Pair: 4,8 in r9c16 => r9c45<>4, r9c457<>8
Naked Single: r9c7=2
Hidden Single: r8c4=2
X-Wing: 1 r38 c69 => r1c9<>1
Remote Pair: 4/8 r5c3 -8- r6c1 -4- r9c1 -8- r9c6 => r5c6<>4, r5c6<>8
Naked Pair: 3,9 in r5c68 => r5c5<>3, r5c5<>9
X-Wing: 4 r57 c35 => r13c5<>4
Hidden Pair: 1,4 in r1c4,r3c6 => r1c4<>6, r1c4<>9, r3c6<>3
Skyscraper: 8 in r6c4,r9c6 (connected by r69c1) => r7c4<>8
Naked Triple: 1,4,9 in r147c4 => r2c4<>9, r6c4<>4
X-Wing: 9 r25 c68 => r1c8,r8c6<>9
Hidden Single: r8c7=9
Full House: r7c7=8
Locked Candidates Type 1 (Pointing): 8 in b8 => r2c6<>8
Skyscraper: 8 in r2c4,r5c5 (connected by r25c3) => r13c5,r6c4<>8
Naked Single: r6c4=3
Naked Single: r5c6=9
Naked Single: r6c9=4
Full House: r6c1=8
Full House: r5c3=4
Full House: r9c1=4
Naked Single: r9c4=6
Naked Single: r2c6=3
Naked Single: r4c4=4
Full House: r4c9=9
Full House: r5c8=3
Full House: r5c5=8
Naked Single: r7c3=3
Full House: r8c2=8
Naked Single: r9c6=8
Full House: r9c5=3
Naked Single: r2c4=8
Naked Single: r3c5=6
Naked Single: r1c4=1
Full House: r7c4=9
Naked Single: r1c9=8
Naked Single: r7c8=1
Full House: r7c5=4
Full House: r8c6=1
Full House: r1c5=9
Full House: r3c6=4
Full House: r8c9=3
Full House: r3c9=1
Naked Single: r1c2=4
Full House: r1c8=6
Full House: r3c2=3
Full House: r3c3=8
Full House: r2c3=6
Full House: r2c8=9
|
sudoku_normal_extremely_hard_129
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.....23..21..7...59..5.........1..8.16......2..9.26.7.52...7..6..7....4..9.......
|
745192368216873495938564721372415689164789532859326174523947816687251943491638257
|
. . . . . 2 3 . .
2 1 . . 7 . . . 5
9 . . 5 . . . . .
. . . . 1 . . 8 .
1 6 . . . . . . 2
. . 9 . 2 6 . 7 .
5 2 . . . 7 . . 6
. . 7 . . . . 4 .
. 9 . . . . . . .
|
7 4 5 1 9 2 3 6 8
2 1 6 8 7 3 4 9 5
9 3 8 5 6 4 7 2 1
3 7 2 4 1 5 6 8 9
1 6 4 7 8 9 5 3 2
8 5 9 3 2 6 1 7 4
5 2 3 9 4 7 8 1 6
6 8 7 2 5 1 9 4 3
4 9 1 6 3 8 2 5 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3075_hard
|
745192368216873495938564721372415689164789532859326174523947816687251943491638257 #1 Extreme (23968) bf
Hidden Single: r4c3=2
Hidden Single: r4c7=6
Hidden Single: r5c4=7
Empty Rectangle: 5 in b5 (r59c8) => r9c6<>5
Brute Force: r5c7=5
Hidden Single: r1c3=5
Hidden Single: r4c6=5
Hidden Single: r9c8=5
Hidden Single: r6c2=5
Hidden Single: r8c5=5
Hidden Single: r3c8=2
Empty Rectangle: 3 in b5 (r57c8) => r7c4<>3
Finned Swordfish: 1 r368 c679 fr8c4 => r9c6<>1
Finned Franken Swordfish: 9 c67b6 r258 fr4c9 fr7c7 => r8c9<>9
Forcing Chain Contradiction in c4 => r1c1<>6
r1c1=6 r89c1<>6 r9c3=6 r9c3<>1 r7c3=1 r7c8<>1 r1c8=1 r1c4<>1
r1c1=6 r89c1<>6 r9c3=6 r9c3<>1 r7c3=1 r7c4<>1
r1c1=6 r8c1<>6 r8c4=6 r8c4<>1
r1c1=6 r8c1<>6 r8c4=6 r8c4<>2 r9c4=2 r9c4<>1
Locked Candidates Type 1 (Pointing): 6 in b1 => r9c3<>6
Forcing Chain Contradiction in c5 => r8c4<>3
r8c4=3 r46c4<>3 r5c56=3 r5c8<>3 r5c8=9 r4c9<>9 r1c9=9 r1c5<>9
r8c4=3 r46c4<>3 r5c56=3 r5c8<>3 r5c8=9 r5c5<>9
r8c4=3 r8c4<>2 r8c7=2 r8c7<>9 r7c78=9 r7c5<>9
Forcing Net Contradiction in r3c6 => r3c3<>4
r3c3=4 (r3c2<>4 r4c2=4 r6c1<>4 r9c1=4 r9c1<>6) r3c3<>6 r3c5=6 (r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c7<>1) (r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c9<>1) r9c5<>6 r9c4=6 r9c4<>2 r9c7=2 r8c7<>2 r8c4=2 r8c4<>1 r8c6=1 r3c6<>1
r3c3=4 (r3c3<>3) r3c3<>6 r2c3=6 r2c3<>3 r3c2=3 r3c6<>3
r3c3=4 r3c6<>4
r3c3=4 (r7c3<>4) (r7c3<>4) r3c3<>6 (r2c3=6 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r7c3<>8) r3c5=6 (r1c4<>6) r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r7c3<>1 r7c3=3 (r7c8<>3 r5c8=3 r5c5<>3 r9c5=3 r9c6<>3) r7c3<>1 r9c3=1 r9c3<>4 r9c1=4 r9c6<>4 r9c6=8 r3c6<>8
Forcing Net Contradiction in r2 => r5c3<>3
r5c3=3 r2c3<>3
r5c3=3 (r6c1<>3) (r4c1<>3) (r4c2<>3) r5c8<>3 r5c8=9 r4c9<>9 r4c4=9 r4c4<>3 r4c9=3 r6c9<>3 r6c4=3 r2c4<>3
r5c3=3 r5c8<>3 r5c8=9 (r2c8<>9) r4c9<>9 (r4c4=9 r2c4<>9) r1c9=9 r2c7<>9 r2c6=9 r2c6<>3
Forcing Net Verity => r4c2<>3
r4c4=3 r4c2<>3
r5c5=3 (r3c5<>3) r5c8<>3 (r5c8=9 r2c8<>9 r2c8=6 r2c3<>6 r3c3=6 r3c3<>3) r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>3 r3c2=3 r4c2<>3
r5c6=3 (r8c6<>3) r5c8<>3 (r5c8=9 r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r8c6<>9) r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r8c6<>1 r8c6=8 r8c2<>8 r8c2=3 r4c2<>3
r6c4=3 (r4c4<>3) (r5c5<>3) r5c6<>3 r5c8=3 r5c8<>9 r4c9=9 r4c4<>9 r4c4=4 r5c6<>4 r5c3=4 (r4c1<>4) (r9c3<>4 r9c1=4 r1c1<>4) (r5c5<>4) r5c3<>8 r6c1=8 r1c1<>8 r1c1=7 r4c1<>7 r4c1=3 r4c2<>3
Locked Candidates Type 1 (Pointing): 3 in b4 => r89c1<>3
Forcing Net Verity => r8c1=6
r3c2=3 r8c2<>3 r8c2=8 r8c1<>8 r8c1=6
r3c3=3 (r3c2<>3 r8c2=3 r8c9<>3) r3c3<>6 r3c5=6 (r1c4<>6) r1c5<>6 r1c8=6 r1c8<>1 r7c8=1 r8c9<>1 r8c9=8 r8c1<>8 r8c1=6
r3c5=3 (r9c5<>3) (r5c5<>3) (r7c5<>3) (r2c4<>3) r2c6<>3 r2c3=3 (r9c3<>3) r7c3<>3 r7c8=3 (r9c9<>3) r5c8<>3 r5c6=3 r9c6<>3 r9c4=3 r9c4<>2 r9c7=2 r8c7<>2 r8c4=2 r8c4<>6 r8c1=6
r3c6=3 (r3c2<>3 r8c2=3 r8c9<>3) r3c6<>1 r8c6=1 r8c9<>1 r8c9=8 r8c1<>8 r8c1=6
Forcing Chain Contradiction in b9 => r3c3<>3
r3c3=3 r3c3<>6 r3c5=6 r1c45<>6 r1c8=6 r1c8<>1 r7c8=1 r7c8<>3
r3c3=3 r3c2<>3 r8c2=3 r8c9<>3
r3c3=3 r3c3<>6 r3c5=6 r9c5<>6 r9c4=6 r9c4<>2 r9c7=2 r9c7<>7 r9c9=7 r9c9<>3
Forcing Net Contradiction in b9 => r1c9<>7
r1c9=7 (r1c1<>7 r4c1=7 r4c2<>7 r4c2=4 r5c3<>4 r5c3=8 r7c3<>8) (r1c1<>7 r4c1=7 r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) (r1c9<>9 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r3c7<>7) r3c9<>7 r3c2=7 r3c2<>3 r8c2=3 r7c3<>3 r7c5=3 r7c5<>8 r7c7=8
r1c9=7 (r1c9<>9 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r3c7<>7) r3c9<>7 r3c2=7 (r3c2<>3) r3c2<>3 r8c2=3 (r8c9<>3) r7c3<>3 r7c5=3 r3c5<>3 r3c6=3 r3c6<>1 r8c6=1 r8c9<>1 r8c9=8
Locked Candidates Type 1 (Pointing): 7 in b3 => r3c2<>7
Hidden Rectangle: 4/7 in r1c12,r4c12 => r1c1<>4
Forcing Net Verity => r3c6<>8
r2c4=3 r46c4<>3 r5c56=3 r5c8<>3 r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>8
r2c6=3 (r9c6<>3) (r3c5<>3) r3c6<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r9c6<>4 r9c6=8 r3c6<>8
r3c5=3 (r7c5<>3) (r2c4<>3) r2c6<>3 r2c3=3 r7c3<>3 r7c8=3 r7c8<>1 r1c8=1 (r3c7<>1) r3c9<>1 r3c6=1 r3c6<>8
r3c6=3 r3c6<>8
Forcing Net Contradiction in c7 => r4c9<>3
r4c9=3 (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r2c4<>8) (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r5c6<>8 r5c3=8 r2c3<>8) (r5c8<>3 r5c8=9 r2c8<>9) r4c9<>9 (r4c4=9 r2c4<>9) r1c9=9 r2c7<>9 r2c6=9 r2c6<>8 r2c7=8
r4c9=3 (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) (r4c1<>3 r6c1=3 r6c1<>8 r6c4=8 r5c6<>8 r5c3=8 r7c3<>8) (r5c8<>3 r5c8=9 r5c5<>9) r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r7c5<>8 r7c7=8
Forcing Net Contradiction in c9 => r1c1=7
r1c1<>7 r1c1=8 r1c9<>8
r1c1<>7 (r1c2=7 r4c2<>7 r4c1=7 r4c1<>3 r4c4=3 r2c4<>3) r1c1=8 (r2c3<>8) (r6c1<>8 r6c4=8 r2c4<>8) (r1c2<>8) r3c2<>8 r8c2=8 r8c2<>3 r3c2=3 r2c3<>3 r2c6=3 r2c6<>8 r2c7=8 r3c9<>8
r1c1<>7 r1c1=8 (r1c2<>8) r3c2<>8 r8c2=8 r8c9<>8
r1c1<>7 (r1c2=7 r4c2<>7 r4c1=7 r4c1<>3 r4c4=3 r2c4<>3) r1c1=8 (r9c1<>8 r9c1=4 r9c6<>4) (r1c2<>8) r3c2<>8 r8c2=8 r8c2<>3 r3c2=3 r2c3<>3 r2c6=3 r9c6<>3 r9c6=8 r9c9<>8
Hidden Single: r4c2=7
Locked Candidates Type 2 (Claiming): 4 in c2 => r2c3<>4
Forcing Net Verity => r2c7=4
r4c4=3 (r5c6<>3 r5c8=3 r7c8<>3) r4c1<>3 (r6c1=3 r6c1<>8 r6c4=8 r8c4<>8) (r6c1=3 r6c1<>8 r6c4=8 r7c4<>8) r4c1=4 (r5c3<>4 r5c3=8 r7c3<>8) r9c1<>4 r9c1=8 (r8c2<>8) r8c2<>8 r8c2=3 (r7c3<>3) (r3c2<>3) r7c3<>3 r7c5=3 r7c5<>8 r7c7=8 (r7c7<>1) (r8c7<>8) r8c9<>8 r8c6=8 r8c6<>1 r3c6=1 r3c6<>3 r3c5=3 r7c5<>3 r7c8=3 (r7c8<>9 r78c7=9 r2c7<>9) r5c8<>3 r5c8=9 (r5c5<>9) r4c9<>9 r1c9=9 r1c5<>9 r7c5=9 r7c7<>9 r7c7=8 (r7c7<>1) (r8c7<>8) r2c7<>8 r2c7=4
r4c4=4 (r2c4<>4) (r5c6<>4) (r4c9<>4 r4c9=9 r5c8<>9 r5c8=3 r6c9<>3) (r4c9<>4 r4c9=9 r5c8<>9 r5c8=3 r7c8<>3) (r7c4<>4) (r5c5<>4) r5c6<>4 r5c3=4 (r6c1<>4 r9c1=4 r9c6<>4) r7c3<>4 r7c5=4 r7c5<>3 r7c3=3 (r2c3<>3) r8c2<>3 r8c2=8 r9c1<>8 r6c1=8 r6c1<>3 r6c4=3 r2c4<>3 r2c6=3 r2c6<>4 r3c6=4 r2c6<>4 r2c7=4
r4c4=9 (r5c5<>9) r4c9<>9 (r4c9=4 r6c7<>4 r6c7=1 r7c7<>1) r1c9=9 (r2c7<>9) r1c5<>9 r7c5=9 r7c7<>9 r7c7=8 r2c7<>8 r2c7=4
Naked Single: r6c7=1
Locked Candidates Type 2 (Claiming): 9 in c7 => r7c8<>9
Hidden Rectangle: 7/8 in r3c79,r9c79 => r9c9<>8
Forcing Chain Contradiction in c6 => r1c4<>8
r1c4=8 r1c4<>1 r3c6=1 r3c6<>4
r1c4=8 r6c4<>8 r6c1=8 r5c3<>8 r5c3=4 r5c6<>4
r1c4=8 r6c4<>8 r6c1=8 r9c1<>8 r9c1=4 r9c6<>4
Forcing Chain Contradiction in c6 => r2c4<>3
r2c4=3 r46c4<>3 r5c56=3 r5c8<>3 r7c8=3 r7c8<>1 r1c8=1 r1c4<>1 r3c6=1 r3c6<>4
r2c4=3 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r46c1<>4 r5c3=4 r5c6<>4
r2c4=3 r2c3<>3 r3c2=3 r8c2<>3 r8c2=8 r9c1<>8 r9c1=4 r9c6<>4
2-String Kite: 3 in r2c6,r8c2 (connected by r2c3,r3c2) => r8c6<>3
Discontinuous Nice Loop: 3 r9c3 -3- r8c2 =3= r8c9 -3- r7c8 -1- r7c3 =1= r9c3 => r9c3<>3
Grouped Discontinuous Nice Loop: 1 r9c4 -1- r9c3 =1= r7c3 -1- r7c8 -3- r5c8 =3= r5c56 -3- r46c4 =3= r9c4 => r9c4<>1
Grouped Discontinuous Nice Loop: 4/8 r9c3 =1= r9c9 =7= r9c7 =2= r9c4 =3= r46c4 -3- r5c56 =3= r5c8 -3- r7c8 -1- r7c3 =1= r9c3 => r9c3<>4, r9c3<>8
Naked Single: r9c3=1
Empty Rectangle: 4 in b5 (r57c3) => r7c4<>4
Forcing Chain Contradiction in r7c4 => r3c7=7
r3c7<>7 r3c7=8 r789c7<>8 r8c9=8 r8c9<>1 r7c8=1 r7c4<>1
r3c7<>7 r3c9=7 r9c9<>7 r9c9=3 r9c456<>3 r7c5=3 r7c5<>4 r7c3=4 r5c3<>4 r5c3=8 r6c1<>8 r6c4=8 r7c4<>8
r3c7<>7 r3c7=8 r7c7<>8 r7c7=9 r7c4<>9
Hidden Single: r9c9=7
Locked Candidates Type 1 (Pointing): 8 in b3 => r8c9<>8
Locked Candidates Type 2 (Claiming): 3 in r9 => r7c5<>3
XY-Wing: 1/3/8 in r38c9,r8c2 => r3c2<>8
Hidden Rectangle: 2/8 in r8c47,r9c47 => r8c4<>8
XY-Chain: 4 4- r4c9 -9- r5c8 -3- r7c8 -1- r8c9 -3- r8c2 -8- r9c1 -4 => r4c1<>4
Naked Single: r4c1=3
Simple Colors Trap: 3 (r2c3,r6c9,r7c8,r8c2,r9c4) / (r2c6,r3c2,r5c8,r6c4,r7c3,r8c9) => r9c6<>3
Naked Pair: 4,8 in r9c16 => r9c45<>4, r9c457<>8
Naked Single: r9c7=2
Hidden Single: r8c4=2
X-Wing: 1 r38 c69 => r1c9<>1
Remote Pair: 4/8 r5c3 -8- r6c1 -4- r9c1 -8- r9c6 => r5c6<>4, r5c6<>8
Naked Pair: 3,9 in r5c68 => r5c5<>3, r5c5<>9
X-Wing: 4 r57 c35 => r13c5<>4
Hidden Pair: 1,4 in r1c4,r3c6 => r1c4<>6, r1c4<>9, r3c6<>3
Skyscraper: 8 in r6c4,r9c6 (connected by r69c1) => r7c4<>8
Naked Triple: 1,4,9 in r147c4 => r2c4<>9, r6c4<>4
X-Wing: 9 r25 c68 => r1c8,r8c6<>9
Hidden Single: r8c7=9
Full House: r7c7=8
Locked Candidates Type 1 (Pointing): 8 in b8 => r2c6<>8
Skyscraper: 8 in r2c4,r5c5 (connected by r25c3) => r13c5,r6c4<>8
Naked Single: r6c4=3
Naked Single: r5c6=9
Naked Single: r6c9=4
Full House: r6c1=8
Full House: r5c3=4
Full House: r9c1=4
Naked Single: r9c4=6
Naked Single: r2c6=3
Naked Single: r4c4=4
Full House: r4c9=9
Full House: r5c8=3
Full House: r5c5=8
Naked Single: r7c3=3
Full House: r8c2=8
Naked Single: r9c6=8
Full House: r9c5=3
Naked Single: r2c4=8
Naked Single: r3c5=6
Naked Single: r1c4=1
Full House: r7c4=9
Naked Single: r1c9=8
Naked Single: r7c8=1
Full House: r7c5=4
Full House: r8c6=1
Full House: r1c5=9
Full House: r3c6=4
Full House: r8c9=3
Full House: r3c9=1
Naked Single: r1c2=4
Full House: r1c8=6
Full House: r3c2=3
Full House: r3c3=8
Full House: r2c3=6
Full House: r2c8=9
|
sudoku_normal_hard_130
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.896.2.172.1...9.6....9182...81...726..2.8149412.7968..23........4...2..8..92...1
|
389652417251487936746391825938146572675238149412579683123865794594713268867924351
|
. 8 9 6 . 2 . 1 7
2 . 1 . . . 9 . 6
. . . . 9 1 8 2 .
. . 8 1 . . . 7 2
6 . . 2 . 8 1 4 9
4 1 2 . 7 9 6 8 .
. 2 3 . . . . . .
. . 4 . . . 2 . .
8 . . 9 2 . . . 1
|
3 8 9 6 5 2 4 1 7
2 5 1 4 8 7 9 3 6
7 4 6 3 9 1 8 2 5
9 3 8 1 4 6 5 7 2
6 7 5 2 3 8 1 4 9
4 1 2 5 7 9 6 8 3
1 2 3 8 6 5 7 9 4
5 9 4 7 1 3 2 6 8
8 6 7 9 2 4 3 5 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5088_hard
|
389652417251487936746391825938146572675238149412579683123865794594713268867924351 #1 Extreme (13472) bf
Hidden Single: r5c7=1
Hidden Single: r6c7=6
Hidden Single: r2c1=2
Hidden Single: r4c9=2
Hidden Single: r4c3=8
Hidden Single: r3c5=9
Hidden Single: r9c5=2
Hidden Single: r5c4=2
Hidden Single: r2c3=1
Hidden Single: r9c9=1
Brute Force: r6c1=4
Swordfish: 4 c249 r237 => r2c568,r7c5678<>4
Skyscraper: 4 in r1c7,r5c8 (connected by r15c5) => r4c7<>4
Hidden Single: r5c8=4
Naked Pair: 3,5 in r5c5,r6c4 => r4c56<>3, r4c56<>5
Almost Locked Set XY-Wing: A=r7c15678 {156789}, B=r2368c4 {34578}, C=r125c5 {3458}, X,Y=4,8, Z=5,7 => r7c4<>5, r7c4<>7
Forcing Chain Contradiction in r3 => r1c7<>3
r1c7=3 r1c1<>3 r1c1=5 r3c1<>5
r1c7=3 r1c1<>3 r1c1=5 r3c2<>5
r1c7=3 r1c1<>3 r1c1=5 r3c3<>5
r1c7=3 r4c7<>3 r4c7=5 r6c9<>5 r6c4=5 r3c4<>5
r1c7=3 r1c7<>4 r3c9=4 r3c9<>5
Skyscraper: 3 in r1c1,r5c2 (connected by r15c5) => r23c2,r4c1<>3
Turbot Fish: 3 r2c8 =3= r3c9 -3- r6c9 =3= r6c4 => r2c4<>3
Discontinuous Nice Loop: 3 r2c5 -3- r2c8 =3= r3c9 =4= r7c9 -4- r7c4 -8- r2c4 =8= r2c5 => r2c5<>3
Empty Rectangle: 3 in b8 (r2c68) => r8c8<>3
AIC: 8 8- r2c5 -5- r5c5 -3- r5c2 =3= r4c2 -3- r4c7 =3= r9c7 =4= r9c6 -4- r7c4 -8 => r2c4,r78c5<>8
Hidden Single: r2c5=8
Hidden Pair: 4,8 in r7c49 => r7c9<>5
Discontinuous Nice Loop: 5 r8c9 -5- r6c9 -3- r4c7 =3= r9c7 =4= r7c9 =8= r8c9 => r8c9<>5
Sue de Coq: r8c456 - {135678} (r8c9 - {38}, r7c56 - {1567}) => r9c6<>5, r9c6<>6, r9c6<>7
Grouped Discontinuous Nice Loop: 5 r1c1 =3= r1c5 -3- r2c6 =3= r2c8 =5= r789c8 -5- r7c7 -7- r9c7 =7= r9c23 -7- r78c1 =7= r3c1 =3= r1c1 => r1c1<>5
Naked Single: r1c1=3
X-Wing: 3 r36 c49 => r8c49<>3
Naked Single: r8c9=8
Naked Single: r7c9=4
Naked Single: r7c4=8
Hidden Single: r1c7=4
Full House: r1c5=5
Naked Single: r5c5=3
Naked Single: r6c4=5
Full House: r6c9=3
Full House: r3c9=5
Full House: r4c7=5
Full House: r2c8=3
Naked Single: r8c4=7
Naked Single: r3c1=7
Naked Single: r4c1=9
Naked Single: r7c7=7
Full House: r9c7=3
Naked Single: r2c6=7
Naked Single: r2c4=4
Full House: r2c2=5
Full House: r3c4=3
Naked Single: r3c3=6
Full House: r3c2=4
Naked Single: r4c2=3
Naked Single: r9c6=4
Naked Single: r5c2=7
Full House: r5c3=5
Full House: r9c3=7
Naked Single: r4c6=6
Full House: r4c5=4
Naked Single: r9c2=6
Full House: r8c2=9
Full House: r9c8=5
Naked Single: r7c6=5
Full House: r8c6=3
Naked Single: r8c8=6
Full House: r7c8=9
Naked Single: r7c1=1
Full House: r7c5=6
Full House: r8c5=1
Full House: r8c1=5
|
sudoku_normal_extremely_hard_130
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.896.2.17......9.6.....182....1...7.6....8..9.12.79.8..23........4...2..8..9.....
|
389652417251487936746391825938146572675238149412579683123865794594713268867924351
|
. 8 9 6 . 2 . 1 7
. . . . . . 9 . 6
. . . . . 1 8 2 .
. . . 1 . . . 7 .
6 . . . . 8 . . 9
. 1 2 . 7 9 . 8 .
. 2 3 . . . . . .
. . 4 . . . 2 . .
8 . . 9 . . . . .
|
3 8 9 6 5 2 4 1 7
2 5 1 4 8 7 9 3 6
7 4 6 3 9 1 8 2 5
9 3 8 1 4 6 5 7 2
6 7 5 2 3 8 1 4 9
4 1 2 5 7 9 6 8 3
1 2 3 8 6 5 7 9 4
5 9 4 7 1 3 2 6 8
8 6 7 9 2 4 3 5 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5088_hard
|
389652417251487936746391825938146572675238149412579683123865794594713268867924351 #1 Extreme (13472) bf
Hidden Single: r5c7=1
Hidden Single: r6c7=6
Hidden Single: r2c1=2
Hidden Single: r4c9=2
Hidden Single: r4c3=8
Hidden Single: r3c5=9
Hidden Single: r9c5=2
Hidden Single: r5c4=2
Hidden Single: r2c3=1
Hidden Single: r9c9=1
Brute Force: r6c1=4
Swordfish: 4 c249 r237 => r2c568,r7c5678<>4
Skyscraper: 4 in r1c7,r5c8 (connected by r15c5) => r4c7<>4
Hidden Single: r5c8=4
Naked Pair: 3,5 in r5c5,r6c4 => r4c56<>3, r4c56<>5
Almost Locked Set XY-Wing: A=r7c15678 {156789}, B=r2368c4 {34578}, C=r125c5 {3458}, X,Y=4,8, Z=5,7 => r7c4<>5, r7c4<>7
Forcing Chain Contradiction in r3 => r1c7<>3
r1c7=3 r1c1<>3 r1c1=5 r3c1<>5
r1c7=3 r1c1<>3 r1c1=5 r3c2<>5
r1c7=3 r1c1<>3 r1c1=5 r3c3<>5
r1c7=3 r4c7<>3 r4c7=5 r6c9<>5 r6c4=5 r3c4<>5
r1c7=3 r1c7<>4 r3c9=4 r3c9<>5
Skyscraper: 3 in r1c1,r5c2 (connected by r15c5) => r23c2,r4c1<>3
Turbot Fish: 3 r2c8 =3= r3c9 -3- r6c9 =3= r6c4 => r2c4<>3
Discontinuous Nice Loop: 3 r2c5 -3- r2c8 =3= r3c9 =4= r7c9 -4- r7c4 -8- r2c4 =8= r2c5 => r2c5<>3
Empty Rectangle: 3 in b8 (r2c68) => r8c8<>3
AIC: 8 8- r2c5 -5- r5c5 -3- r5c2 =3= r4c2 -3- r4c7 =3= r9c7 =4= r9c6 -4- r7c4 -8 => r2c4,r78c5<>8
Hidden Single: r2c5=8
Hidden Pair: 4,8 in r7c49 => r7c9<>5
Discontinuous Nice Loop: 5 r8c9 -5- r6c9 -3- r4c7 =3= r9c7 =4= r7c9 =8= r8c9 => r8c9<>5
Sue de Coq: r8c456 - {135678} (r8c9 - {38}, r7c56 - {1567}) => r9c6<>5, r9c6<>6, r9c6<>7
Grouped Discontinuous Nice Loop: 5 r1c1 =3= r1c5 -3- r2c6 =3= r2c8 =5= r789c8 -5- r7c7 -7- r9c7 =7= r9c23 -7- r78c1 =7= r3c1 =3= r1c1 => r1c1<>5
Naked Single: r1c1=3
X-Wing: 3 r36 c49 => r8c49<>3
Naked Single: r8c9=8
Naked Single: r7c9=4
Naked Single: r7c4=8
Hidden Single: r1c7=4
Full House: r1c5=5
Naked Single: r5c5=3
Naked Single: r6c4=5
Full House: r6c9=3
Full House: r3c9=5
Full House: r4c7=5
Full House: r2c8=3
Naked Single: r8c4=7
Naked Single: r3c1=7
Naked Single: r4c1=9
Naked Single: r7c7=7
Full House: r9c7=3
Naked Single: r2c6=7
Naked Single: r2c4=4
Full House: r2c2=5
Full House: r3c4=3
Naked Single: r3c3=6
Full House: r3c2=4
Naked Single: r4c2=3
Naked Single: r9c6=4
Naked Single: r5c2=7
Full House: r5c3=5
Full House: r9c3=7
Naked Single: r4c6=6
Full House: r4c5=4
Naked Single: r9c2=6
Full House: r8c2=9
Full House: r9c8=5
Naked Single: r7c6=5
Full House: r8c6=3
Naked Single: r8c8=6
Full House: r7c8=9
Naked Single: r7c1=1
Full House: r7c5=6
Full House: r8c5=1
Full House: r8c1=5
|
sudoku_normal_hard_131
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..46..3..6...9..4..2...4..8..6.3...2.4..867..38...9.5...8.1...44..9...1.17...5...
|
814672395635198247729354168596731482241586739387429651968213574452967813173845926
|
. . 4 6 . . 3 . .
6 . . . 9 . . 4 .
. 2 . . . 4 . . 8
. . 6 . 3 . . . 2
. 4 . . 8 6 7 . .
3 8 . . . 9 . 5 .
. . 8 . 1 . . . 4
4 . . 9 . . . 1 .
1 7 . . . 5 . . .
|
8 1 4 6 7 2 3 9 5
6 3 5 1 9 8 2 4 7
7 2 9 3 5 4 1 6 8
5 9 6 7 3 1 4 8 2
2 4 1 5 8 6 7 3 9
3 8 7 4 2 9 6 5 1
9 6 8 2 1 3 5 7 4
4 5 2 9 6 7 8 1 3
1 7 3 8 4 5 9 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5844_hard
|
814672395635198247729354168596731482241586739387429651968213574452967813173845926 #1 Extreme (16972) bf
Brute Force: r5c5=8
Locked Candidates Type 1 (Pointing): 5 in b5 => r23c4<>5
Finned Swordfish: 8 r168 c267 fr1c1 => r2c2<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r1c6<>8
Discontinuous Nice Loop: 7 r1c3 -7- r6c3 =7= r4c1 =8= r1c1 =4= r1c3 => r1c3<>7
Almost Locked Set XZ-Rule: A=r4c6 {17}, B=r1c56,r3c5 {1257}, X=1, Z=7 => r2c6<>7
Forcing Net Contradiction in r7c7 => r1c1=8
r1c1<>8 r4c1=8 (r4c1<>7 r6c3=7 r2c3<>7) r4c8<>8 r9c8=8 r8c7<>8 r8c6=8 (r8c6<>7) r2c6<>8 r2c4=8 r2c4<>7 r2c9=7 (r1c8<>7) r8c9<>7 r8c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 r1c8<>2 r1c8=9 r4c8<>9 r4c8=8 r4c1<>8 r1c1=8
Hidden Single: r1c3=4
Hidden Single: r8c1=4
Forcing Net Verity => r2c7=2
r7c4=7 (r6c4<>7) (r2c4<>7) (r8c5<>7) r8c6<>7 r8c9=7 r2c9<>7 r2c3=7 r6c3<>7 r6c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 (r2c4<>2) r2c6<>2 r2c7=2
r7c6=7 (r1c6<>7) r4c6<>7 r4c6=1 r1c6<>1 r1c6=2 (r2c4<>2) r2c6<>2 r2c7=2
r8c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 (r2c4<>2) r2c6<>2 r2c7=2
r8c6=7 (r8c6<>8 r2c6=8 r2c6<>2) (r1c6<>7) r4c6<>7 r4c6=1 r1c6<>1 r1c6=2 r2c4<>2 r2c7=2
Finned Swordfish: 2 r168 c356 fr6c4 => r5c6<>2
Grouped Discontinuous Nice Loop: 6 r5c8 -6- r3c8 =6= r3c7 =1= r46c7 -1- r6c9 -6- r5c8 => r5c8<>6
Almost Locked Set Chain: 7- r3c15 {579} -9- r457c1 {2579} -7- r45c6 {167} -1- r1c56,r3c5 {1257} -7 => r3c4<>7
Forcing Chain Contradiction in r7c4 => r8c9<>6
r8c9=6 r9c789<>6 r9c5=6 r9c5<>4 r6c5=4 r6c5<>2 r56c4=2 r7c4<>2
r8c9=6 r6c9<>6 r6c9=1 r46c7<>1 r3c7=1 r3c4<>1 r3c4=3 r7c4<>3
r8c9=6 r8c9<>7 r7c8=7 r7c4<>7
Forcing Net Verity => r4c6=1
r2c4=7 (r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 r6c5<>2) (r7c4<>7) (r2c4<>3) r2c4<>8 r2c6=8 r2c6<>3 r3c4=3 r7c4<>3 r7c4=2 r6c4<>2 r6c3=2 r6c3<>7 r4c1=7 r4c6<>7 r4c6=1
r4c4=7 r4c6<>7 r4c6=1
r6c4=7 r4c6<>7 r4c6=1
r7c4=7 (r2c4<>7) (r8c5<>7) r8c6<>7 r8c9=7 r2c9<>7 r2c3=7 r3c1<>7 r4c1=7 r4c6<>7 r4c6=1
Naked Single: r5c6=6
Naked Triple: 2,5,7 in r1c56,r3c5 => r2c4<>7
Skyscraper: 1 in r1c2,r5c3 (connected by r15c9) => r23c3,r6c2<>1
Naked Single: r6c2=8
XYZ-Wing: 2/5/9 in r4c2,r5c14 => r5c3<>5
AIC: 8 8- r4c8 =8= r4c7 =4= r6c7 =1= r3c7 -1- r3c4 -3- r2c6 -8- r8c6 =8= r8c7 -8 => r4c7,r9c8<>8
Hidden Single: r4c8=8
Almost Locked Set XZ-Rule: A=r1248c2 {13569}, B=r7c46,r8c5 {2367}, X=6, Z=3 => r7c2<>3
Discontinuous Nice Loop: 6 r7c8 -6- r7c2 =6= r8c2 =3= r2c2 -3- r3c3 =3= r3c4 =1= r3c7 =6= r3c8 -6- r7c8 => r7c8<>6
Discontinuous Nice Loop: 6 r8c2 -6- r8c5 =6= r9c5 =4= r9c4 =8= r2c4 -8- r2c6 -3- r2c2 =3= r8c2 => r8c2<>6
Hidden Single: r7c2=6
Discontinuous Nice Loop: 9 r4c1 -9- r4c2 =9= r1c2 -9- r1c8 -7- r2c9 =7= r2c3 -7- r6c3 =7= r4c1 => r4c1<>9
Empty Rectangle: 9 in b1 (r4c27) => r3c7<>9
Discontinuous Nice Loop: 9 r1c2 -9- r4c2 =9= r4c7 =4= r6c7 =1= r3c7 -1- r1c9 =1= r1c2 => r1c2<>9
Hidden Single: r4c2=9
Naked Single: r4c7=4
Locked Pair: 1,6 in r6c79 => r5c9,r6c3<>1
Hidden Single: r5c3=1
Locked Candidates Type 1 (Pointing): 9 in b1 => r3c8<>9
Locked Candidates Type 1 (Pointing): 5 in b4 => r37c1<>5
Hidden Single: r7c7=5
Hidden Single: r9c7=9
Hidden Single: r7c1=9
Naked Single: r3c1=7
Naked Single: r3c5=5
Naked Single: r3c8=6
Naked Single: r4c1=5
Full House: r4c4=7
Full House: r5c1=2
Full House: r6c3=7
Naked Single: r3c7=1
Naked Single: r5c4=5
Naked Single: r3c4=3
Full House: r3c3=9
Naked Single: r6c7=6
Full House: r8c7=8
Naked Single: r2c6=8
Naked Single: r7c4=2
Naked Single: r6c9=1
Naked Single: r2c4=1
Naked Single: r6c4=4
Full House: r6c5=2
Full House: r9c4=8
Naked Single: r1c5=7
Full House: r1c6=2
Naked Single: r1c8=9
Naked Single: r8c5=6
Full House: r9c5=4
Naked Single: r1c9=5
Full House: r1c2=1
Full House: r2c9=7
Naked Single: r5c8=3
Full House: r5c9=9
Naked Single: r8c9=3
Full House: r9c9=6
Naked Single: r7c8=7
Full House: r9c8=2
Full House: r7c6=3
Full House: r8c6=7
Full House: r9c3=3
Naked Single: r8c2=5
Full House: r2c2=3
Full House: r2c3=5
Full House: r8c3=2
|
sudoku_normal_extremely_hard_131
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
...6..3..6...9..4..2...4..8..6.3...2.4....7..3....9.5...8.1...4...9...1.17...5...
|
814672395635198247729354168596731482241586739387429651968213574452967813173845926
|
. . . 6 . . 3 . .
6 . . . 9 . . 4 .
. 2 . . . 4 . . 8
. . 6 . 3 . . . 2
. 4 . . . . 7 . .
3 . . . . 9 . 5 .
. . 8 . 1 . . . 4
. . . 9 . . . 1 .
1 7 . . . 5 . . .
|
8 1 4 6 7 2 3 9 5
6 3 5 1 9 8 2 4 7
7 2 9 3 5 4 1 6 8
5 9 6 7 3 1 4 8 2
2 4 1 5 8 6 7 3 9
3 8 7 4 2 9 6 5 1
9 6 8 2 1 3 5 7 4
4 5 2 9 6 7 8 1 3
1 7 3 8 4 5 9 2 6
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5844_hard
|
814672395635198247729354168596731482241586739387429651968213574452967813173845926 #1 Extreme (16972) bf
Brute Force: r5c5=8
Locked Candidates Type 1 (Pointing): 5 in b5 => r23c4<>5
Finned Swordfish: 8 r168 c267 fr1c1 => r2c2<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r1c6<>8
Discontinuous Nice Loop: 7 r1c3 -7- r6c3 =7= r4c1 =8= r1c1 =4= r1c3 => r1c3<>7
Almost Locked Set XZ-Rule: A=r4c6 {17}, B=r1c56,r3c5 {1257}, X=1, Z=7 => r2c6<>7
Forcing Net Contradiction in r7c7 => r1c1=8
r1c1<>8 r4c1=8 (r4c1<>7 r6c3=7 r2c3<>7) r4c8<>8 r9c8=8 r8c7<>8 r8c6=8 (r8c6<>7) r2c6<>8 r2c4=8 r2c4<>7 r2c9=7 (r1c8<>7) r8c9<>7 r8c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 r1c8<>2 r1c8=9 r4c8<>9 r4c8=8 r4c1<>8 r1c1=8
Hidden Single: r1c3=4
Hidden Single: r8c1=4
Forcing Net Verity => r2c7=2
r7c4=7 (r6c4<>7) (r2c4<>7) (r8c5<>7) r8c6<>7 r8c9=7 r2c9<>7 r2c3=7 r6c3<>7 r6c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 (r2c4<>2) r2c6<>2 r2c7=2
r7c6=7 (r1c6<>7) r4c6<>7 r4c6=1 r1c6<>1 r1c6=2 (r2c4<>2) r2c6<>2 r2c7=2
r8c5=7 (r1c5<>7) r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 (r2c4<>2) r2c6<>2 r2c7=2
r8c6=7 (r8c6<>8 r2c6=8 r2c6<>2) (r1c6<>7) r4c6<>7 r4c6=1 r1c6<>1 r1c6=2 r2c4<>2 r2c7=2
Finned Swordfish: 2 r168 c356 fr6c4 => r5c6<>2
Grouped Discontinuous Nice Loop: 6 r5c8 -6- r3c8 =6= r3c7 =1= r46c7 -1- r6c9 -6- r5c8 => r5c8<>6
Almost Locked Set Chain: 7- r3c15 {579} -9- r457c1 {2579} -7- r45c6 {167} -1- r1c56,r3c5 {1257} -7 => r3c4<>7
Forcing Chain Contradiction in r7c4 => r8c9<>6
r8c9=6 r9c789<>6 r9c5=6 r9c5<>4 r6c5=4 r6c5<>2 r56c4=2 r7c4<>2
r8c9=6 r6c9<>6 r6c9=1 r46c7<>1 r3c7=1 r3c4<>1 r3c4=3 r7c4<>3
r8c9=6 r8c9<>7 r7c8=7 r7c4<>7
Forcing Net Verity => r4c6=1
r2c4=7 (r3c5<>7 r3c5=5 r1c5<>5 r1c5=2 r6c5<>2) (r7c4<>7) (r2c4<>3) r2c4<>8 r2c6=8 r2c6<>3 r3c4=3 r7c4<>3 r7c4=2 r6c4<>2 r6c3=2 r6c3<>7 r4c1=7 r4c6<>7 r4c6=1
r4c4=7 r4c6<>7 r4c6=1
r6c4=7 r4c6<>7 r4c6=1
r7c4=7 (r2c4<>7) (r8c5<>7) r8c6<>7 r8c9=7 r2c9<>7 r2c3=7 r3c1<>7 r4c1=7 r4c6<>7 r4c6=1
Naked Single: r5c6=6
Naked Triple: 2,5,7 in r1c56,r3c5 => r2c4<>7
Skyscraper: 1 in r1c2,r5c3 (connected by r15c9) => r23c3,r6c2<>1
Naked Single: r6c2=8
XYZ-Wing: 2/5/9 in r4c2,r5c14 => r5c3<>5
AIC: 8 8- r4c8 =8= r4c7 =4= r6c7 =1= r3c7 -1- r3c4 -3- r2c6 -8- r8c6 =8= r8c7 -8 => r4c7,r9c8<>8
Hidden Single: r4c8=8
Almost Locked Set XZ-Rule: A=r1248c2 {13569}, B=r7c46,r8c5 {2367}, X=6, Z=3 => r7c2<>3
Discontinuous Nice Loop: 6 r7c8 -6- r7c2 =6= r8c2 =3= r2c2 -3- r3c3 =3= r3c4 =1= r3c7 =6= r3c8 -6- r7c8 => r7c8<>6
Discontinuous Nice Loop: 6 r8c2 -6- r8c5 =6= r9c5 =4= r9c4 =8= r2c4 -8- r2c6 -3- r2c2 =3= r8c2 => r8c2<>6
Hidden Single: r7c2=6
Discontinuous Nice Loop: 9 r4c1 -9- r4c2 =9= r1c2 -9- r1c8 -7- r2c9 =7= r2c3 -7- r6c3 =7= r4c1 => r4c1<>9
Empty Rectangle: 9 in b1 (r4c27) => r3c7<>9
Discontinuous Nice Loop: 9 r1c2 -9- r4c2 =9= r4c7 =4= r6c7 =1= r3c7 -1- r1c9 =1= r1c2 => r1c2<>9
Hidden Single: r4c2=9
Naked Single: r4c7=4
Locked Pair: 1,6 in r6c79 => r5c9,r6c3<>1
Hidden Single: r5c3=1
Locked Candidates Type 1 (Pointing): 9 in b1 => r3c8<>9
Locked Candidates Type 1 (Pointing): 5 in b4 => r37c1<>5
Hidden Single: r7c7=5
Hidden Single: r9c7=9
Hidden Single: r7c1=9
Naked Single: r3c1=7
Naked Single: r3c5=5
Naked Single: r3c8=6
Naked Single: r4c1=5
Full House: r4c4=7
Full House: r5c1=2
Full House: r6c3=7
Naked Single: r3c7=1
Naked Single: r5c4=5
Naked Single: r3c4=3
Full House: r3c3=9
Naked Single: r6c7=6
Full House: r8c7=8
Naked Single: r2c6=8
Naked Single: r7c4=2
Naked Single: r6c9=1
Naked Single: r2c4=1
Naked Single: r6c4=4
Full House: r6c5=2
Full House: r9c4=8
Naked Single: r1c5=7
Full House: r1c6=2
Naked Single: r1c8=9
Naked Single: r8c5=6
Full House: r9c5=4
Naked Single: r1c9=5
Full House: r1c2=1
Full House: r2c9=7
Naked Single: r5c8=3
Full House: r5c9=9
Naked Single: r8c9=3
Full House: r9c9=6
Naked Single: r7c8=7
Full House: r9c8=2
Full House: r7c6=3
Full House: r8c6=7
Full House: r9c3=3
Naked Single: r8c2=5
Full House: r2c2=3
Full House: r2c3=5
Full House: r8c3=2
|
sudoku_normal_hard_132
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
6.....8.2.728..46..1.6..57...17...2.23918675476...4....9..3...71..9...8...7.6...5
|
645379812972815463813642579451793628239186754768524931596238147124957386387461295
|
6 . . . . . 8 . 2
. 7 2 8 . . 4 6 .
. 1 . 6 . . 5 7 .
. . 1 7 . . . 2 .
2 3 9 1 8 6 7 5 4
7 6 . . . 4 . . .
. 9 . . 3 . . . 7
1 . . 9 . . . 8 .
. . 7 . 6 . . . 5
|
6 4 5 3 7 9 8 1 2
9 7 2 8 1 5 4 6 3
8 1 3 6 4 2 5 7 9
4 5 1 7 9 3 6 2 8
2 3 9 1 8 6 7 5 4
7 6 8 5 2 4 9 3 1
5 9 6 2 3 8 1 4 7
1 2 4 9 5 7 3 8 6
3 8 7 4 6 1 2 9 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7147_hard
|
645379812972815463813642579451793628239186754768524931596238147124957386387461295 #1 Extreme (22132) bf
Brute Force: r5c8=5
Forcing Net Contradiction in c9 => r1c5<>5
r1c5=5 (r1c5<>9) (r1c5<>7 r1c6=7 r1c6<>9) (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r1c3<>9 r1c8=9 r2c9<>9
r1c5=5 (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r3c9<>9
r1c5=5 r4c5<>5 r4c5=9 r4c9<>9
r1c5=5 (r1c5<>1) (r1c5<>7 r1c6=7 r1c6<>1) (r1c5<>9) (r1c5<>7 r1c6=7 r1c6<>9) (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r1c3<>9 r1c8=9 r1c8<>1 r1c4=1 r5c4<>1 r5c4=3 (r5c3<>3) r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r5c9<>9
r1c5=5 (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r3c1<>8 r3c3=8 r6c3<>8 r6c9=8 r6c9<>9
Forcing Net Contradiction in r8 => r5c6<>3
r5c6=3 r5c2<>3 r5c2=4 r8c2<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r8c3<>4
r5c6=3 (r5c4<>3) r6c4<>3 r1c4=3 r1c4<>4 r79c4=4 r8c5<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r1c8<>4 r79c8=4 r8c7<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r1c8<>4 r79c8=4 r8c9<>4
Brute Force: r5c9=4
Naked Single: r5c2=3
Naked Single: r5c3=9
Naked Single: r5c4=1
Naked Single: r5c6=6
Full House: r5c7=7
Locked Candidates Type 1 (Pointing): 1 in b8 => r12c6<>1
Naked Triple: 3,4,5 in r1c234 => r1c58<>4, r1c68<>3, r1c6<>5
Hidden Single: r2c7=4
Locked Candidates Type 1 (Pointing): 3 in b3 => r468c9<>3
Hidden Pair: 1,8 in r79c6 => r79c6<>2, r7c6<>5, r79c6<>7
Hidden Single: r9c3=7
Hidden Single: r7c9=7
Naked Single: r8c9=6
Hidden Single: r4c7=6
Hidden Single: r7c3=6
Hidden Single: r4c6=3
Hidden Single: r1c4=3
Hidden Single: r3c5=4
Hidden Single: r3c6=2
Locked Candidates Type 1 (Pointing): 5 in b2 => r2c1<>5
Locked Candidates Type 1 (Pointing): 9 in b5 => r12c5<>9
Locked Candidates Type 2 (Claiming): 4 in r8 => r79c1,r9c2<>4
Hidden Single: r4c1=4
Hidden Single: r7c1=5
Hidden Single: r6c4=5
Naked Single: r4c5=9
Full House: r6c5=2
Naked Single: r6c3=8
Full House: r4c2=5
Full House: r4c9=8
Naked Single: r3c3=3
Naked Single: r1c2=4
Naked Single: r2c1=9
Naked Single: r3c9=9
Full House: r3c1=8
Full House: r1c3=5
Full House: r8c3=4
Full House: r9c1=3
Naked Single: r8c2=2
Full House: r9c2=8
Naked Single: r2c6=5
Naked Single: r1c8=1
Full House: r2c9=3
Full House: r6c9=1
Full House: r2c5=1
Naked Single: r8c7=3
Naked Single: r9c6=1
Naked Single: r8c6=7
Full House: r8c5=5
Full House: r1c5=7
Full House: r1c6=9
Full House: r7c6=8
Naked Single: r7c8=4
Naked Single: r6c7=9
Full House: r6c8=3
Full House: r9c8=9
Naked Single: r7c4=2
Full House: r7c7=1
Full House: r9c7=2
Full House: r9c4=4
|
sudoku_normal_extremely_hard_132
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
6.....8.2.728...6..1.6..57...17...2.2...8....76...4....9..3....1..9...8.....6...5
|
645379812972815463813642579451793628239186754768524931596238147124957386387461295
|
6 . . . . . 8 . 2
. 7 2 8 . . . 6 .
. 1 . 6 . . 5 7 .
. . 1 7 . . . 2 .
2 . . . 8 . . . .
7 6 . . . 4 . . .
. 9 . . 3 . . . .
1 . . 9 . . . 8 .
. . . . 6 . . . 5
|
6 4 5 3 7 9 8 1 2
9 7 2 8 1 5 4 6 3
8 1 3 6 4 2 5 7 9
4 5 1 7 9 3 6 2 8
2 3 9 1 8 6 7 5 4
7 6 8 5 2 4 9 3 1
5 9 6 2 3 8 1 4 7
1 2 4 9 5 7 3 8 6
3 8 7 4 6 1 2 9 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7147_hard
|
645379812972815463813642579451793628239186754768524931596238147124957386387461295 #1 Extreme (22132) bf
Brute Force: r5c8=5
Forcing Net Contradiction in c9 => r1c5<>5
r1c5=5 (r1c5<>9) (r1c5<>7 r1c6=7 r1c6<>9) (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r1c3<>9 r1c8=9 r2c9<>9
r1c5=5 (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r3c9<>9
r1c5=5 r4c5<>5 r4c5=9 r4c9<>9
r1c5=5 (r1c5<>1) (r1c5<>7 r1c6=7 r1c6<>1) (r1c5<>9) (r1c5<>7 r1c6=7 r1c6<>9) (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r1c3<>9 r1c8=9 r1c8<>1 r1c4=1 r5c4<>1 r5c4=3 (r5c3<>3) r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r5c9<>9
r1c5=5 (r4c5<>5 r4c5=9 r4c1<>9) (r2c5<>5) r2c6<>5 r2c1=5 r2c1<>9 r3c1=9 r3c1<>8 r3c3=8 r6c3<>8 r6c9=8 r6c9<>9
Forcing Net Contradiction in r8 => r5c6<>3
r5c6=3 r5c2<>3 r5c2=4 r8c2<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r8c3<>4
r5c6=3 (r5c4<>3) r6c4<>3 r1c4=3 r1c4<>4 r79c4=4 r8c5<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r1c8<>4 r79c8=4 r8c7<>4
r5c6=3 (r5c2<>3 r5c2=4 r5c3<>4 r5c3=9 r1c3<>9) (r5c2<>3 r5c2=4 r1c2<>4) (r5c4<>3) r6c4<>3 r1c4=3 (r1c3<>3) r1c2<>3 r1c2=5 r1c3<>5 r1c3=4 r1c8<>4 r79c8=4 r8c9<>4
Brute Force: r5c9=4
Naked Single: r5c2=3
Naked Single: r5c3=9
Naked Single: r5c4=1
Naked Single: r5c6=6
Full House: r5c7=7
Locked Candidates Type 1 (Pointing): 1 in b8 => r12c6<>1
Naked Triple: 3,4,5 in r1c234 => r1c58<>4, r1c68<>3, r1c6<>5
Hidden Single: r2c7=4
Locked Candidates Type 1 (Pointing): 3 in b3 => r468c9<>3
Hidden Pair: 1,8 in r79c6 => r79c6<>2, r7c6<>5, r79c6<>7
Hidden Single: r9c3=7
Hidden Single: r7c9=7
Naked Single: r8c9=6
Hidden Single: r4c7=6
Hidden Single: r7c3=6
Hidden Single: r4c6=3
Hidden Single: r1c4=3
Hidden Single: r3c5=4
Hidden Single: r3c6=2
Locked Candidates Type 1 (Pointing): 5 in b2 => r2c1<>5
Locked Candidates Type 1 (Pointing): 9 in b5 => r12c5<>9
Locked Candidates Type 2 (Claiming): 4 in r8 => r79c1,r9c2<>4
Hidden Single: r4c1=4
Hidden Single: r7c1=5
Hidden Single: r6c4=5
Naked Single: r4c5=9
Full House: r6c5=2
Naked Single: r6c3=8
Full House: r4c2=5
Full House: r4c9=8
Naked Single: r3c3=3
Naked Single: r1c2=4
Naked Single: r2c1=9
Naked Single: r3c9=9
Full House: r3c1=8
Full House: r1c3=5
Full House: r8c3=4
Full House: r9c1=3
Naked Single: r8c2=2
Full House: r9c2=8
Naked Single: r2c6=5
Naked Single: r1c8=1
Full House: r2c9=3
Full House: r6c9=1
Full House: r2c5=1
Naked Single: r8c7=3
Naked Single: r9c6=1
Naked Single: r8c6=7
Full House: r8c5=5
Full House: r1c5=7
Full House: r1c6=9
Full House: r7c6=8
Naked Single: r7c8=4
Naked Single: r6c7=9
Full House: r6c8=3
Full House: r9c8=9
Naked Single: r7c4=2
Full House: r7c7=1
Full House: r9c7=2
Full House: r9c4=4
|
sudoku_normal_hard_133
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
4.8...6.2.25...4..69.4...582.9.4.56..86.5.21454.....89..4.....6..2.31.458....4.2.
|
438517692125896437697423158279148563386759214541362789914285376762931845853674921
|
4 . 8 . . . 6 . 2
. 2 5 . . . 4 . .
6 9 . 4 . . . 5 8
2 . 9 . 4 . 5 6 .
. 8 6 . 5 . 2 1 4
5 4 . . . . . 8 9
. . 4 . . . . . 6
. . 2 . 3 1 . 4 5
8 . . . . 4 . 2 .
|
4 3 8 5 1 7 6 9 2
1 2 5 8 9 6 4 3 7
6 9 7 4 2 3 1 5 8
2 7 9 1 4 8 5 6 3
3 8 6 7 5 9 2 1 4
5 4 1 3 6 2 7 8 9
9 1 4 2 8 5 3 7 6
7 6 2 9 3 1 8 4 5
8 5 3 6 7 4 9 2 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4685_hard
|
438517692125896437697423158279148563386759214541362789914285376762931845853674921 #1 Extreme (14022) bf
Hidden Single: r6c1=5
Hidden Single: r4c8=6
Hidden Single: r1c3=8
Hidden Single: r4c5=4
Hidden Single: r1c9=2
Hidden Single: r4c1=2
Hidden Single: r1c1=4
Hidden Single: r7c3=4
Hidden Single: r5c9=4
Hidden Single: r8c8=4
Locked Candidates Type 1 (Pointing): 9 in b3 => r7c8<>9
Brute Force: r5c8=1
Skyscraper: 1 in r7c1,r9c9 (connected by r2c19) => r7c7,r9c23<>1
Finned X-Wing: 1 r14 c24 fr1c5 => r2c4<>1
Forcing Chain Contradiction in r3 => r4c6<>3
r4c6=3 r4c6<>8 r4c4=8 r4c4<>1 r4c2=1 r6c3<>1 r3c3=1 r3c3<>3
r4c6=3 r3c6<>3
r4c6=3 r4c9<>3 r6c7=3 r3c7<>3
Forcing Chain Contradiction in r9c9 => r6c3<>3
r6c3=3 r6c3<>1 r3c3=1 r3c7<>1 r9c7=1 r9c9<>1
r6c3=3 r6c7<>3 r4c9=3 r9c9<>3
r6c3=3 r9c3<>3 r9c3=7 r9c9<>7
Discontinuous Nice Loop: 7 r4c4 -7- r4c9 =7= r6c7 -7- r6c3 -1- r4c2 =1= r4c4 => r4c4<>7
Discontinuous Nice Loop: 8 r4c4 -8- r4c6 -7- r4c9 =7= r6c7 -7- r6c3 -1- r4c2 =1= r4c4 => r4c4<>8
Hidden Single: r4c6=8
Finned Franken Swordfish: 3 c39b4 r249 fr3c3 fr5c1 => r2c1<>3
Forcing Chain Contradiction in c9 => r4c4=1
r4c4<>1 r4c2=1 r6c3<>1 r3c3=1 r3c7<>1 r2c9=1 r2c9<>3
r4c4<>1 r4c4=3 r4c9<>3
r4c4<>1 r4c2=1 r6c3<>1 r6c3=7 r9c3<>7 r9c3=3 r9c9<>3
Hidden Single: r6c3=1
W-Wing: 7/3 in r4c2,r7c8 connected by 3 in r57c1 => r7c2<>7
W-Wing: 7/3 in r4c2,r9c3 connected by 3 in r57c1 => r89c2<>7
Naked Single: r8c2=6
Sashimi Swordfish: 7 c239 r249 fr1c2 fr3c3 => r2c1<>7
Naked Single: r2c1=1
Hidden Single: r1c5=1
Hidden Single: r7c2=1
Hidden Single: r9c9=1
Hidden Single: r3c7=1
Hidden Single: r9c2=5
Remote Pair: 3/7 r1c2 -7- r4c2 -3- r4c9 -7- r2c9 => r1c8<>3, r1c8<>7
Naked Single: r1c8=9
Locked Candidates Type 1 (Pointing): 3 in b3 => r2c46<>3
Locked Candidates Type 1 (Pointing): 7 in b3 => r2c456<>7
Remote Pair: 3/7 r7c8 -7- r2c8 -3- r2c9 -7- r4c9 -3- r4c2 -7- r1c2 -3- r3c3 -7- r9c3 => r7c1,r9c7<>3, r7c1,r9c7<>7
Naked Single: r7c1=9
Naked Single: r9c7=9
Naked Single: r8c1=7
Full House: r5c1=3
Full House: r9c3=3
Full House: r4c2=7
Full House: r3c3=7
Full House: r1c2=3
Full House: r4c9=3
Full House: r2c9=7
Full House: r6c7=7
Full House: r2c8=3
Full House: r7c8=7
Naked Single: r8c7=8
Full House: r7c7=3
Full House: r8c4=9
Naked Single: r3c5=2
Full House: r3c6=3
Naked Single: r5c4=7
Full House: r5c6=9
Naked Single: r6c5=6
Naked Single: r7c5=8
Naked Single: r1c4=5
Full House: r1c6=7
Naked Single: r9c4=6
Full House: r9c5=7
Full House: r2c5=9
Naked Single: r2c6=6
Full House: r2c4=8
Naked Single: r6c6=2
Full House: r6c4=3
Full House: r7c4=2
Full House: r7c6=5
|
sudoku_normal_extremely_hard_133
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
......6...25...4..69.4...58..9...5...86.5.2...4.....89........6..2.31..58....4.2.
|
438517692125896437697423158279148563386759214541362789914285376762931845853674921
|
. . . . . . 6 . .
. 2 5 . . . 4 . .
6 9 . 4 . . . 5 8
. . 9 . . . 5 . .
. 8 6 . 5 . 2 . .
. 4 . . . . . 8 9
. . . . . . . . 6
. . 2 . 3 1 . . 5
8 . . . . 4 . 2 .
|
4 3 8 5 1 7 6 9 2
1 2 5 8 9 6 4 3 7
6 9 7 4 2 3 1 5 8
2 7 9 1 4 8 5 6 3
3 8 6 7 5 9 2 1 4
5 4 1 3 6 2 7 8 9
9 1 4 2 8 5 3 7 6
7 6 2 9 3 1 8 4 5
8 5 3 6 7 4 9 2 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4685_hard
|
438517692125896437697423158279148563386759214541362789914285376762931845853674921 #1 Extreme (14022) bf
Hidden Single: r6c1=5
Hidden Single: r4c8=6
Hidden Single: r1c3=8
Hidden Single: r4c5=4
Hidden Single: r1c9=2
Hidden Single: r4c1=2
Hidden Single: r1c1=4
Hidden Single: r7c3=4
Hidden Single: r5c9=4
Hidden Single: r8c8=4
Locked Candidates Type 1 (Pointing): 9 in b3 => r7c8<>9
Brute Force: r5c8=1
Skyscraper: 1 in r7c1,r9c9 (connected by r2c19) => r7c7,r9c23<>1
Finned X-Wing: 1 r14 c24 fr1c5 => r2c4<>1
Forcing Chain Contradiction in r3 => r4c6<>3
r4c6=3 r4c6<>8 r4c4=8 r4c4<>1 r4c2=1 r6c3<>1 r3c3=1 r3c3<>3
r4c6=3 r3c6<>3
r4c6=3 r4c9<>3 r6c7=3 r3c7<>3
Forcing Chain Contradiction in r9c9 => r6c3<>3
r6c3=3 r6c3<>1 r3c3=1 r3c7<>1 r9c7=1 r9c9<>1
r6c3=3 r6c7<>3 r4c9=3 r9c9<>3
r6c3=3 r9c3<>3 r9c3=7 r9c9<>7
Discontinuous Nice Loop: 7 r4c4 -7- r4c9 =7= r6c7 -7- r6c3 -1- r4c2 =1= r4c4 => r4c4<>7
Discontinuous Nice Loop: 8 r4c4 -8- r4c6 -7- r4c9 =7= r6c7 -7- r6c3 -1- r4c2 =1= r4c4 => r4c4<>8
Hidden Single: r4c6=8
Finned Franken Swordfish: 3 c39b4 r249 fr3c3 fr5c1 => r2c1<>3
Forcing Chain Contradiction in c9 => r4c4=1
r4c4<>1 r4c2=1 r6c3<>1 r3c3=1 r3c7<>1 r2c9=1 r2c9<>3
r4c4<>1 r4c4=3 r4c9<>3
r4c4<>1 r4c2=1 r6c3<>1 r6c3=7 r9c3<>7 r9c3=3 r9c9<>3
Hidden Single: r6c3=1
W-Wing: 7/3 in r4c2,r7c8 connected by 3 in r57c1 => r7c2<>7
W-Wing: 7/3 in r4c2,r9c3 connected by 3 in r57c1 => r89c2<>7
Naked Single: r8c2=6
Sashimi Swordfish: 7 c239 r249 fr1c2 fr3c3 => r2c1<>7
Naked Single: r2c1=1
Hidden Single: r1c5=1
Hidden Single: r7c2=1
Hidden Single: r9c9=1
Hidden Single: r3c7=1
Hidden Single: r9c2=5
Remote Pair: 3/7 r1c2 -7- r4c2 -3- r4c9 -7- r2c9 => r1c8<>3, r1c8<>7
Naked Single: r1c8=9
Locked Candidates Type 1 (Pointing): 3 in b3 => r2c46<>3
Locked Candidates Type 1 (Pointing): 7 in b3 => r2c456<>7
Remote Pair: 3/7 r7c8 -7- r2c8 -3- r2c9 -7- r4c9 -3- r4c2 -7- r1c2 -3- r3c3 -7- r9c3 => r7c1,r9c7<>3, r7c1,r9c7<>7
Naked Single: r7c1=9
Naked Single: r9c7=9
Naked Single: r8c1=7
Full House: r5c1=3
Full House: r9c3=3
Full House: r4c2=7
Full House: r3c3=7
Full House: r1c2=3
Full House: r4c9=3
Full House: r2c9=7
Full House: r6c7=7
Full House: r2c8=3
Full House: r7c8=7
Naked Single: r8c7=8
Full House: r7c7=3
Full House: r8c4=9
Naked Single: r3c5=2
Full House: r3c6=3
Naked Single: r5c4=7
Full House: r5c6=9
Naked Single: r6c5=6
Naked Single: r7c5=8
Naked Single: r1c4=5
Full House: r1c6=7
Naked Single: r9c4=6
Full House: r9c5=7
Full House: r2c5=9
Naked Single: r2c6=6
Full House: r2c4=8
Naked Single: r6c6=2
Full House: r6c4=3
Full House: r7c4=2
Full House: r7c6=5
|
sudoku_normal_hard_134
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
52...7..387.31.5..9134567..638...9.1...9..3...9213...5367........96.3....8.7..639
|
526897413874312596913456728638275941451968372792134865367529184149683257285741639
|
5 2 . . . 7 . . 3
8 7 . 3 1 . 5 . .
9 1 3 4 5 6 7 . .
6 3 8 . . . 9 . 1
. . . 9 . . 3 . .
. 9 2 1 3 . . . 5
3 6 7 . . . . . .
. . 9 6 . 3 . . .
. 8 . 7 . . 6 3 9
|
5 2 6 8 9 7 4 1 3
8 7 4 3 1 2 5 9 6
9 1 3 4 5 6 7 2 8
6 3 8 2 7 5 9 4 1
4 5 1 9 6 8 3 7 2
7 9 2 1 3 4 8 6 5
3 6 7 5 2 9 1 8 4
1 4 9 6 8 3 2 5 7
2 8 5 7 4 1 6 3 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_578_easy
|
526897413874312596913456728638275941451968372792134865367529184149683257285741639 #1 Easy (420)
Naked Single: r3c3=3
Hidden Single: r3c5=5
Hidden Single: r6c2=9
Hidden Single: r2c1=8
Hidden Single: r8c4=6
Hidden Single: r7c1=3
Hidden Single: r8c3=9
Hidden Single: r1c9=3
Hidden Single: r4c2=3
Hidden Single: r2c2=7
Hidden Single: r9c7=6
Hidden Single: r6c5=3
Hidden Single: r1c2=2
Naked Single: r1c4=8
Naked Single: r1c5=9
Full House: r2c6=2
Hidden Single: r6c8=6
Hidden Single: r5c5=6
Hidden Single: r2c8=9
Hidden Single: r7c6=9
Hidden Single: r1c3=6
Full House: r2c3=4
Full House: r2c9=6
Hidden Single: r6c1=7
Hidden Single: r4c5=7
Hidden Single: r9c6=1
Naked Single: r9c3=5
Full House: r5c3=1
Naked Single: r8c2=4
Full House: r5c2=5
Full House: r5c1=4
Naked Single: r9c1=2
Full House: r8c1=1
Full House: r9c5=4
Naked Single: r5c6=8
Naked Single: r6c6=4
Full House: r4c6=5
Full House: r6c7=8
Full House: r4c4=2
Full House: r4c8=4
Full House: r7c4=5
Naked Single: r8c7=2
Naked Single: r1c8=1
Full House: r1c7=4
Full House: r7c7=1
Naked Single: r8c5=8
Full House: r7c5=2
Naked Single: r7c8=8
Full House: r7c9=4
Naked Single: r8c9=7
Full House: r8c8=5
Naked Single: r3c8=2
Full House: r3c9=8
Full House: r5c9=2
Full House: r5c8=7
|
sudoku_normal_extremely_hard_134
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
5....7......31.5..91.4.67..6.8...9.1...9..3....21....5.67...........3....8.7...39
|
526897413874312596913456728638275941451968372792134865367529184149683257285741639
|
5 . . . . 7 . . .
. . . 3 1 . 5 . .
9 1 . 4 . 6 7 . .
6 . 8 . . . 9 . 1
. . . 9 . . 3 . .
. . 2 1 . . . . 5
. 6 7 . . . . . .
. . . . . 3 . . .
. 8 . 7 . . . 3 9
|
5 2 6 8 9 7 4 1 3
8 7 4 3 1 2 5 9 6
9 1 3 4 5 6 7 2 8
6 3 8 2 7 5 9 4 1
4 5 1 9 6 8 3 7 2
7 9 2 1 3 4 8 6 5
3 6 7 5 2 9 1 8 4
1 4 9 6 8 3 2 5 7
2 8 5 7 4 1 6 3 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_578_easy
|
526897413874312596913456728638275941451968372792134865367529184149683257285741639 #1 Easy (420)
Naked Single: r3c3=3
Hidden Single: r3c5=5
Hidden Single: r6c2=9
Hidden Single: r2c1=8
Hidden Single: r8c4=6
Hidden Single: r7c1=3
Hidden Single: r8c3=9
Hidden Single: r1c9=3
Hidden Single: r4c2=3
Hidden Single: r2c2=7
Hidden Single: r9c7=6
Hidden Single: r6c5=3
Hidden Single: r1c2=2
Naked Single: r1c4=8
Naked Single: r1c5=9
Full House: r2c6=2
Hidden Single: r6c8=6
Hidden Single: r5c5=6
Hidden Single: r2c8=9
Hidden Single: r7c6=9
Hidden Single: r1c3=6
Full House: r2c3=4
Full House: r2c9=6
Hidden Single: r6c1=7
Hidden Single: r4c5=7
Hidden Single: r9c6=1
Naked Single: r9c3=5
Full House: r5c3=1
Naked Single: r8c2=4
Full House: r5c2=5
Full House: r5c1=4
Naked Single: r9c1=2
Full House: r8c1=1
Full House: r9c5=4
Naked Single: r5c6=8
Naked Single: r6c6=4
Full House: r4c6=5
Full House: r6c7=8
Full House: r4c4=2
Full House: r4c8=4
Full House: r7c4=5
Naked Single: r8c7=2
Naked Single: r1c8=1
Full House: r1c7=4
Full House: r7c7=1
Naked Single: r8c5=8
Full House: r7c5=2
Naked Single: r7c8=8
Full House: r7c9=4
Naked Single: r8c9=7
Full House: r8c8=5
Naked Single: r3c8=2
Full House: r3c9=8
Full House: r5c9=2
Full House: r5c8=7
|
sudoku_normal_hard_135
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
1293.756.3.4...7987.8..9213983.1.42..4..9..3....8.3.5.......3.....63....832...671
|
129387564364521798758469213983715426541296837276843159695178342417632985832954671
|
1 2 9 3 . 7 5 6 .
3 . 4 . . . 7 9 8
7 . 8 . . 9 2 1 3
9 8 3 . 1 . 4 2 .
. 4 . . 9 . . 3 .
. . . 8 . 3 . 5 .
. . . . . . 3 . .
. . . 6 3 . . . .
8 3 2 . . . 6 7 1
|
1 2 9 3 8 7 5 6 4
3 6 4 5 2 1 7 9 8
7 5 8 4 6 9 2 1 3
9 8 3 7 1 5 4 2 6
5 4 1 2 9 6 8 3 7
2 7 6 8 4 3 1 5 9
6 9 5 1 7 8 3 4 2
4 1 7 6 3 2 9 8 5
8 3 2 9 5 4 6 7 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_421_easy
|
129387564364521798758469213983715426541296837276843159695178342417632985832954671 #1 Easy (354)
Hidden Single: r5c8=3
Hidden Single: r4c2=8
Hidden Single: r9c2=3
Hidden Single: r2c1=3
Hidden Single: r3c8=1
Hidden Single: r4c3=3
Hidden Single: r1c4=3
Hidden Single: r9c7=6
Naked Single: r4c7=4
Naked Single: r3c7=2
Hidden Single: r2c3=4
Hidden Single: r1c8=6
Naked Single: r1c2=2
Naked Single: r2c9=8
Full House: r1c9=4
Full House: r1c5=8
Hidden Single: r9c4=9
Hidden Single: r6c5=4
Naked Single: r9c5=5
Full House: r9c6=4
Naked Single: r3c5=6
Naked Single: r2c5=2
Full House: r7c5=7
Naked Single: r3c2=5
Full House: r2c2=6
Full House: r3c4=4
Hidden Single: r5c7=8
Naked Single: r8c7=9
Full House: r6c7=1
Naked Single: r6c2=7
Naked Single: r6c3=6
Naked Single: r8c2=1
Full House: r7c2=9
Naked Single: r6c1=2
Full House: r6c9=9
Naked Single: r7c3=5
Naked Single: r5c1=5
Full House: r5c3=1
Full House: r8c3=7
Naked Single: r7c9=2
Naked Single: r8c1=4
Full House: r7c1=6
Naked Single: r7c4=1
Naked Single: r8c9=5
Naked Single: r8c8=8
Full House: r7c8=4
Full House: r7c6=8
Full House: r8c6=2
Naked Single: r2c4=5
Full House: r2c6=1
Naked Single: r5c6=6
Full House: r4c6=5
Naked Single: r4c4=7
Full House: r4c9=6
Full House: r5c9=7
Full House: r5c4=2
|
sudoku_normal_extremely_hard_135
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
1.9..75........79.7.8..9..39...1..2..4..9.......8.3.5.......3.....63....8.2....71
|
129387564364521798758469213983715426541296837276843159695178342417632985832954671
|
1 . 9 . . 7 5 . .
. . . . . . 7 9 .
7 . 8 . . 9 . . 3
9 . . . 1 . . 2 .
. 4 . . 9 . . . .
. . . 8 . 3 . 5 .
. . . . . . 3 . .
. . . 6 3 . . . .
8 . 2 . . . . 7 1
|
1 2 9 3 8 7 5 6 4
3 6 4 5 2 1 7 9 8
7 5 8 4 6 9 2 1 3
9 8 3 7 1 5 4 2 6
5 4 1 2 9 6 8 3 7
2 7 6 8 4 3 1 5 9
6 9 5 1 7 8 3 4 2
4 1 7 6 3 2 9 8 5
8 3 2 9 5 4 6 7 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_421_easy
|
129387564364521798758469213983715426541296837276843159695178342417632985832954671 #1 Easy (354)
Hidden Single: r5c8=3
Hidden Single: r4c2=8
Hidden Single: r9c2=3
Hidden Single: r2c1=3
Hidden Single: r3c8=1
Hidden Single: r4c3=3
Hidden Single: r1c4=3
Hidden Single: r9c7=6
Naked Single: r4c7=4
Naked Single: r3c7=2
Hidden Single: r2c3=4
Hidden Single: r1c8=6
Naked Single: r1c2=2
Naked Single: r2c9=8
Full House: r1c9=4
Full House: r1c5=8
Hidden Single: r9c4=9
Hidden Single: r6c5=4
Naked Single: r9c5=5
Full House: r9c6=4
Naked Single: r3c5=6
Naked Single: r2c5=2
Full House: r7c5=7
Naked Single: r3c2=5
Full House: r2c2=6
Full House: r3c4=4
Hidden Single: r5c7=8
Naked Single: r8c7=9
Full House: r6c7=1
Naked Single: r6c2=7
Naked Single: r6c3=6
Naked Single: r8c2=1
Full House: r7c2=9
Naked Single: r6c1=2
Full House: r6c9=9
Naked Single: r7c3=5
Naked Single: r5c1=5
Full House: r5c3=1
Full House: r8c3=7
Naked Single: r7c9=2
Naked Single: r8c1=4
Full House: r7c1=6
Naked Single: r7c4=1
Naked Single: r8c9=5
Naked Single: r8c8=8
Full House: r7c8=4
Full House: r7c6=8
Full House: r8c6=2
Naked Single: r2c4=5
Full House: r2c6=1
Naked Single: r5c6=6
Full House: r4c6=5
Naked Single: r4c4=7
Full House: r4c9=6
Full House: r5c9=7
Full House: r5c4=2
|
sudoku_normal_hard_136
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..65..1...2......9....9.24.65.1....8..1.859..78..6.5......43....6......2..86..73.
|
936524187524718369817396245659137428341285976782469513275843691463971852198652734
|
. . 6 5 . . 1 . .
. 2 . . . . . . 9
. . . . 9 . 2 4 .
6 5 . 1 . . . . 8
. . 1 . 8 5 9 . .
7 8 . . 6 . 5 . .
. . . . 4 3 . . .
. 6 . . . . . . 2
. . 8 6 . . 7 3 .
|
9 3 6 5 2 4 1 8 7
5 2 4 7 1 8 3 6 9
8 1 7 3 9 6 2 4 5
6 5 9 1 3 7 4 2 8
3 4 1 2 8 5 9 7 6
7 8 2 4 6 9 5 1 3
2 7 5 8 4 3 6 9 1
4 6 3 9 7 1 8 5 2
1 9 8 6 5 2 7 3 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9709_hard
|
936524187524718369817396245659137428341285976782469513275843691463971852198652734 #1 Extreme (36400) bf
Brute Force: r5c6=5
Brute Force: r5c5=8
Brute Force: r5c7=9
Locked Candidates Type 1 (Pointing): 9 in b4 => r78c3<>9
Empty Rectangle: 3 in b5 (r24c7) => r2c4<>3
Forcing Chain Contradiction in r4 => r4c6<>2
r4c6=2 r4c6<>9 r4c3=9 r4c3<>4
r4c6=2 r4c6<>4
r4c6=2 r56c4<>2 r7c4=2 r7c4<>8 r7c78=8 r8c7<>8 r8c7=4 r4c7<>4
Forcing Net Contradiction in r7c8 => r6c8=1
r6c8<>1 r6c8=2 (r5c8<>2) r4c8<>2 r4c8=7 (r5c8<>7) r5c9<>7 r5c4=7 (r5c4<>2) r5c4<>2 r5c1=2 (r4c3<>2) r6c3<>2 r7c3=2 r7c4<>2 r6c4=2 r6c8<>2 r6c8=1
Naked Pair: 3,4 in r4c7,r6c9 => r5c9<>3, r5c9<>4
Forcing Chain Contradiction in c3 => r4c5<>2
r4c5=2 r1c5<>2 r1c6=2 r1c6<>4 r1c12=4 r2c3<>4
r4c5=2 r6c46<>2 r6c3=2 r6c3<>9 r4c3=9 r4c3<>4
r4c5=2 r6c46<>2 r6c3=2 r6c3<>4
r4c5=2 r56c4<>2 r7c4=2 r7c4<>8 r7c78=8 r8c7<>8 r8c7=4 r8c3<>4
W-Wing: 7/3 in r1c9,r4c5 connected by 3 in r24c7 => r1c5<>7
Forcing Chain Contradiction in c3 => r4c6<>4
r4c6=4 r1c6<>4 r1c12=4 r2c3<>4
r4c6=4 r4c3<>4
r4c6=4 r4c7<>4 r6c9=4 r6c3<>4
r4c6=4 r4c7<>4 r8c7=4 r8c3<>4
W-Wing: 3/4 in r5c2,r6c9 connected by 4 in r4c37 => r6c3<>3
Forcing Chain Contradiction in r2 => r2c1<>1
r2c1=1 r2c1<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c9=4 r4c7<>4 r4c3=4 r2c3<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c9=4 r6c6<>4 r56c4=4 r2c4<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r2c6=6 r2c6<>4
Locked Candidates Type 1 (Pointing): 1 in b1 => r3c6<>1
Forcing Chain Contradiction in c5 => r3c6=6
r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r1c5<>3
r3c6<>6 r2c6=6 r2c6<>1 r2c5=1 r2c5<>3
r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c4=3 r4c5<>3
Grouped AIC: 8 8- r1c8 -7- r45c8 =7= r5c9 =6= r7c9 -6- r7c7 -8 => r2c7,r78c8<>8
Discontinuous Nice Loop: 3 r3c2 -3- r5c2 -4- r4c3 =4= r4c7 -4- r8c7 -8- r7c7 =8= r7c4 -8- r3c4 =8= r3c1 =1= r3c2 => r3c2<>3
Sashimi Swordfish: 3 c257 r124 fr5c2 => r4c3<>3
Locked Candidates Type 1 (Pointing): 3 in b4 => r5c4<>3
Forcing Chain Contradiction in r6c6 => r1c5=2
r1c5<>2 r1c6=2 r6c6<>2
r1c5<>2 r1c5=3 r4c5<>3 r4c7=3 r4c7<>4 r6c9=4 r6c6<>4
r1c5<>2 r1c5=3 r4c5<>3 r4c5=7 r4c6<>7 r4c6=9 r6c6<>9
X-Wing: 3 c57 r24 => r2c13<>3
Discontinuous Nice Loop: 4 r8c3 -4- r8c7 =4= r4c7 =3= r4c5 -3- r2c5 =3= r3c4 -3- r3c3 =3= r8c3 => r8c3<>4
Skyscraper: 4 in r4c3,r8c1 (connected by r48c7) => r5c1<>4
Discontinuous Nice Loop: 1/9 r9c6 =2= r9c1 -2- r5c1 -3- r5c2 -4- r4c3 =4= r4c7 -4- r8c7 -8- r7c7 =8= r7c4 =2= r9c6 => r9c6<>1, r9c6<>9
Naked Single: r9c6=2
Locked Candidates Type 2 (Claiming): 9 in r9 => r7c12,r8c1<>9
Naked Pair: 1,7 in r37c2 => r1c2<>7, r9c2<>1
Hidden Rectangle: 4/9 in r4c36,r6c36 => r4c3<>4
Hidden Single: r4c7=4
Naked Single: r6c9=3
Naked Single: r8c7=8
Naked Single: r1c9=7
Naked Single: r7c7=6
Full House: r2c7=3
Naked Single: r1c8=8
Naked Single: r3c9=5
Full House: r2c8=6
Naked Single: r5c9=6
Naked Single: r1c6=4
Naked Single: r7c9=1
Full House: r9c9=4
Naked Single: r6c6=9
Naked Single: r7c2=7
Naked Single: r9c2=9
Naked Single: r4c6=7
Naked Single: r3c2=1
Naked Single: r1c2=3
Full House: r1c1=9
Full House: r5c2=4
Naked Single: r4c5=3
Naked Single: r4c8=2
Full House: r4c3=9
Full House: r5c8=7
Naked Single: r8c6=1
Full House: r2c6=8
Naked Single: r3c1=8
Naked Single: r3c3=7
Full House: r3c4=3
Naked Single: r5c4=2
Full House: r5c1=3
Full House: r6c3=2
Full House: r6c4=4
Naked Single: r9c5=5
Full House: r9c1=1
Naked Single: r2c4=7
Full House: r2c5=1
Full House: r8c5=7
Naked Single: r7c3=5
Naked Single: r8c4=9
Full House: r7c4=8
Naked Single: r2c3=4
Full House: r8c3=3
Full House: r2c1=5
Naked Single: r7c1=2
Full House: r7c8=9
Full House: r8c1=4
Full House: r8c8=5
|
sudoku_normal_extremely_hard_136
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..65..1...2......9....9.24.65.1....8..1......78..6.5......43....6......2..86..73.
|
936524187524718369817396245659137428341285976782469513275843691463971852198652734
|
. . 6 5 . . 1 . .
. 2 . . . . . . 9
. . . . 9 . 2 4 .
6 5 . 1 . . . . 8
. . 1 . . . . . .
7 8 . . 6 . 5 . .
. . . . 4 3 . . .
. 6 . . . . . . 2
. . 8 6 . . 7 3 .
|
9 3 6 5 2 4 1 8 7
5 2 4 7 1 8 3 6 9
8 1 7 3 9 6 2 4 5
6 5 9 1 3 7 4 2 8
3 4 1 2 8 5 9 7 6
7 8 2 4 6 9 5 1 3
2 7 5 8 4 3 6 9 1
4 6 3 9 7 1 8 5 2
1 9 8 6 5 2 7 3 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_9709_hard
|
936524187524718369817396245659137428341285976782469513275843691463971852198652734 #1 Extreme (36400) bf
Brute Force: r5c6=5
Brute Force: r5c5=8
Brute Force: r5c7=9
Locked Candidates Type 1 (Pointing): 9 in b4 => r78c3<>9
Empty Rectangle: 3 in b5 (r24c7) => r2c4<>3
Forcing Chain Contradiction in r4 => r4c6<>2
r4c6=2 r4c6<>9 r4c3=9 r4c3<>4
r4c6=2 r4c6<>4
r4c6=2 r56c4<>2 r7c4=2 r7c4<>8 r7c78=8 r8c7<>8 r8c7=4 r4c7<>4
Forcing Net Contradiction in r7c8 => r6c8=1
r6c8<>1 r6c8=2 (r5c8<>2) r4c8<>2 r4c8=7 (r5c8<>7) r5c9<>7 r5c4=7 (r5c4<>2) r5c4<>2 r5c1=2 (r4c3<>2) r6c3<>2 r7c3=2 r7c4<>2 r6c4=2 r6c8<>2 r6c8=1
Naked Pair: 3,4 in r4c7,r6c9 => r5c9<>3, r5c9<>4
Forcing Chain Contradiction in c3 => r4c5<>2
r4c5=2 r1c5<>2 r1c6=2 r1c6<>4 r1c12=4 r2c3<>4
r4c5=2 r6c46<>2 r6c3=2 r6c3<>9 r4c3=9 r4c3<>4
r4c5=2 r6c46<>2 r6c3=2 r6c3<>4
r4c5=2 r56c4<>2 r7c4=2 r7c4<>8 r7c78=8 r8c7<>8 r8c7=4 r8c3<>4
W-Wing: 7/3 in r1c9,r4c5 connected by 3 in r24c7 => r1c5<>7
Forcing Chain Contradiction in c3 => r4c6<>4
r4c6=4 r1c6<>4 r1c12=4 r2c3<>4
r4c6=4 r4c3<>4
r4c6=4 r4c7<>4 r6c9=4 r6c3<>4
r4c6=4 r4c7<>4 r8c7=4 r8c3<>4
W-Wing: 3/4 in r5c2,r6c9 connected by 4 in r4c37 => r6c3<>3
Forcing Chain Contradiction in r2 => r2c1<>1
r2c1=1 r2c1<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c9=4 r4c7<>4 r4c3=4 r2c3<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c9=4 r6c6<>4 r56c4=4 r2c4<>4
r2c1=1 r2c56<>1 r3c6=1 r3c6<>6 r2c6=6 r2c6<>4
Locked Candidates Type 1 (Pointing): 1 in b1 => r3c6<>1
Forcing Chain Contradiction in c5 => r3c6=6
r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r1c5<>3
r3c6<>6 r2c6=6 r2c6<>1 r2c5=1 r2c5<>3
r3c6<>6 r3c9=6 r5c9<>6 r5c9=7 r1c9<>7 r1c9=3 r6c9<>3 r6c4=3 r4c5<>3
Grouped AIC: 8 8- r1c8 -7- r45c8 =7= r5c9 =6= r7c9 -6- r7c7 -8 => r2c7,r78c8<>8
Discontinuous Nice Loop: 3 r3c2 -3- r5c2 -4- r4c3 =4= r4c7 -4- r8c7 -8- r7c7 =8= r7c4 -8- r3c4 =8= r3c1 =1= r3c2 => r3c2<>3
Sashimi Swordfish: 3 c257 r124 fr5c2 => r4c3<>3
Locked Candidates Type 1 (Pointing): 3 in b4 => r5c4<>3
Forcing Chain Contradiction in r6c6 => r1c5=2
r1c5<>2 r1c6=2 r6c6<>2
r1c5<>2 r1c5=3 r4c5<>3 r4c7=3 r4c7<>4 r6c9=4 r6c6<>4
r1c5<>2 r1c5=3 r4c5<>3 r4c5=7 r4c6<>7 r4c6=9 r6c6<>9
X-Wing: 3 c57 r24 => r2c13<>3
Discontinuous Nice Loop: 4 r8c3 -4- r8c7 =4= r4c7 =3= r4c5 -3- r2c5 =3= r3c4 -3- r3c3 =3= r8c3 => r8c3<>4
Skyscraper: 4 in r4c3,r8c1 (connected by r48c7) => r5c1<>4
Discontinuous Nice Loop: 1/9 r9c6 =2= r9c1 -2- r5c1 -3- r5c2 -4- r4c3 =4= r4c7 -4- r8c7 -8- r7c7 =8= r7c4 =2= r9c6 => r9c6<>1, r9c6<>9
Naked Single: r9c6=2
Locked Candidates Type 2 (Claiming): 9 in r9 => r7c12,r8c1<>9
Naked Pair: 1,7 in r37c2 => r1c2<>7, r9c2<>1
Hidden Rectangle: 4/9 in r4c36,r6c36 => r4c3<>4
Hidden Single: r4c7=4
Naked Single: r6c9=3
Naked Single: r8c7=8
Naked Single: r1c9=7
Naked Single: r7c7=6
Full House: r2c7=3
Naked Single: r1c8=8
Naked Single: r3c9=5
Full House: r2c8=6
Naked Single: r5c9=6
Naked Single: r1c6=4
Naked Single: r7c9=1
Full House: r9c9=4
Naked Single: r6c6=9
Naked Single: r7c2=7
Naked Single: r9c2=9
Naked Single: r4c6=7
Naked Single: r3c2=1
Naked Single: r1c2=3
Full House: r1c1=9
Full House: r5c2=4
Naked Single: r4c5=3
Naked Single: r4c8=2
Full House: r4c3=9
Full House: r5c8=7
Naked Single: r8c6=1
Full House: r2c6=8
Naked Single: r3c1=8
Naked Single: r3c3=7
Full House: r3c4=3
Naked Single: r5c4=2
Full House: r5c1=3
Full House: r6c3=2
Full House: r6c4=4
Naked Single: r9c5=5
Full House: r9c1=1
Naked Single: r2c4=7
Full House: r2c5=1
Full House: r8c5=7
Naked Single: r7c3=5
Naked Single: r8c4=9
Full House: r7c4=8
Naked Single: r2c3=4
Full House: r8c3=3
Full House: r2c1=5
Naked Single: r7c1=2
Full House: r7c8=9
Full House: r8c1=4
Full House: r8c8=5
|
sudoku_normal_hard_137
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.3.4...2.1...9.5....7..2.......8..1.8..2...59..69..8....13...7.7...6.1...4...7..5
|
935418726162793584487652391293586417874231659516974832651349278729865143348127965
|
. 3 . 4 . . . 2 .
1 . . . 9 . 5 . .
. . 7 . . 2 . . .
. . . . 8 . . 1 .
8 . . 2 . . . 5 9
. . 6 9 . . 8 . .
. . 1 3 . . . 7 .
7 . . . 6 . 1 . .
. 4 . . . 7 . . 5
|
9 3 5 4 1 8 7 2 6
1 6 2 7 9 3 5 8 4
4 8 7 6 5 2 3 9 1
2 9 3 5 8 6 4 1 7
8 7 4 2 3 1 6 5 9
5 1 6 9 7 4 8 3 2
6 5 1 3 4 9 2 7 8
7 2 9 8 6 5 1 4 3
3 4 8 1 2 7 9 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4848_hard
|
935418726162793584487652391293586417874231659516974832651349278729865143348127965 #1 Extreme (26792) bf
Brute Force: r5c4=2
Finned Swordfish: 2 r268 c239 fr6c1 => r4c23<>2
Forcing Chain Contradiction in r1 => r7c7<>6
r7c7=6 r7c2<>6 r79c1=6 r1c1<>6
r7c7=6 r5c7<>6 r5c6=6 r1c6<>6
r7c7=6 r1c7<>6
r7c7=6 r9c8<>6 r23c8=6 r1c9<>6
Forcing Net Contradiction in c7 => r3c8<>4
r3c8=4 (r6c8<>4 r6c8=3 r6c5<>3) (r2c8<>4) r2c9<>4 r2c3=4 r5c3<>4 r5c3=3 r5c5<>3 r3c5=3 r3c7<>3
r3c8=4 r6c8<>4 r6c8=3 r4c7<>3
r3c8=4 r6c8<>4 r6c8=3 r5c7<>3
r3c8=4 (r6c8<>4 r6c8=3 r6c1<>3) (r2c8<>4) r2c9<>4 r2c3=4 r5c3<>4 r5c3=3 r4c1<>3 r9c1=3 r9c7<>3
Forcing Net Contradiction in c7 => r5c7<>3
r5c7=3 r5c3<>3 r5c3=4 (r4c1<>4) r6c1<>4 r3c1=4 r3c7<>4
r5c7=3 r6c8<>3 r6c8=4 r4c7<>4
r5c7=3 r5c7<>4
r5c7=3 (r5c3<>3 r5c3=4 r5c5<>4) r6c8<>3 r6c8=4 r6c5<>4 r7c5=4 r7c7<>4
Forcing Chain Verity => r4c6<>3
r3c7=3 r3c5<>3 r2c6=3 r4c6<>3
r4c7=3 r4c6<>3
r9c7=3 r9c1<>3 r46c1=3 r5c3<>3 r5c56=3 r4c6<>3
Grouped AIC: 4 4- r5c3 -3- r4c13 =3= r4c79 -3- r6c8 -4 => r5c7,r6c1<>4
Sashimi Swordfish: 4 c157 r347 fr5c5 fr6c5 => r4c6<>4
Grouped Discontinuous Nice Loop: 3 r6c1 -3- r6c8 -4- r4c79 =4= r4c13 -4- r5c3 -3- r6c1 => r6c1<>3
Forcing Chain Contradiction in r6c9 => r3c1<>9
r3c1=9 r3c1<>4 r4c1=4 r4c1<>2 r4c79=2 r6c9<>2
r3c1=9 r3c1<>4 r4c1=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c9<>3
r3c1=9 r3c1<>4 r4c1=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c8<>3 r6c8=4 r6c9<>4
r3c1=9 r1c13<>9 r1c7=9 r1c7<>7 r45c7=7 r6c9<>7
Forcing Chain Contradiction in r7c7 => r6c9<>3
r6c9=3 r6c8<>3 r6c8=4 r4c79<>4 r4c13=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c9<>3
Empty Rectangle: 3 in b6 (r49c1) => r9c8<>3
Forcing Chain Contradiction in r7c7 => r6c9<>4
r6c9=4 r6c8<>4 r6c8=3 r4c79<>3 r4c13=3 r5c3<>3 r5c3=4 r4c13<>4 r4c79=4 r6c9<>4
Almost Locked Set XY-Wing: A=r123c9,r23c8,r3c7 {1346789}, B=r456c2,r6c1 {12579}, C=r6c9 {27}, X,Y=2,7, Z=9 => r3c2<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r1c7<>9
Naked Pair: 6,7 in r15c7 => r349c7<>6, r4c7<>7
Forcing Chain Contradiction in r4c4 => r1c9<>7
r1c9=7 r1c7<>7 r1c7=6 r5c7<>6 r5c6=6 r4c6<>6 r4c6=5 r4c4<>5
r1c9=7 r1c7<>7 r1c7=6 r5c7<>6 r5c6=6 r4c4<>6
r1c9=7 r1c5<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c1<>5
r4c1=5 r4c4<>5
r4c1=5 r4c6<>5 r4c6=6 r4c4<>6
r4c1=5 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c2<>5
r4c2=5 r4c4<>5
r4c2=5 r4c6<>5 r4c6=6 r4c4<>6
r4c2=5 r6c1<>5 r6c1=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c3<>5
r4c3=5 r4c4<>5
r4c3=5 r4c6<>5 r4c6=6 r4c4<>6
r4c3=5 r6c1<>5 r6c1=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Locked Candidates Type 1 (Pointing): 5 in b4 => r6c56<>5
Almost Locked Set XY-Wing: A=r13467c1 {234569}, B=r235678c2 {1256789}, C=r4c23,r5c3 {3479}, X,Y=3,7, Z=9 => r9c1<>9
Forcing Chain Verity => r3c1<>5
r2c3=2 r2c3<>4 r3c1=4 r3c1<>5
r8c3=2 r8c3<>5 r1c3=5 r3c1<>5
r9c3=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r3c1<>5
Forcing Chain Contradiction in r1c5 => r9c1<>2
r9c1=2 r9c5<>2 r9c5=1 r1c5<>1
r9c1=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r1c5<>5
r9c1=2 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Chain Contradiction in r1c5 => r9c3<>2
r9c3=2 r9c5<>2 r9c5=1 r1c5<>1
r9c3=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r1c5<>5
r9c3=2 r8c23<>2 r8c9=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Chain Contradiction in r1c5 => r3c9<>4
r3c9=4 r3c9<>1 r1c9=1 r1c5<>1
r3c9=4 r3c1<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 r1c5<>5
r3c9=4 r3c1<>4 r4c1=4 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Net Contradiction in r3c4 => r3c1=4
r3c1<>4 (r3c1=6 r9c1<>6 r9c1=3 r9c3<>3) r4c1=4 (r4c3<>4) r5c3<>4 r5c3=3 r4c3<>3 r4c3=9 r9c3<>9 r9c3=8 r9c4<>8 r9c4=1 r3c4<>1
r3c1<>4 r3c7=4 (r3c7<>3 r4c7=3 r4c7<>2 r4c9=2 r6c9<>2 r6c1=2 r6c1<>5) (r2c8<>4) r2c9<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 (r1c5<>5) r1c1<>5 r7c1=5 r7c5<>5 r3c5=5 r3c4<>5
r3c1<>4 r3c1=6 r3c4<>6
r3c1<>4 (r3c1=6 r3c2<>6) r3c7=4 (r2c8<>4) r2c9<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 r3c2<>5 r3c2=8 r3c4<>8
Finned Swordfish: 4 r268 c689 fr6c5 => r5c6<>4
Forcing Chain Contradiction in c5 => r6c5<>3
r6c5=3 r6c8<>3 r6c8=4 r2c8<>4 r2c9=4 r2c9<>7 r2c4=7 r1c5<>7
r6c5=3 r6c8<>3 r6c8=4 r6c56<>4 r5c5=4 r5c5<>7
r6c5=3 r6c5<>7
2-String Kite: 3 in r3c5,r6c8 (connected by r5c5,r6c6) => r3c8<>3
Forcing Chain Verity => r4c9<>3
r3c7=3 r3c5<>3 r5c5=3 r5c3<>3 r4c13=3 r4c9<>3
r4c7=3 r4c9<>3
r9c7=3 r9c1<>3 r4c1=3 r4c9<>3
Forcing Chain Contradiction in r2 => r8c8<>3
r8c8=3 r6c8<>3 r6c6=3 r2c6<>3
r8c8=3 r2c8<>3
r8c8=3 r6c8<>3 r6c8=4 r2c8<>4 r2c9=4 r2c9<>3
Forcing Chain Contradiction in r1c5 => r3c9<>3
r3c9=3 r3c9<>1 r1c9=1 r1c5<>1
r3c9=3 r8c9<>3 r8c3=3 r8c3<>5 r1c3=5 r1c5<>5
r3c9=3 r8c9<>3 r8c3=3 r9c1<>3 r9c1=6 r9c8<>6 r23c8=6 r1c7<>6 r1c7=7 r1c5<>7
Forcing Chain Contradiction in r7 => r7c2<>2
r7c2=2 r7c2<>8
r7c2=2 r8c23<>2 r8c9=2 r79c7<>2 r4c7=2 r4c7<>4 r7c7=4 r7c56<>4 r8c6=4 r8c6<>9 r7c6=9 r7c6<>8
r7c2=2 r8c23<>2 r8c9=2 r8c9<>3 r8c3=3 r9c1<>3 r9c1=6 r9c8<>6 r7c9=6 r7c9<>8
Forcing Chain Contradiction in r3 => r8c9<>8
r8c9=8 r8c9<>3 r8c3=3 r8c3<>5 r1c3=5 r3c2<>5
r8c9=8 r8c4<>8 r8c4=5 r3c4<>5
r8c9=8 r8c9<>3 r2c9=3 r2c6<>3 r3c5=3 r3c5<>5
Forcing Net Contradiction in c1 => r1c7=7
r1c7<>7 r1c7=6 r5c7<>6 r5c7=7 r6c9<>7 r6c9=2 r6c1<>2 r6c1=5
r1c7<>7 (r1c5=7 r2c4<>7 r2c9=7 r2c9<>4 r2c8=4 r8c8<>4) (r1c5=7 r2c4<>7 r2c9=7 r2c9<>4) r1c7=6 (r5c7<>6 r5c7=7 r6c9<>7 r6c9=2 r6c1<>2 r6c1=5 r1c1<>5 r1c3=5 r8c3<>5) (r5c7<>6 r5c6=6 r4c6<>6 r4c9=6 r4c9<>4) (r2c8<>6) r3c8<>6 r9c8=6 (r9c8<>8 r8c8=8 r8c4<>8 r8c4=5 r8c2<>5) r9c1<>6 r9c1=3 r8c3<>3 r8c9=3 r8c9<>4 r7c9=4 (r7c9<>8) r8c9<>4 r8c6=4 r8c6<>9 r7c6=9 r7c6<>8 r7c2=8 r7c2<>5 r7c1=5
Naked Single: r5c7=6
Hidden Single: r2c4=7
AIC: 1 1- r1c5 -5- r1c3 =5= r8c3 -5- r8c4 -8- r9c4 -1 => r3c4,r9c5<>1
Naked Single: r9c5=2
Hidden Single: r9c4=1
Naked Pair: 3,9 in r39c7 => r4c7<>3, r7c7<>9
Hidden Single: r6c8=3
Locked Candidates Type 1 (Pointing): 3 in b5 => r5c3<>3
Naked Single: r5c3=4
W-Wing: 9/3 in r4c3,r9c7 connected by 3 in r8c39 => r9c3<>9
Locked Candidates Type 2 (Claiming): 9 in r9 => r8c8<>9
XY-Wing: 5/8/4 in r7c5,r8c48 => r7c79,r8c6<>4
Naked Single: r7c7=2
Naked Single: r4c7=4
Locked Candidates Type 2 (Claiming): 2 in c1 => r6c2<>2
Naked Triple: 1,6,8 in r137c9 => r2c9<>6, r2c9<>8
Hidden Rectangle: 2/8 in r2c23,r8c23 => r8c2<>8
Continuous Nice Loop: 1/3/7/9 3= r4c1 =2= r4c9 =7= r4c2 -7- r5c2 =7= r5c5 =3= r3c5 -3- r3c7 =3= r9c7 -3- r9c1 =3= r4c1 =2 => r5c5<>1, r9c3<>3, r6c2<>7, r4c1<>9
Naked Single: r9c3=8
Naked Single: r2c3=2
Hidden Single: r8c2=2
X-Wing: 8 r17 c69 => r28c6,r3c9<>8
XY-Chain: 1 1- r1c5 -5- r1c3 -9- r4c3 -3- r4c1 -2- r6c1 -5- r6c2 -1- r5c2 -7- r5c5 -3- r5c6 -1 => r1c6,r6c5<>1
XY-Chain: 2 2- r4c1 -3- r9c1 -6- r9c8 -9- r9c7 -3- r8c9 -4- r8c8 -8- r8c4 -5- r7c5 -4- r6c5 -7- r6c9 -2 => r4c9,r6c1<>2
Naked Single: r4c9=7
Full House: r6c9=2
Naked Single: r6c1=5
Naked Single: r4c2=9
Naked Single: r6c2=1
Naked Single: r4c3=3
Naked Single: r5c2=7
Full House: r4c1=2
Naked Single: r6c6=4
Full House: r6c5=7
Naked Single: r5c5=3
Full House: r5c6=1
Hidden Single: r9c1=3
Naked Single: r9c7=9
Full House: r3c7=3
Full House: r9c8=6
Naked Single: r2c9=4
Naked Single: r7c9=8
Naked Single: r2c8=8
Naked Single: r8c9=3
Full House: r8c8=4
Full House: r3c8=9
Naked Single: r2c2=6
Full House: r2c6=3
Naked Single: r1c1=9
Full House: r7c1=6
Naked Single: r7c2=5
Full House: r3c2=8
Full House: r1c3=5
Full House: r8c3=9
Naked Single: r7c5=4
Full House: r7c6=9
Naked Single: r1c5=1
Full House: r3c5=5
Naked Single: r8c6=5
Full House: r8c4=8
Naked Single: r1c9=6
Full House: r1c6=8
Full House: r3c4=6
Full House: r4c6=6
Full House: r3c9=1
Full House: r4c4=5
|
sudoku_normal_extremely_hard_137
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.3.4...2.1...9.5....7..2.......8..1.8......59..69..8....13...7.7...6.1...4...7..5
|
935418726162793584487652391293586417874231659516974832651349278729865143348127965
|
. 3 . 4 . . . 2 .
1 . . . 9 . 5 . .
. . 7 . . 2 . . .
. . . . 8 . . 1 .
8 . . . . . . 5 9
. . 6 9 . . 8 . .
. . 1 3 . . . 7 .
7 . . . 6 . 1 . .
. 4 . . . 7 . . 5
|
9 3 5 4 1 8 7 2 6
1 6 2 7 9 3 5 8 4
4 8 7 6 5 2 3 9 1
2 9 3 5 8 6 4 1 7
8 7 4 2 3 1 6 5 9
5 1 6 9 7 4 8 3 2
6 5 1 3 4 9 2 7 8
7 2 9 8 6 5 1 4 3
3 4 8 1 2 7 9 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4848_hard
|
935418726162793584487652391293586417874231659516974832651349278729865143348127965 #1 Extreme (26792) bf
Brute Force: r5c4=2
Finned Swordfish: 2 r268 c239 fr6c1 => r4c23<>2
Forcing Chain Contradiction in r1 => r7c7<>6
r7c7=6 r7c2<>6 r79c1=6 r1c1<>6
r7c7=6 r5c7<>6 r5c6=6 r1c6<>6
r7c7=6 r1c7<>6
r7c7=6 r9c8<>6 r23c8=6 r1c9<>6
Forcing Net Contradiction in c7 => r3c8<>4
r3c8=4 (r6c8<>4 r6c8=3 r6c5<>3) (r2c8<>4) r2c9<>4 r2c3=4 r5c3<>4 r5c3=3 r5c5<>3 r3c5=3 r3c7<>3
r3c8=4 r6c8<>4 r6c8=3 r4c7<>3
r3c8=4 r6c8<>4 r6c8=3 r5c7<>3
r3c8=4 (r6c8<>4 r6c8=3 r6c1<>3) (r2c8<>4) r2c9<>4 r2c3=4 r5c3<>4 r5c3=3 r4c1<>3 r9c1=3 r9c7<>3
Forcing Net Contradiction in c7 => r5c7<>3
r5c7=3 r5c3<>3 r5c3=4 (r4c1<>4) r6c1<>4 r3c1=4 r3c7<>4
r5c7=3 r6c8<>3 r6c8=4 r4c7<>4
r5c7=3 r5c7<>4
r5c7=3 (r5c3<>3 r5c3=4 r5c5<>4) r6c8<>3 r6c8=4 r6c5<>4 r7c5=4 r7c7<>4
Forcing Chain Verity => r4c6<>3
r3c7=3 r3c5<>3 r2c6=3 r4c6<>3
r4c7=3 r4c6<>3
r9c7=3 r9c1<>3 r46c1=3 r5c3<>3 r5c56=3 r4c6<>3
Grouped AIC: 4 4- r5c3 -3- r4c13 =3= r4c79 -3- r6c8 -4 => r5c7,r6c1<>4
Sashimi Swordfish: 4 c157 r347 fr5c5 fr6c5 => r4c6<>4
Grouped Discontinuous Nice Loop: 3 r6c1 -3- r6c8 -4- r4c79 =4= r4c13 -4- r5c3 -3- r6c1 => r6c1<>3
Forcing Chain Contradiction in r6c9 => r3c1<>9
r3c1=9 r3c1<>4 r4c1=4 r4c1<>2 r4c79=2 r6c9<>2
r3c1=9 r3c1<>4 r4c1=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c9<>3
r3c1=9 r3c1<>4 r4c1=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c8<>3 r6c8=4 r6c9<>4
r3c1=9 r1c13<>9 r1c7=9 r1c7<>7 r45c7=7 r6c9<>7
Forcing Chain Contradiction in r7c7 => r6c9<>3
r6c9=3 r6c8<>3 r6c8=4 r4c79<>4 r4c13=4 r5c3<>4 r5c3=3 r4c13<>3 r4c79=3 r6c9<>3
Empty Rectangle: 3 in b6 (r49c1) => r9c8<>3
Forcing Chain Contradiction in r7c7 => r6c9<>4
r6c9=4 r6c8<>4 r6c8=3 r4c79<>3 r4c13=3 r5c3<>3 r5c3=4 r4c13<>4 r4c79=4 r6c9<>4
Almost Locked Set XY-Wing: A=r123c9,r23c8,r3c7 {1346789}, B=r456c2,r6c1 {12579}, C=r6c9 {27}, X,Y=2,7, Z=9 => r3c2<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r1c7<>9
Naked Pair: 6,7 in r15c7 => r349c7<>6, r4c7<>7
Forcing Chain Contradiction in r4c4 => r1c9<>7
r1c9=7 r1c7<>7 r1c7=6 r5c7<>6 r5c6=6 r4c6<>6 r4c6=5 r4c4<>5
r1c9=7 r1c7<>7 r1c7=6 r5c7<>6 r5c6=6 r4c4<>6
r1c9=7 r1c5<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c1<>5
r4c1=5 r4c4<>5
r4c1=5 r4c6<>5 r4c6=6 r4c4<>6
r4c1=5 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c2<>5
r4c2=5 r4c4<>5
r4c2=5 r4c6<>5 r4c6=6 r4c4<>6
r4c2=5 r6c1<>5 r6c1=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Forcing Chain Contradiction in r4c4 => r4c3<>5
r4c3=5 r4c4<>5
r4c3=5 r4c6<>5 r4c6=6 r4c4<>6
r4c3=5 r6c1<>5 r6c1=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r4c4<>7
Locked Candidates Type 1 (Pointing): 5 in b4 => r6c56<>5
Almost Locked Set XY-Wing: A=r13467c1 {234569}, B=r235678c2 {1256789}, C=r4c23,r5c3 {3479}, X,Y=3,7, Z=9 => r9c1<>9
Forcing Chain Verity => r3c1<>5
r2c3=2 r2c3<>4 r3c1=4 r3c1<>5
r8c3=2 r8c3<>5 r1c3=5 r3c1<>5
r9c3=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r3c1<>5
Forcing Chain Contradiction in r1c5 => r9c1<>2
r9c1=2 r9c5<>2 r9c5=1 r1c5<>1
r9c1=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r1c5<>5
r9c1=2 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Chain Contradiction in r1c5 => r9c3<>2
r9c3=2 r9c5<>2 r9c5=1 r1c5<>1
r9c3=2 r9c5<>2 r9c5=1 r9c4<>1 r9c4=8 r8c4<>8 r8c4=5 r8c3<>5 r1c3=5 r1c5<>5
r9c3=2 r8c23<>2 r8c9=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Chain Contradiction in r1c5 => r3c9<>4
r3c9=4 r3c9<>1 r1c9=1 r1c5<>1
r3c9=4 r3c1<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 r1c5<>5
r3c9=4 r3c1<>4 r4c1=4 r4c1<>2 r4c79=2 r6c9<>2 r6c9=7 r2c9<>7 r2c4=7 r1c5<>7
Forcing Net Contradiction in r3c4 => r3c1=4
r3c1<>4 (r3c1=6 r9c1<>6 r9c1=3 r9c3<>3) r4c1=4 (r4c3<>4) r5c3<>4 r5c3=3 r4c3<>3 r4c3=9 r9c3<>9 r9c3=8 r9c4<>8 r9c4=1 r3c4<>1
r3c1<>4 r3c7=4 (r3c7<>3 r4c7=3 r4c7<>2 r4c9=2 r6c9<>2 r6c1=2 r6c1<>5) (r2c8<>4) r2c9<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 (r1c5<>5) r1c1<>5 r7c1=5 r7c5<>5 r3c5=5 r3c4<>5
r3c1<>4 r3c1=6 r3c4<>6
r3c1<>4 (r3c1=6 r3c2<>6) r3c7=4 (r2c8<>4) r2c9<>4 r2c3=4 r2c3<>2 r8c3=2 r8c3<>5 r1c3=5 r3c2<>5 r3c2=8 r3c4<>8
Finned Swordfish: 4 r268 c689 fr6c5 => r5c6<>4
Forcing Chain Contradiction in c5 => r6c5<>3
r6c5=3 r6c8<>3 r6c8=4 r2c8<>4 r2c9=4 r2c9<>7 r2c4=7 r1c5<>7
r6c5=3 r6c8<>3 r6c8=4 r6c56<>4 r5c5=4 r5c5<>7
r6c5=3 r6c5<>7
2-String Kite: 3 in r3c5,r6c8 (connected by r5c5,r6c6) => r3c8<>3
Forcing Chain Verity => r4c9<>3
r3c7=3 r3c5<>3 r5c5=3 r5c3<>3 r4c13=3 r4c9<>3
r4c7=3 r4c9<>3
r9c7=3 r9c1<>3 r4c1=3 r4c9<>3
Forcing Chain Contradiction in r2 => r8c8<>3
r8c8=3 r6c8<>3 r6c6=3 r2c6<>3
r8c8=3 r2c8<>3
r8c8=3 r6c8<>3 r6c8=4 r2c8<>4 r2c9=4 r2c9<>3
Forcing Chain Contradiction in r1c5 => r3c9<>3
r3c9=3 r3c9<>1 r1c9=1 r1c5<>1
r3c9=3 r8c9<>3 r8c3=3 r8c3<>5 r1c3=5 r1c5<>5
r3c9=3 r8c9<>3 r8c3=3 r9c1<>3 r9c1=6 r9c8<>6 r23c8=6 r1c7<>6 r1c7=7 r1c5<>7
Forcing Chain Contradiction in r7 => r7c2<>2
r7c2=2 r7c2<>8
r7c2=2 r8c23<>2 r8c9=2 r79c7<>2 r4c7=2 r4c7<>4 r7c7=4 r7c56<>4 r8c6=4 r8c6<>9 r7c6=9 r7c6<>8
r7c2=2 r8c23<>2 r8c9=2 r8c9<>3 r8c3=3 r9c1<>3 r9c1=6 r9c8<>6 r7c9=6 r7c9<>8
Forcing Chain Contradiction in r3 => r8c9<>8
r8c9=8 r8c9<>3 r8c3=3 r8c3<>5 r1c3=5 r3c2<>5
r8c9=8 r8c4<>8 r8c4=5 r3c4<>5
r8c9=8 r8c9<>3 r2c9=3 r2c6<>3 r3c5=3 r3c5<>5
Forcing Net Contradiction in c1 => r1c7=7
r1c7<>7 r1c7=6 r5c7<>6 r5c7=7 r6c9<>7 r6c9=2 r6c1<>2 r6c1=5
r1c7<>7 (r1c5=7 r2c4<>7 r2c9=7 r2c9<>4 r2c8=4 r8c8<>4) (r1c5=7 r2c4<>7 r2c9=7 r2c9<>4) r1c7=6 (r5c7<>6 r5c7=7 r6c9<>7 r6c9=2 r6c1<>2 r6c1=5 r1c1<>5 r1c3=5 r8c3<>5) (r5c7<>6 r5c6=6 r4c6<>6 r4c9=6 r4c9<>4) (r2c8<>6) r3c8<>6 r9c8=6 (r9c8<>8 r8c8=8 r8c4<>8 r8c4=5 r8c2<>5) r9c1<>6 r9c1=3 r8c3<>3 r8c9=3 r8c9<>4 r7c9=4 (r7c9<>8) r8c9<>4 r8c6=4 r8c6<>9 r7c6=9 r7c6<>8 r7c2=8 r7c2<>5 r7c1=5
Naked Single: r5c7=6
Hidden Single: r2c4=7
AIC: 1 1- r1c5 -5- r1c3 =5= r8c3 -5- r8c4 -8- r9c4 -1 => r3c4,r9c5<>1
Naked Single: r9c5=2
Hidden Single: r9c4=1
Naked Pair: 3,9 in r39c7 => r4c7<>3, r7c7<>9
Hidden Single: r6c8=3
Locked Candidates Type 1 (Pointing): 3 in b5 => r5c3<>3
Naked Single: r5c3=4
W-Wing: 9/3 in r4c3,r9c7 connected by 3 in r8c39 => r9c3<>9
Locked Candidates Type 2 (Claiming): 9 in r9 => r8c8<>9
XY-Wing: 5/8/4 in r7c5,r8c48 => r7c79,r8c6<>4
Naked Single: r7c7=2
Naked Single: r4c7=4
Locked Candidates Type 2 (Claiming): 2 in c1 => r6c2<>2
Naked Triple: 1,6,8 in r137c9 => r2c9<>6, r2c9<>8
Hidden Rectangle: 2/8 in r2c23,r8c23 => r8c2<>8
Continuous Nice Loop: 1/3/7/9 3= r4c1 =2= r4c9 =7= r4c2 -7- r5c2 =7= r5c5 =3= r3c5 -3- r3c7 =3= r9c7 -3- r9c1 =3= r4c1 =2 => r5c5<>1, r9c3<>3, r6c2<>7, r4c1<>9
Naked Single: r9c3=8
Naked Single: r2c3=2
Hidden Single: r8c2=2
X-Wing: 8 r17 c69 => r28c6,r3c9<>8
XY-Chain: 1 1- r1c5 -5- r1c3 -9- r4c3 -3- r4c1 -2- r6c1 -5- r6c2 -1- r5c2 -7- r5c5 -3- r5c6 -1 => r1c6,r6c5<>1
XY-Chain: 2 2- r4c1 -3- r9c1 -6- r9c8 -9- r9c7 -3- r8c9 -4- r8c8 -8- r8c4 -5- r7c5 -4- r6c5 -7- r6c9 -2 => r4c9,r6c1<>2
Naked Single: r4c9=7
Full House: r6c9=2
Naked Single: r6c1=5
Naked Single: r4c2=9
Naked Single: r6c2=1
Naked Single: r4c3=3
Naked Single: r5c2=7
Full House: r4c1=2
Naked Single: r6c6=4
Full House: r6c5=7
Naked Single: r5c5=3
Full House: r5c6=1
Hidden Single: r9c1=3
Naked Single: r9c7=9
Full House: r3c7=3
Full House: r9c8=6
Naked Single: r2c9=4
Naked Single: r7c9=8
Naked Single: r2c8=8
Naked Single: r8c9=3
Full House: r8c8=4
Full House: r3c8=9
Naked Single: r2c2=6
Full House: r2c6=3
Naked Single: r1c1=9
Full House: r7c1=6
Naked Single: r7c2=5
Full House: r3c2=8
Full House: r1c3=5
Full House: r8c3=9
Naked Single: r7c5=4
Full House: r7c6=9
Naked Single: r1c5=1
Full House: r3c5=5
Naked Single: r8c6=5
Full House: r8c4=8
Naked Single: r1c9=6
Full House: r1c6=8
Full House: r3c4=6
Full House: r4c6=6
Full House: r3c9=1
Full House: r4c4=5
|
sudoku_normal_hard_138
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
9....471..719....3.5.........32..4..7...4923..2.....5.6..79.....8.46.9.......8...
|
968354712271986543354172896893215467715649238426837159642791385587463921139528674
|
9 . . . . 4 7 1 .
. 7 1 9 . . . . 3
. 5 . . . . . . .
. . 3 2 . . 4 . .
7 . . . 4 9 2 3 .
. 2 . . . . . 5 .
6 . . 7 9 . . . .
. 8 . 4 6 . 9 . .
. . . . . 8 . . .
|
9 6 8 3 5 4 7 1 2
2 7 1 9 8 6 5 4 3
3 5 4 1 7 2 8 9 6
8 9 3 2 1 5 4 6 7
7 1 5 6 4 9 2 3 8
4 2 6 8 3 7 1 5 9
6 4 2 7 9 1 3 8 5
5 8 7 4 6 3 9 2 1
1 3 9 5 2 8 6 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3325_hard
|
968354712271986543354172896893215467715649238426837159642791385587463921139528674 #1 Extreme (34122) bf
Brute Force: r5c8=3
Brute Force: r5c5=4
Locked Candidates Type 2 (Claiming): 4 in c2 => r79c3,r9c1<>4
XYZ-Wing: 2/5/7 in r78c3,r8c8 => r8c1<>2
Discontinuous Nice Loop: 2 r2c8 -2- r8c8 -7- r8c3 =7= r9c3 =9= r6c3 =4= r6c1 -4- r2c1 =4= r2c8 => r2c8<>2
Discontinuous Nice Loop: 4 r3c8 -4- r3c3 =4= r6c3 =9= r6c9 -9- r3c9 =9= r3c8 => r3c8<>4
Forcing Chain Contradiction in c9 => r9c9<>2
r9c9=2 r789c8<>2 r3c8=2 r3c8<>9 r3c9=9 r3c9<>4
r9c9=2 r8c8<>2 r8c8=7 r8c3<>7 r9c3=7 r9c3<>9 r9c2=9 r9c2<>4 r7c2=4 r7c9<>4
r9c9=2 r9c9<>4
Forcing Net Contradiction in c1 => r3c3<>2
r3c3=2 r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 (r4c5<>5) r4c6<>5 r4c1=5 r4c1<>1
r3c3=2 (r7c3<>2 r7c3=5 r8c3<>5 r8c3=7 r8c9<>7) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r4c6<>5) (r7c3<>2 r7c3=5 r7c6<>5) (r3c8<>2) r3c9<>2 r1c9=2 (r8c9<>2) r1c9<>5 r2c7=5 r2c6<>5 r8c6=5 r8c9<>5 r8c9=1 (r7c7<>1) r9c7<>1 r6c7=1 r6c1<>1
r3c3=2 (r7c3<>2 r7c3=5 r8c3<>5 r8c3=7 r8c9<>7) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r4c6<>5) (r7c3<>2 r7c3=5 r7c6<>5) (r3c8<>2) r3c9<>2 r1c9=2 (r8c9<>2) r1c9<>5 r2c7=5 r2c6<>5 r8c6=5 r8c9<>5 r8c9=1 r8c1<>1
r3c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>1
Forcing Net Contradiction in b8 => r2c8<>8
r2c8=8 (r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r1c9<>5 r1c9=2 r1c3<>2) r2c8<>4 r2c1=4 r6c1<>4 r6c3=4 r6c3<>9 r9c3=9 (r9c3<>2) r9c3<>7 r8c3=7 r8c3<>2 r7c3=2 r7c6<>2
r2c8=8 r2c8<>4 r2c1=4 r6c1<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
r2c8=8 (r2c5<>8) (r2c7<>8) r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r2c5<>5 r2c5=2 r9c5<>2
Forcing Net Contradiction in c6 => r3c3<>8
r3c3=8 r3c7<>8 r3c7=6 (r2c7<>6) r2c8<>6 r2c6=6 r2c6<>2
r3c3=8 (r3c7<>8 r3c7=6 r3c9<>6) (r3c9<>8) (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r3c9<>4) r3c3<>4 r6c3=4 r6c3<>9 r6c9=9 r3c9<>9 r3c9=2 r3c6<>2
r3c3=8 (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r2c1<>4 r2c1=2 r1c3<>2) r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 (r9c3<>2) r9c3<>7 r8c3=7 r8c3<>2 r7c3=2 r7c6<>2
r3c3=8 r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
Forcing Net Verity => r3c8<>2
r1c9=2 r3c8<>2
r3c9=2 r3c8<>2
r7c9=2 (r1c9<>2) (r7c3<>2 r7c3=5 r8c3<>5) r8c8<>2 r8c8=7 r8c3<>7 r8c3=2 r1c3<>2 r1c5=2 (r2c5<>2) r2c5<>2 r2c6=2 (r2c1<>2) (r1c5<>2) r3c5<>2 r9c5=2 r9c1<>2 r3c1=2 r3c8<>2
r8c9=2 (r1c9<>2) (r8c3<>2) r8c8<>2 r8c8=7 r8c3<>7 r8c3=5 r7c3<>5 r7c3=2 r1c3<>2 r1c5=2 (r2c5<>2) r2c5<>2 r2c6=2 (r2c1<>2) (r1c5<>2) r3c5<>2 r9c5=2 r9c1<>2 r3c1=2 r3c8<>2
Locked Candidates Type 1 (Pointing): 2 in b3 => r78c9<>2
Forcing Net Verity => r3c5<>2
r2c1=8 r2c1<>2 r2c56=2 r3c5<>2
r3c1=8 (r3c9<>8) (r3c8<>8) r3c7<>8 r3c7=6 (r3c9<>6) (r2c8<>6 r2c8=4 r3c9<>4) r3c8<>6 r3c8=9 r3c9<>9 r3c9=2 r3c5<>2
r4c1=8 r4c1<>5 r5c3=5 (r8c3<>5) r7c3<>5 r7c3=2 (r9c1<>2) (r9c3<>2) r8c3<>2 r8c3=7 r8c8<>7 r8c8=2 r9c8<>2 r9c5=2 r3c5<>2
r6c1=8 (r5c3<>8) r6c1<>4 r6c3=4 (r6c3<>9 r9c3=9 r9c3<>2) r3c3<>4 r3c3=6 r5c3<>6 r5c3=5 (r8c3<>5) r7c3<>5 r7c3=2 (r9c1<>2) r8c3<>2 r8c3=7 r8c8<>7 r8c8=2 r9c8<>2 r9c5=2 r3c5<>2
Forcing Net Contradiction in c9 => r3c8<>8
r3c8=8 (r2c7<>8) r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r1c9<>5
r3c8=8 (r7c8<>8) r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r7c8<>4 r7c8=2 r7c3<>2 r7c3=5 r7c9<>5
r3c8=8 (r3c8<>9 r3c9=9 r3c9<>2 r1c9=2 r1c3<>2 r23c1=2 r9c1<>2) (r3c8<>9 r4c8=9 r4c8<>6 r9c8=6 r9c8<>2) (r7c8<>8) r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r7c8<>4 r7c8=2 (r7c3<>2 r7c3=5 r7c6<>5) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r9c4<>5) (r7c3<>2 r7c3=5 r8c3<>5) r8c8<>2 r8c8=7 r8c3<>7 r8c3=2 r9c3<>2 r9c5=2 r9c5<>5 r8c6=5 r8c9<>5
r3c8=8 (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r9c8<>4) r3c8<>9 r3c9=9 r6c9<>9 r6c3=9 r9c3<>9 r9c2=9 r9c2<>4 r9c9=4 r9c9<>5
Forcing Net Verity => r6c9<>6
r1c4=6 (r1c2<>6) r1c3<>6 r3c3=6 r3c3<>4 r6c3=4 r6c3<>9 r6c9=9 r6c9<>6
r3c4=6 (r3c3<>6 r3c3=4 r3c1<>4) (r3c7<>6 r3c7=8 r3c1<>8) (r3c9<>6) (r3c3<>6 r3c3=4 r3c9<>4) (r3c7<>6 r3c7=8 r3c9<>8) r3c8<>6 r3c8=9 r3c9<>9 r3c9=2 r3c1<>2 r3c1=3 r1c2<>3 r1c2=6 (r4c2<>6) r5c2<>6 r5c2=1 r4c2<>1 r4c2=9 r6c3<>9 r6c9=9 r6c9<>6
r5c4=6 r5c4<>5 r5c3=5 (r9c3<>5) (r8c3<>5) r7c3<>5 r7c3=2 (r9c3<>2) r8c3<>2 r8c3=7 r9c3<>7 r9c3=9 r6c3<>9 r6c9=9 r6c9<>6
r6c4=6 r6c9<>6
Forcing Net Contradiction in r9c9 => r7c7<>5
r7c7=5 (r7c3<>5 r7c3=2 r9c1<>2) (r7c3<>5 r7c3=2 r9c3<>2) (r7c3<>5 r7c3=2 r1c3<>2) (r7c9<>5) (r8c9<>5) r9c9<>5 r1c9=5 r1c9<>2 r1c5=2 r9c5<>2 r9c8=2 (r9c8<>4) (r9c8<>7) r8c8<>2 r8c8=7 r9c9<>7 r9c3=7 r9c3<>9 r9c2=9 r9c2<>4 r9c9=4
r7c7=5 (r7c7<>3 r9c7=3 r9c7<>6) (r7c3<>5 r7c3=2 r9c1<>2) (r7c3<>5 r7c3=2 r9c3<>2) (r7c3<>5 r7c3=2 r1c3<>2) (r7c9<>5) (r8c9<>5) r9c9<>5 r1c9=5 r1c9<>2 r1c5=2 r9c5<>2 r9c8=2 r9c8<>6 r9c9=6
Empty Rectangle: 5 in b8 (r29c7) => r2c6<>5
Forcing Chain Contradiction in r1 => r2c7<>6
r2c7=6 r2c6<>6 r2c6=2 r12c5<>2 r9c5=2 r9c1<>2 r23c1=2 r1c3<>2
r2c7=6 r2c6<>6 r2c6=2 r1c5<>2
r2c7=6 r2c7<>5 r1c9=5 r1c9<>2
AIC: 6 6- r2c6 =6= r2c8 =4= r2c1 -4- r3c3 -6 => r3c46<>6
Forcing Net Contradiction in c1 => r1c3<>2
r1c3=2 r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 (r4c5<>5) r4c6<>5 r4c1=5 r4c1<>1
r1c3=2 r7c3<>2 r7c3=5 (r8c3<>5 r8c3=7 r8c9<>7) (r7c6<>5) r5c3<>5 r5c4=5 r4c6<>5 r8c6=5 r8c9<>5 r8c9=1 (r7c7<>1) r9c7<>1 r6c7=1 r6c1<>1
r1c3=2 r7c3<>2 r7c3=5 (r8c3<>5 r8c3=7 r8c9<>7) (r7c6<>5) r5c3<>5 r5c4=5 r4c6<>5 r8c6=5 r8c9<>5 r8c9=1 r8c1<>1
r1c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>1
Locked Candidates Type 1 (Pointing): 2 in b1 => r9c1<>2
Almost Locked Set XZ-Rule: A=r45c2 {169}, B=r136c3 {4689}, X=9, Z=6 => r5c3<>6
Almost Locked Set XY-Wing: A=r1c2345 {23568}, B=r3c7 {68}, C=r9c1457 {12356}, X,Y=2,6, Z=8 => r1c9<>8
Almost Locked Set XY-Wing: A=r1c2345 {23568}, B=r23c7 {568}, C=r9c1457 {12356}, X,Y=2,6, Z=5 => r1c9,r2c5<>5
Hidden Single: r2c7=5
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c145<>8
Forcing Chain Contradiction in b8 => r1c9=2
r1c9<>2 r1c9=6 r1c3<>6 r1c3=8 r5c3<>8 r5c3=5 r7c3<>5 r7c3=2 r7c6<>2
r1c9<>2 r1c9=6 r1c23<>6 r3c3=6 r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
r1c9<>2 r1c5=2 r9c5<>2
Naked Quadruple: 4,6,8,9 in r3c3789 => r3c1<>4
Forcing Chain Contradiction in r9c4 => r1c5<>3
r1c5=3 r3c4<>3 r3c4=1 r9c4<>1
r1c5=3 r1c2<>3 r3c1=3 r8c1<>3 r8c6=3 r9c4<>3
r1c5=3 r1c5<>5 r1c4=5 r9c4<>5
Forcing Chain Contradiction in r4 => r4c6<>6
r4c6=6 r2c6<>6 r1c4=6 r1c3<>6 r1c3=8 r5c3<>8 r5c3=5 r4c1<>5
r4c6=6 r2c6<>6 r1c4=6 r1c4<>5 r1c5=5 r4c5<>5
r4c6=6 r4c6<>5
Forcing Chain Contradiction in r6c7 => r6c1<>1
r6c1=1 r6c7<>1
r6c1=1 r5c2<>1 r5c2=6 r5c4<>6 r6c46=6 r6c7<>6
r6c1=1 r6c1<>4 r6c3=4 r3c3<>4 r3c3=6 r3c7<>6 r3c7=8 r6c7<>8
Forcing Chain Verity => r6c3<>8
r9c3=2 r9c3<>9 r6c3=9 r6c3<>8
r9c5=2 r2c5<>2 r2c5=8 r2c1<>8 r1c3=8 r6c3<>8
r9c8=2 r8c8<>2 r8c8=7 r8c3<>7 r9c3=7 r9c3<>9 r6c3=9 r6c3<>8
AIC: 5 5- r1c5 -8- r1c3 =8= r5c3 =5= r5c4 -5 => r1c4,r4c5<>5
Hidden Single: r1c5=5
2-String Kite: 5 in r4c1,r9c4 (connected by r4c6,r5c4) => r9c1<>5
Almost Locked Set XY-Wing: A=r9c145 {1235}, B=r57c3 {258}, C=r5c249 {1568}, X,Y=5,8, Z=2 => r7c6,r9c3<>2
Continuous Nice Loop: 1/5 5= r8c1 =3= r8c6 =2= r9c5 -2- r2c5 -8- r2c1 =8= r1c3 -8- r5c3 -5- r4c1 =5= r8c1 =3 => r8c16<>1, r8c6<>5
Hidden Single: r8c9=1
Hidden Single: r6c7=1
Locked Candidates Type 2 (Claiming): 5 in r8 => r79c3<>5
Naked Single: r7c3=2
Skyscraper: 1 in r5c4,r7c6 (connected by r57c2) => r4c6,r9c4<>1
XY-Wing: 4/6/8 in r27c8,r3c7 => r7c7<>8
Naked Single: r7c7=3
Naked Single: r9c7=6
Full House: r3c7=8
XY-Wing: 3/5/1 in r39c4,r7c6 => r3c6<>1
Hidden Single: r7c6=1
Naked Single: r7c2=4
Naked Single: r7c8=8
Full House: r7c9=5
Hidden Single: r4c6=5
Hidden Single: r9c4=5
Hidden Single: r8c1=5
Naked Single: r8c3=7
Naked Single: r8c8=2
Full House: r8c6=3
Full House: r9c5=2
Naked Single: r9c3=9
Naked Single: r2c5=8
Hidden Single: r5c3=5
Hidden Single: r6c9=9
Hidden Single: r4c2=9
Hidden Single: r1c3=8
Hidden Single: r3c8=9
Locked Candidates Type 1 (Pointing): 7 in b6 => r4c5<>7
Naked Single: r4c5=1
Naked Single: r4c1=8
Naked Single: r6c1=4
Naked Single: r2c1=2
Naked Single: r6c3=6
Full House: r3c3=4
Full House: r5c2=1
Naked Single: r2c6=6
Full House: r2c8=4
Full House: r3c9=6
Naked Single: r3c1=3
Full House: r1c2=6
Full House: r9c2=3
Full House: r1c4=3
Full House: r9c1=1
Naked Single: r6c6=7
Full House: r3c6=2
Naked Single: r9c8=7
Full House: r4c8=6
Full House: r4c9=7
Full House: r5c9=8
Full House: r9c9=4
Full House: r5c4=6
Naked Single: r3c4=1
Full House: r3c5=7
Full House: r6c4=8
Full House: r6c5=3
|
sudoku_normal_extremely_hard_138
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
9....471..719....3.5.........32..4..7....92...2.....5.6..79.....8.46.9.......8...
|
968354712271986543354172896893215467715649238426837159642791385587463921139528674
|
9 . . . . 4 7 1 .
. 7 1 9 . . . . 3
. 5 . . . . . . .
. . 3 2 . . 4 . .
7 . . . . 9 2 . .
. 2 . . . . . 5 .
6 . . 7 9 . . . .
. 8 . 4 6 . 9 . .
. . . . . 8 . . .
|
9 6 8 3 5 4 7 1 2
2 7 1 9 8 6 5 4 3
3 5 4 1 7 2 8 9 6
8 9 3 2 1 5 4 6 7
7 1 5 6 4 9 2 3 8
4 2 6 8 3 7 1 5 9
6 4 2 7 9 1 3 8 5
5 8 7 4 6 3 9 2 1
1 3 9 5 2 8 6 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_3325_hard
|
968354712271986543354172896893215467715649238426837159642791385587463921139528674 #1 Extreme (34122) bf
Brute Force: r5c8=3
Brute Force: r5c5=4
Locked Candidates Type 2 (Claiming): 4 in c2 => r79c3,r9c1<>4
XYZ-Wing: 2/5/7 in r78c3,r8c8 => r8c1<>2
Discontinuous Nice Loop: 2 r2c8 -2- r8c8 -7- r8c3 =7= r9c3 =9= r6c3 =4= r6c1 -4- r2c1 =4= r2c8 => r2c8<>2
Discontinuous Nice Loop: 4 r3c8 -4- r3c3 =4= r6c3 =9= r6c9 -9- r3c9 =9= r3c8 => r3c8<>4
Forcing Chain Contradiction in c9 => r9c9<>2
r9c9=2 r789c8<>2 r3c8=2 r3c8<>9 r3c9=9 r3c9<>4
r9c9=2 r8c8<>2 r8c8=7 r8c3<>7 r9c3=7 r9c3<>9 r9c2=9 r9c2<>4 r7c2=4 r7c9<>4
r9c9=2 r9c9<>4
Forcing Net Contradiction in c1 => r3c3<>2
r3c3=2 r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 (r4c5<>5) r4c6<>5 r4c1=5 r4c1<>1
r3c3=2 (r7c3<>2 r7c3=5 r8c3<>5 r8c3=7 r8c9<>7) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r4c6<>5) (r7c3<>2 r7c3=5 r7c6<>5) (r3c8<>2) r3c9<>2 r1c9=2 (r8c9<>2) r1c9<>5 r2c7=5 r2c6<>5 r8c6=5 r8c9<>5 r8c9=1 (r7c7<>1) r9c7<>1 r6c7=1 r6c1<>1
r3c3=2 (r7c3<>2 r7c3=5 r8c3<>5 r8c3=7 r8c9<>7) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r4c6<>5) (r7c3<>2 r7c3=5 r7c6<>5) (r3c8<>2) r3c9<>2 r1c9=2 (r8c9<>2) r1c9<>5 r2c7=5 r2c6<>5 r8c6=5 r8c9<>5 r8c9=1 r8c1<>1
r3c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>1
Forcing Net Contradiction in b8 => r2c8<>8
r2c8=8 (r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r1c9<>5 r1c9=2 r1c3<>2) r2c8<>4 r2c1=4 r6c1<>4 r6c3=4 r6c3<>9 r9c3=9 (r9c3<>2) r9c3<>7 r8c3=7 r8c3<>2 r7c3=2 r7c6<>2
r2c8=8 r2c8<>4 r2c1=4 r6c1<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
r2c8=8 (r2c5<>8) (r2c7<>8) r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r2c5<>5 r2c5=2 r9c5<>2
Forcing Net Contradiction in c6 => r3c3<>8
r3c3=8 r3c7<>8 r3c7=6 (r2c7<>6) r2c8<>6 r2c6=6 r2c6<>2
r3c3=8 (r3c7<>8 r3c7=6 r3c9<>6) (r3c9<>8) (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r3c9<>4) r3c3<>4 r6c3=4 r6c3<>9 r6c9=9 r3c9<>9 r3c9=2 r3c6<>2
r3c3=8 (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r2c1<>4 r2c1=2 r1c3<>2) r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 (r9c3<>2) r9c3<>7 r8c3=7 r8c3<>2 r7c3=2 r7c6<>2
r3c3=8 r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
Forcing Net Verity => r3c8<>2
r1c9=2 r3c8<>2
r3c9=2 r3c8<>2
r7c9=2 (r1c9<>2) (r7c3<>2 r7c3=5 r8c3<>5) r8c8<>2 r8c8=7 r8c3<>7 r8c3=2 r1c3<>2 r1c5=2 (r2c5<>2) r2c5<>2 r2c6=2 (r2c1<>2) (r1c5<>2) r3c5<>2 r9c5=2 r9c1<>2 r3c1=2 r3c8<>2
r8c9=2 (r1c9<>2) (r8c3<>2) r8c8<>2 r8c8=7 r8c3<>7 r8c3=5 r7c3<>5 r7c3=2 r1c3<>2 r1c5=2 (r2c5<>2) r2c5<>2 r2c6=2 (r2c1<>2) (r1c5<>2) r3c5<>2 r9c5=2 r9c1<>2 r3c1=2 r3c8<>2
Locked Candidates Type 1 (Pointing): 2 in b3 => r78c9<>2
Forcing Net Verity => r3c5<>2
r2c1=8 r2c1<>2 r2c56=2 r3c5<>2
r3c1=8 (r3c9<>8) (r3c8<>8) r3c7<>8 r3c7=6 (r3c9<>6) (r2c8<>6 r2c8=4 r3c9<>4) r3c8<>6 r3c8=9 r3c9<>9 r3c9=2 r3c5<>2
r4c1=8 r4c1<>5 r5c3=5 (r8c3<>5) r7c3<>5 r7c3=2 (r9c1<>2) (r9c3<>2) r8c3<>2 r8c3=7 r8c8<>7 r8c8=2 r9c8<>2 r9c5=2 r3c5<>2
r6c1=8 (r5c3<>8) r6c1<>4 r6c3=4 (r6c3<>9 r9c3=9 r9c3<>2) r3c3<>4 r3c3=6 r5c3<>6 r5c3=5 (r8c3<>5) r7c3<>5 r7c3=2 (r9c1<>2) r8c3<>2 r8c3=7 r8c8<>7 r8c8=2 r9c8<>2 r9c5=2 r3c5<>2
Forcing Net Contradiction in c9 => r3c8<>8
r3c8=8 (r2c7<>8) r3c7<>8 r3c7=6 r2c7<>6 r2c7=5 r1c9<>5
r3c8=8 (r7c8<>8) r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r7c8<>4 r7c8=2 r7c3<>2 r7c3=5 r7c9<>5
r3c8=8 (r3c8<>9 r3c9=9 r3c9<>2 r1c9=2 r1c3<>2 r23c1=2 r9c1<>2) (r3c8<>9 r4c8=9 r4c8<>6 r9c8=6 r9c8<>2) (r7c8<>8) r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r7c8<>4 r7c8=2 (r7c3<>2 r7c3=5 r7c6<>5) (r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 r9c4<>5) (r7c3<>2 r7c3=5 r8c3<>5) r8c8<>2 r8c8=7 r8c3<>7 r8c3=2 r9c3<>2 r9c5=2 r9c5<>5 r8c6=5 r8c9<>5
r3c8=8 (r3c7<>8 r3c7=6 r2c8<>6 r2c8=4 r9c8<>4) r3c8<>9 r3c9=9 r6c9<>9 r6c3=9 r9c3<>9 r9c2=9 r9c2<>4 r9c9=4 r9c9<>5
Forcing Net Verity => r6c9<>6
r1c4=6 (r1c2<>6) r1c3<>6 r3c3=6 r3c3<>4 r6c3=4 r6c3<>9 r6c9=9 r6c9<>6
r3c4=6 (r3c3<>6 r3c3=4 r3c1<>4) (r3c7<>6 r3c7=8 r3c1<>8) (r3c9<>6) (r3c3<>6 r3c3=4 r3c9<>4) (r3c7<>6 r3c7=8 r3c9<>8) r3c8<>6 r3c8=9 r3c9<>9 r3c9=2 r3c1<>2 r3c1=3 r1c2<>3 r1c2=6 (r4c2<>6) r5c2<>6 r5c2=1 r4c2<>1 r4c2=9 r6c3<>9 r6c9=9 r6c9<>6
r5c4=6 r5c4<>5 r5c3=5 (r9c3<>5) (r8c3<>5) r7c3<>5 r7c3=2 (r9c3<>2) r8c3<>2 r8c3=7 r9c3<>7 r9c3=9 r6c3<>9 r6c9=9 r6c9<>6
r6c4=6 r6c9<>6
Forcing Net Contradiction in r9c9 => r7c7<>5
r7c7=5 (r7c3<>5 r7c3=2 r9c1<>2) (r7c3<>5 r7c3=2 r9c3<>2) (r7c3<>5 r7c3=2 r1c3<>2) (r7c9<>5) (r8c9<>5) r9c9<>5 r1c9=5 r1c9<>2 r1c5=2 r9c5<>2 r9c8=2 (r9c8<>4) (r9c8<>7) r8c8<>2 r8c8=7 r9c9<>7 r9c3=7 r9c3<>9 r9c2=9 r9c2<>4 r9c9=4
r7c7=5 (r7c7<>3 r9c7=3 r9c7<>6) (r7c3<>5 r7c3=2 r9c1<>2) (r7c3<>5 r7c3=2 r9c3<>2) (r7c3<>5 r7c3=2 r1c3<>2) (r7c9<>5) (r8c9<>5) r9c9<>5 r1c9=5 r1c9<>2 r1c5=2 r9c5<>2 r9c8=2 r9c8<>6 r9c9=6
Empty Rectangle: 5 in b8 (r29c7) => r2c6<>5
Forcing Chain Contradiction in r1 => r2c7<>6
r2c7=6 r2c6<>6 r2c6=2 r12c5<>2 r9c5=2 r9c1<>2 r23c1=2 r1c3<>2
r2c7=6 r2c6<>6 r2c6=2 r1c5<>2
r2c7=6 r2c7<>5 r1c9=5 r1c9<>2
AIC: 6 6- r2c6 =6= r2c8 =4= r2c1 -4- r3c3 -6 => r3c46<>6
Forcing Net Contradiction in c1 => r1c3<>2
r1c3=2 r7c3<>2 r7c3=5 r5c3<>5 r5c4=5 (r4c5<>5) r4c6<>5 r4c1=5 r4c1<>1
r1c3=2 r7c3<>2 r7c3=5 (r8c3<>5 r8c3=7 r8c9<>7) (r7c6<>5) r5c3<>5 r5c4=5 r4c6<>5 r8c6=5 r8c9<>5 r8c9=1 (r7c7<>1) r9c7<>1 r6c7=1 r6c1<>1
r1c3=2 r7c3<>2 r7c3=5 (r8c3<>5 r8c3=7 r8c9<>7) (r7c6<>5) r5c3<>5 r5c4=5 r4c6<>5 r8c6=5 r8c9<>5 r8c9=1 r8c1<>1
r1c3=2 (r2c1<>2) r3c1<>2 r9c1=2 r9c1<>1
Locked Candidates Type 1 (Pointing): 2 in b1 => r9c1<>2
Almost Locked Set XZ-Rule: A=r45c2 {169}, B=r136c3 {4689}, X=9, Z=6 => r5c3<>6
Almost Locked Set XY-Wing: A=r1c2345 {23568}, B=r3c7 {68}, C=r9c1457 {12356}, X,Y=2,6, Z=8 => r1c9<>8
Almost Locked Set XY-Wing: A=r1c2345 {23568}, B=r23c7 {568}, C=r9c1457 {12356}, X,Y=2,6, Z=5 => r1c9,r2c5<>5
Hidden Single: r2c7=5
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c145<>8
Forcing Chain Contradiction in b8 => r1c9=2
r1c9<>2 r1c9=6 r1c3<>6 r1c3=8 r5c3<>8 r5c3=5 r7c3<>5 r7c3=2 r7c6<>2
r1c9<>2 r1c9=6 r1c23<>6 r3c3=6 r3c3<>4 r6c3=4 r6c3<>9 r9c3=9 r9c3<>7 r8c3=7 r8c8<>7 r8c8=2 r8c6<>2
r1c9<>2 r1c5=2 r9c5<>2
Naked Quadruple: 4,6,8,9 in r3c3789 => r3c1<>4
Forcing Chain Contradiction in r9c4 => r1c5<>3
r1c5=3 r3c4<>3 r3c4=1 r9c4<>1
r1c5=3 r1c2<>3 r3c1=3 r8c1<>3 r8c6=3 r9c4<>3
r1c5=3 r1c5<>5 r1c4=5 r9c4<>5
Forcing Chain Contradiction in r4 => r4c6<>6
r4c6=6 r2c6<>6 r1c4=6 r1c3<>6 r1c3=8 r5c3<>8 r5c3=5 r4c1<>5
r4c6=6 r2c6<>6 r1c4=6 r1c4<>5 r1c5=5 r4c5<>5
r4c6=6 r4c6<>5
Forcing Chain Contradiction in r6c7 => r6c1<>1
r6c1=1 r6c7<>1
r6c1=1 r5c2<>1 r5c2=6 r5c4<>6 r6c46=6 r6c7<>6
r6c1=1 r6c1<>4 r6c3=4 r3c3<>4 r3c3=6 r3c7<>6 r3c7=8 r6c7<>8
Forcing Chain Verity => r6c3<>8
r9c3=2 r9c3<>9 r6c3=9 r6c3<>8
r9c5=2 r2c5<>2 r2c5=8 r2c1<>8 r1c3=8 r6c3<>8
r9c8=2 r8c8<>2 r8c8=7 r8c3<>7 r9c3=7 r9c3<>9 r6c3=9 r6c3<>8
AIC: 5 5- r1c5 -8- r1c3 =8= r5c3 =5= r5c4 -5 => r1c4,r4c5<>5
Hidden Single: r1c5=5
2-String Kite: 5 in r4c1,r9c4 (connected by r4c6,r5c4) => r9c1<>5
Almost Locked Set XY-Wing: A=r9c145 {1235}, B=r57c3 {258}, C=r5c249 {1568}, X,Y=5,8, Z=2 => r7c6,r9c3<>2
Continuous Nice Loop: 1/5 5= r8c1 =3= r8c6 =2= r9c5 -2- r2c5 -8- r2c1 =8= r1c3 -8- r5c3 -5- r4c1 =5= r8c1 =3 => r8c16<>1, r8c6<>5
Hidden Single: r8c9=1
Hidden Single: r6c7=1
Locked Candidates Type 2 (Claiming): 5 in r8 => r79c3<>5
Naked Single: r7c3=2
Skyscraper: 1 in r5c4,r7c6 (connected by r57c2) => r4c6,r9c4<>1
XY-Wing: 4/6/8 in r27c8,r3c7 => r7c7<>8
Naked Single: r7c7=3
Naked Single: r9c7=6
Full House: r3c7=8
XY-Wing: 3/5/1 in r39c4,r7c6 => r3c6<>1
Hidden Single: r7c6=1
Naked Single: r7c2=4
Naked Single: r7c8=8
Full House: r7c9=5
Hidden Single: r4c6=5
Hidden Single: r9c4=5
Hidden Single: r8c1=5
Naked Single: r8c3=7
Naked Single: r8c8=2
Full House: r8c6=3
Full House: r9c5=2
Naked Single: r9c3=9
Naked Single: r2c5=8
Hidden Single: r5c3=5
Hidden Single: r6c9=9
Hidden Single: r4c2=9
Hidden Single: r1c3=8
Hidden Single: r3c8=9
Locked Candidates Type 1 (Pointing): 7 in b6 => r4c5<>7
Naked Single: r4c5=1
Naked Single: r4c1=8
Naked Single: r6c1=4
Naked Single: r2c1=2
Naked Single: r6c3=6
Full House: r3c3=4
Full House: r5c2=1
Naked Single: r2c6=6
Full House: r2c8=4
Full House: r3c9=6
Naked Single: r3c1=3
Full House: r1c2=6
Full House: r9c2=3
Full House: r1c4=3
Full House: r9c1=1
Naked Single: r6c6=7
Full House: r3c6=2
Naked Single: r9c8=7
Full House: r4c8=6
Full House: r4c9=7
Full House: r5c9=8
Full House: r9c9=4
Full House: r5c4=6
Naked Single: r3c4=1
Full House: r3c5=7
Full House: r6c4=8
Full House: r6c5=3
|
sudoku_normal_hard_139
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2..4..6.5..73.4.......8..7...9.4.8.4..87.3.9819..3.....5.6....6..4.7..5.7.3..6..
|
728549163596731428143628957367914582452876319819253746935162874681497235274385691
|
. 2 . . 4 . . 6 .
5 . . 7 3 . 4 . .
. . . . . 8 . . 7
. . . 9 . 4 . 8 .
4 . . 8 7 . 3 . 9
8 1 9 . . 3 . . .
. . 5 . 6 . . . .
6 . . 4 . 7 . . 5
. 7 . 3 . . 6 . .
|
7 2 8 5 4 9 1 6 3
5 9 6 7 3 1 4 2 8
1 4 3 6 2 8 9 5 7
3 6 7 9 1 4 5 8 2
4 5 2 8 7 6 3 1 9
8 1 9 2 5 3 7 4 6
9 3 5 1 6 2 8 7 4
6 8 1 4 9 7 2 3 5
2 7 4 3 8 5 6 9 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_6848_hard
|
728549163596731428143628957367914582452876319819253746935162874681497235274385691 #1 Extreme (22024) bf
Hidden Pair: 3,4 in r46c6 => r4c6<>1, r46c6<>2, r46c6<>5, r46c6<>6
Brute Force: r5c4=8
Hidden Single: r6c1=8
Hidden Single: r6c6=3
Naked Single: r4c6=4
Locked Candidates Type 1 (Pointing): 7 in b4 => r4c7<>7
Discontinuous Nice Loop: 1 r4c9 -1- r4c5 =1= r5c6 =6= r6c4 -6- r6c9 =6= r4c9 => r4c9<>1
Forcing Chain Contradiction in r4 => r3c5<>5
r3c5=5 r13c4<>5 r6c4=5 r6c4<>6 r5c6=6 r5c2<>6 r5c2=5 r4c2<>5
r3c5=5 r4c5<>5
r3c5=5 r3c8<>5 r13c7=5 r4c7<>5
Forcing Chain Contradiction in r4 => r3c8<>2
r3c8=2 r2c89<>2 r2c6=2 r2c6<>6 r5c6=6 r5c2<>6 r5c2=5 r4c2<>5
r3c8=2 r2c89<>2 r2c6=2 r2c6<>6 r5c6=6 r5c6<>1 r4c5=1 r4c5<>5
r3c8=2 r3c8<>5 r13c7=5 r4c7<>5
Forcing Chain Contradiction in c6 => r7c8<>1
r7c8=1 r5c8<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r7c8=1 r5c8<>1 r5c6=1 r5c6<>2
r7c8=1 r7c4<>1 r7c4=2 r7c6<>2
r7c8=1 r7c4<>1 r7c4=2 r9c6<>2
Forcing Chain Contradiction in c6 => r8c5<>1
r8c5=1 r4c5<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r8c5=1 r4c5<>1 r5c6=1 r5c6<>2
r8c5=1 r7c4<>1 r7c4=2 r7c6<>2
r8c5=1 r7c4<>1 r7c4=2 r9c6<>2
Forcing Chain Contradiction in r2 => r3c8<>1
r3c8=1 r12c9<>1 r79c9=1 r8c78<>1 r8c3=1 r2c3<>1
r3c8=1 r5c8<>1 r5c6=1 r2c6<>1
r3c8=1 r2c8<>1
r3c8=1 r2c9<>1
Forcing Chain Contradiction in c6 => r9c5<>1
r9c5=1 r4c5<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r9c5=1 r4c5<>1 r5c6=1 r5c6<>2
r9c5=1 r7c4<>1 r7c4=2 r7c6<>2
r9c5=1 r9c5<>5 r9c6=5 r9c6<>2
Forcing Chain Contradiction in r2 => r7c9<>1
r7c9=1 r8c78<>1 r8c3=1 r2c3<>1
r7c9=1 r7c4<>1 r13c4=1 r2c6<>1
r7c9=1 r7c4<>1 r79c6=1 r5c6<>1 r5c8=1 r2c8<>1
r7c9=1 r2c9<>1
Forcing Net Contradiction in c9 => r1c6<>5
r1c6=5 (r3c4<>5) (r1c4<>5 r1c4=1 r7c4<>1 r7c4=2 r3c4<>2) (r1c4<>5) r3c4<>5 r6c4=5 r6c5<>5 r6c5=2 r3c5<>2 r3c7=2 r3c7<>5 r3c8=5 r3c8<>3 r1c9=3
r1c6=5 (r1c4<>5) r3c4<>5 r6c4=5 r7c9=3
Locked Candidates Type 1 (Pointing): 5 in b2 => r6c4<>5
XYZ-Wing: 1/2/9 in r17c6,r7c4 => r9c6<>1
Locked Candidates Type 1 (Pointing): 1 in b8 => r7c17<>1
Forcing Net Contradiction in r6 => r1c4=5
r1c4<>5 r1c4=1 (r3c5<>1) r1c6<>1 r1c6=9 r3c5<>9 r3c5=2 r6c5<>2 r6c5=5
r1c4<>5 r1c7=5 r6c7<>5 r6c8=5
Forcing Net Contradiction in c8 => r9c6=5
r9c6<>5 (r9c5=5 r6c5<>5 r6c5=2 r8c5<>2) r5c6=5 (r5c2<>5 r5c2=6 r5c3<>6 r5c3=2 r8c3<>2) (r5c2<>5 r4c2=5 r4c7<>5) r5c6<>1 r5c8=1 (r2c8<>1) r4c7<>1 r4c7=2 r8c7<>2 r8c8=2 r2c8<>2 r2c8=9
r9c6<>5 r5c6=5 (r5c6<>1 r5c8=1 r9c8<>1) (r5c6<>1 r5c8=1 r4c7<>1 r4c7=2 r8c7<>2 r8c8=2 r9c8<>2) (r5c2<>5 r5c2=6 r3c2<>6) r5c6<>6 r2c6=6 r3c4<>6 r3c3=6 r3c3<>4 r9c3=4 r9c8<>4 r9c8=9
Almost Locked Set Chain: 2- r4c1239 {23567} -5- r5c2 {56} -6- r5c36 {126} -1- r46c9,r56c8,r6c7 {124567} -2 => r4c7<>2
Forcing Chain Contradiction in r1c7 => r1c9<>8
r1c9=8 r1c9<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r1c7<>1
r1c9=8 r1c7<>8
r1c9=8 r1c9<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r4c5<>1 r3c5=1 r1c6<>1 r1c6=9 r1c7<>9
Forcing Net Contradiction in r2c3 => r1c9=3
r1c9<>3 (r1c9=1 r2c8<>1) (r1c9=1 r2c9<>1) r7c9=3 (r7c8<>3) r8c8<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r4c5<>1 r3c5=1 r2c6<>1 r2c3=1
r1c9<>3 (r7c9=3 r7c9<>8) r1c9=1 (r1c7<>1) r1c6<>1 r1c6=9 r1c7<>9 r1c7=8 (r2c9<>8) r7c7<>8 r7c2=8 r2c2<>8 r2c3=8
Empty Rectangle: 1 in b7 (r29c9) => r2c3<>1
Forcing Chain Verity => r1c7<>9
r2c6=1 r1c6<>1 r1c6=9 r1c7<>9
r2c8=1 r5c8<>1 r5c6=1 r1c6<>1 r1c6=9 r1c7<>9
r2c9=1 r2c9<>8 r1c7=8 r1c7<>9
Finned Franken Swordfish: 9 r19b3 c158 fr1c6 fr3c7 => r3c5<>9
Locked Candidates Type 1 (Pointing): 9 in b2 => r7c6<>9
Locked Pair: 1,2 in r7c46 => r7c1789,r89c5<>2
W-Wing: 2/1 in r3c5,r7c6 connected by 1 in r37c4 => r2c6<>2
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c7<>2
Discontinuous Nice Loop: 8 r8c7 -8- r7c9 -4- r6c9 =4= r6c8 =7= r6c7 =2= r8c7 => r8c7<>8
Almost Locked Set Chain: 9- r3c4578 {12569} -6- r6c4 {26} -2- r6c578 {2457} -4- r46c9 {246} -2- r13c7,r2c9,r3c8 {12589} -9 => r2c8,r3c12<>9
Naked Triple: 1,2,8 in r1c7,r2c89 => r3c7<>1
Discontinuous Nice Loop: 9 r7c7 -9- r7c1 -3- r3c1 -1- r3c5 =1= r4c5 -1- r4c7 -5- r3c7 -9- r7c7 => r7c7<>9
Sue de Coq: r789c8 - {123479} (r235c8 - {1259}, r7c79 - {478}) => r9c9<>4, r9c9<>8, r6c8<>2, r6c8<>5
Locked Candidates Type 1 (Pointing): 8 in b9 => r7c2<>8
Sue de Coq: r8c78 - {1239} (r8c25 - {389}, r9c9 - {12}) => r9c8<>1, r9c8<>2, r8c3<>3, r8c3<>8
Continuous Nice Loop: 2/6/8 6= r6c9 =4= r7c9 =8= r2c9 -8- r2c3 -6- r2c6 =6= r5c6 -6- r6c4 =6= r6c9 =4 => r6c9<>2, r2c2<>6, r2c2<>8
Naked Single: r2c2=9
Hidden Single: r8c2=8
Naked Single: r8c5=9
Naked Single: r9c5=8
Hidden Single: r1c6=9
Hidden Single: r8c8=3
Hidden Single: r3c7=9
Naked Single: r3c8=5
Hidden Single: r5c2=5
Hidden Pair: 1,5 in r4c57 => r4c5<>2
X-Wing: 6 r25 c36 => r34c3<>6
Finned X-Wing: 1 r18 c37 fr1c1 => r3c3<>1
Sue de Coq: r23c3 - {3468} (r589c3 - {1246}, r1c13,r3c1 - {1378}) => r3c2<>3, r1c3<>1, r4c3<>2
Locked Candidates Type 1 (Pointing): 1 in b1 => r9c1<>1
XY-Wing: 4/6/3 in r3c23,r4c2 => r4c3<>3
Naked Single: r4c3=7
Naked Single: r1c3=8
Naked Single: r1c7=1
Full House: r1c1=7
Naked Single: r2c3=6
Naked Single: r2c8=2
Full House: r2c9=8
Full House: r2c6=1
Naked Single: r4c7=5
Naked Single: r8c7=2
Full House: r8c3=1
Naked Single: r3c2=4
Naked Single: r5c3=2
Naked Single: r5c8=1
Full House: r5c6=6
Full House: r7c6=2
Full House: r7c4=1
Naked Single: r7c9=4
Naked Single: r3c5=2
Full House: r3c4=6
Full House: r6c4=2
Naked Single: r4c5=1
Full House: r6c5=5
Naked Single: r6c7=7
Full House: r7c7=8
Naked Single: r9c9=1
Naked Single: r3c3=3
Full House: r9c3=4
Full House: r3c1=1
Naked Single: r7c2=3
Full House: r4c2=6
Full House: r4c1=3
Full House: r4c9=2
Full House: r6c9=6
Full House: r6c8=4
Naked Single: r9c8=9
Full House: r7c8=7
Full House: r7c1=9
Full House: r9c1=2
|
sudoku_normal_extremely_hard_139
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2..4..6.5..73.4.......8..7...9...8.4...7.3.9.19........5.6....6..4.7..5.7.3..6..
|
728549163596731428143628957367914582452876319819253746935162874681497235274385691
|
. 2 . . 4 . . 6 .
5 . . 7 3 . 4 . .
. . . . . 8 . . 7
. . . 9 . . . 8 .
4 . . . 7 . 3 . 9
. 1 9 . . . . . .
. . 5 . 6 . . . .
6 . . 4 . 7 . . 5
. 7 . 3 . . 6 . .
|
7 2 8 5 4 9 1 6 3
5 9 6 7 3 1 4 2 8
1 4 3 6 2 8 9 5 7
3 6 7 9 1 4 5 8 2
4 5 2 8 7 6 3 1 9
8 1 9 2 5 3 7 4 6
9 3 5 1 6 2 8 7 4
6 8 1 4 9 7 2 3 5
2 7 4 3 8 5 6 9 1
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_6848_hard
|
728549163596731428143628957367914582452876319819253746935162874681497235274385691 #1 Extreme (22024) bf
Hidden Pair: 3,4 in r46c6 => r4c6<>1, r46c6<>2, r46c6<>5, r46c6<>6
Brute Force: r5c4=8
Hidden Single: r6c1=8
Hidden Single: r6c6=3
Naked Single: r4c6=4
Locked Candidates Type 1 (Pointing): 7 in b4 => r4c7<>7
Discontinuous Nice Loop: 1 r4c9 -1- r4c5 =1= r5c6 =6= r6c4 -6- r6c9 =6= r4c9 => r4c9<>1
Forcing Chain Contradiction in r4 => r3c5<>5
r3c5=5 r13c4<>5 r6c4=5 r6c4<>6 r5c6=6 r5c2<>6 r5c2=5 r4c2<>5
r3c5=5 r4c5<>5
r3c5=5 r3c8<>5 r13c7=5 r4c7<>5
Forcing Chain Contradiction in r4 => r3c8<>2
r3c8=2 r2c89<>2 r2c6=2 r2c6<>6 r5c6=6 r5c2<>6 r5c2=5 r4c2<>5
r3c8=2 r2c89<>2 r2c6=2 r2c6<>6 r5c6=6 r5c6<>1 r4c5=1 r4c5<>5
r3c8=2 r3c8<>5 r13c7=5 r4c7<>5
Forcing Chain Contradiction in c6 => r7c8<>1
r7c8=1 r5c8<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r7c8=1 r5c8<>1 r5c6=1 r5c6<>2
r7c8=1 r7c4<>1 r7c4=2 r7c6<>2
r7c8=1 r7c4<>1 r7c4=2 r9c6<>2
Forcing Chain Contradiction in c6 => r8c5<>1
r8c5=1 r4c5<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r8c5=1 r4c5<>1 r5c6=1 r5c6<>2
r8c5=1 r7c4<>1 r7c4=2 r7c6<>2
r8c5=1 r7c4<>1 r7c4=2 r9c6<>2
Forcing Chain Contradiction in r2 => r3c8<>1
r3c8=1 r12c9<>1 r79c9=1 r8c78<>1 r8c3=1 r2c3<>1
r3c8=1 r5c8<>1 r5c6=1 r2c6<>1
r3c8=1 r2c8<>1
r3c8=1 r2c9<>1
Forcing Chain Contradiction in c6 => r9c5<>1
r9c5=1 r4c5<>1 r5c6=1 r5c6<>6 r2c6=6 r2c6<>2
r9c5=1 r4c5<>1 r5c6=1 r5c6<>2
r9c5=1 r7c4<>1 r7c4=2 r7c6<>2
r9c5=1 r9c5<>5 r9c6=5 r9c6<>2
Forcing Chain Contradiction in r2 => r7c9<>1
r7c9=1 r8c78<>1 r8c3=1 r2c3<>1
r7c9=1 r7c4<>1 r13c4=1 r2c6<>1
r7c9=1 r7c4<>1 r79c6=1 r5c6<>1 r5c8=1 r2c8<>1
r7c9=1 r2c9<>1
Forcing Net Contradiction in c9 => r1c6<>5
r1c6=5 (r3c4<>5) (r1c4<>5 r1c4=1 r7c4<>1 r7c4=2 r3c4<>2) (r1c4<>5) r3c4<>5 r6c4=5 r6c5<>5 r6c5=2 r3c5<>2 r3c7=2 r3c7<>5 r3c8=5 r3c8<>3 r1c9=3
r1c6=5 (r1c4<>5) r3c4<>5 r6c4=5 r7c9=3
Locked Candidates Type 1 (Pointing): 5 in b2 => r6c4<>5
XYZ-Wing: 1/2/9 in r17c6,r7c4 => r9c6<>1
Locked Candidates Type 1 (Pointing): 1 in b8 => r7c17<>1
Forcing Net Contradiction in r6 => r1c4=5
r1c4<>5 r1c4=1 (r3c5<>1) r1c6<>1 r1c6=9 r3c5<>9 r3c5=2 r6c5<>2 r6c5=5
r1c4<>5 r1c7=5 r6c7<>5 r6c8=5
Forcing Net Contradiction in c8 => r9c6=5
r9c6<>5 (r9c5=5 r6c5<>5 r6c5=2 r8c5<>2) r5c6=5 (r5c2<>5 r5c2=6 r5c3<>6 r5c3=2 r8c3<>2) (r5c2<>5 r4c2=5 r4c7<>5) r5c6<>1 r5c8=1 (r2c8<>1) r4c7<>1 r4c7=2 r8c7<>2 r8c8=2 r2c8<>2 r2c8=9
r9c6<>5 r5c6=5 (r5c6<>1 r5c8=1 r9c8<>1) (r5c6<>1 r5c8=1 r4c7<>1 r4c7=2 r8c7<>2 r8c8=2 r9c8<>2) (r5c2<>5 r5c2=6 r3c2<>6) r5c6<>6 r2c6=6 r3c4<>6 r3c3=6 r3c3<>4 r9c3=4 r9c8<>4 r9c8=9
Almost Locked Set Chain: 2- r4c1239 {23567} -5- r5c2 {56} -6- r5c36 {126} -1- r46c9,r56c8,r6c7 {124567} -2 => r4c7<>2
Forcing Chain Contradiction in r1c7 => r1c9<>8
r1c9=8 r1c9<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r1c7<>1
r1c9=8 r1c7<>8
r1c9=8 r1c9<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r4c5<>1 r3c5=1 r1c6<>1 r1c6=9 r1c7<>9
Forcing Net Contradiction in r2c3 => r1c9=3
r1c9<>3 (r1c9=1 r2c8<>1) (r1c9=1 r2c9<>1) r7c9=3 (r7c8<>3) r8c8<>3 r3c8=3 r3c8<>5 r3c7=5 r4c7<>5 r4c7=1 r4c5<>1 r3c5=1 r2c6<>1 r2c3=1
r1c9<>3 (r7c9=3 r7c9<>8) r1c9=1 (r1c7<>1) r1c6<>1 r1c6=9 r1c7<>9 r1c7=8 (r2c9<>8) r7c7<>8 r7c2=8 r2c2<>8 r2c3=8
Empty Rectangle: 1 in b7 (r29c9) => r2c3<>1
Forcing Chain Verity => r1c7<>9
r2c6=1 r1c6<>1 r1c6=9 r1c7<>9
r2c8=1 r5c8<>1 r5c6=1 r1c6<>1 r1c6=9 r1c7<>9
r2c9=1 r2c9<>8 r1c7=8 r1c7<>9
Finned Franken Swordfish: 9 r19b3 c158 fr1c6 fr3c7 => r3c5<>9
Locked Candidates Type 1 (Pointing): 9 in b2 => r7c6<>9
Locked Pair: 1,2 in r7c46 => r7c1789,r89c5<>2
W-Wing: 2/1 in r3c5,r7c6 connected by 1 in r37c4 => r2c6<>2
Locked Candidates Type 1 (Pointing): 2 in b2 => r3c7<>2
Discontinuous Nice Loop: 8 r8c7 -8- r7c9 -4- r6c9 =4= r6c8 =7= r6c7 =2= r8c7 => r8c7<>8
Almost Locked Set Chain: 9- r3c4578 {12569} -6- r6c4 {26} -2- r6c578 {2457} -4- r46c9 {246} -2- r13c7,r2c9,r3c8 {12589} -9 => r2c8,r3c12<>9
Naked Triple: 1,2,8 in r1c7,r2c89 => r3c7<>1
Discontinuous Nice Loop: 9 r7c7 -9- r7c1 -3- r3c1 -1- r3c5 =1= r4c5 -1- r4c7 -5- r3c7 -9- r7c7 => r7c7<>9
Sue de Coq: r789c8 - {123479} (r235c8 - {1259}, r7c79 - {478}) => r9c9<>4, r9c9<>8, r6c8<>2, r6c8<>5
Locked Candidates Type 1 (Pointing): 8 in b9 => r7c2<>8
Sue de Coq: r8c78 - {1239} (r8c25 - {389}, r9c9 - {12}) => r9c8<>1, r9c8<>2, r8c3<>3, r8c3<>8
Continuous Nice Loop: 2/6/8 6= r6c9 =4= r7c9 =8= r2c9 -8- r2c3 -6- r2c6 =6= r5c6 -6- r6c4 =6= r6c9 =4 => r6c9<>2, r2c2<>6, r2c2<>8
Naked Single: r2c2=9
Hidden Single: r8c2=8
Naked Single: r8c5=9
Naked Single: r9c5=8
Hidden Single: r1c6=9
Hidden Single: r8c8=3
Hidden Single: r3c7=9
Naked Single: r3c8=5
Hidden Single: r5c2=5
Hidden Pair: 1,5 in r4c57 => r4c5<>2
X-Wing: 6 r25 c36 => r34c3<>6
Finned X-Wing: 1 r18 c37 fr1c1 => r3c3<>1
Sue de Coq: r23c3 - {3468} (r589c3 - {1246}, r1c13,r3c1 - {1378}) => r3c2<>3, r1c3<>1, r4c3<>2
Locked Candidates Type 1 (Pointing): 1 in b1 => r9c1<>1
XY-Wing: 4/6/3 in r3c23,r4c2 => r4c3<>3
Naked Single: r4c3=7
Naked Single: r1c3=8
Naked Single: r1c7=1
Full House: r1c1=7
Naked Single: r2c3=6
Naked Single: r2c8=2
Full House: r2c9=8
Full House: r2c6=1
Naked Single: r4c7=5
Naked Single: r8c7=2
Full House: r8c3=1
Naked Single: r3c2=4
Naked Single: r5c3=2
Naked Single: r5c8=1
Full House: r5c6=6
Full House: r7c6=2
Full House: r7c4=1
Naked Single: r7c9=4
Naked Single: r3c5=2
Full House: r3c4=6
Full House: r6c4=2
Naked Single: r4c5=1
Full House: r6c5=5
Naked Single: r6c7=7
Full House: r7c7=8
Naked Single: r9c9=1
Naked Single: r3c3=3
Full House: r9c3=4
Full House: r3c1=1
Naked Single: r7c2=3
Full House: r4c2=6
Full House: r4c1=3
Full House: r4c9=2
Full House: r6c9=6
Full House: r6c8=4
Naked Single: r9c8=9
Full House: r7c8=7
Full House: r7c1=9
Full House: r9c1=2
|
sudoku_normal_hard_140
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8....6.9..38...7.....58..2.4539..6.19467.2.3..128..96.........23.9.6...97.....2
|
158972463946381257732645891274539186819467325365128749681253974523794618497816532
|
. . 8 . . . . 6 .
9 . . 3 8 . . . 7
. . . . . 5 8 . .
2 . 4 5 3 9 . . 6
. 1 9 4 6 7 . 2 .
3 . . 1 2 8 . . 9
6 . . . . . . . .
. 2 3 . 9 . 6 . .
. 9 7 . . . . . 2
|
1 5 8 9 7 2 4 6 3
9 4 6 3 8 1 2 5 7
7 3 2 6 4 5 8 9 1
2 7 4 5 3 9 1 8 6
8 1 9 4 6 7 3 2 5
3 6 5 1 2 8 7 4 9
6 8 1 2 5 3 9 7 4
5 2 3 7 9 4 6 1 8
4 9 7 8 1 6 5 3 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7032_hard
|
158972463946381257732645891274539186819467325365128749681253974523794618497816532 #1 Extreme (33160) bf
Brute Force: r5c5=6
Hidden Single: r4c4=5
Locked Candidates Type 1 (Pointing): 7 in b5 => r178c6<>7
Locked Candidates Type 1 (Pointing): 8 in b5 => r789c6<>8
Locked Candidates Type 1 (Pointing): 9 in b5 => r1c6<>9
Forcing Net Contradiction in r7c2 => r3c3<>4
r3c3=4 r13c1<>4 r89c1=4 r7c2<>4
r3c3=4 (r2c2<>4) (r3c3<>6) r3c3<>2 r3c4=2 r3c4<>6 r3c2=6 r2c2<>6 r2c2=5 r7c2<>5
r3c3=4 (r4c3<>4 r4c3=9 r5c3<>9 r5c3=5 r5c9<>5) r3c3<>2 r3c4=2 (r3c4<>6 r3c2=6 r3c2<>3) r3c4<>9 r3c8=9 r3c8<>3 r3c9=3 r5c9<>3 r5c9=8 r5c1<>8 r89c1=8 r7c2<>8
Brute Force: r5c6=7
Naked Single: r6c6=8
Full House: r4c6=9
Naked Single: r4c3=4
Hidden Single: r5c3=9
Locked Candidates Type 1 (Pointing): 7 in b4 => r13c2<>7
2-String Kite: 8 in r5c9,r7c2 (connected by r4c2,r5c1) => r7c9<>8
Forcing Chain Verity => r1c4<>7
r7c2=8 r4c2<>8 r4c8=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r1c4<>7
r7c4=8 r8c4<>8 r8c4=7 r1c4<>7
r7c8=8 r7c8<>9 r7c7=9 r1c7<>9 r1c4=9 r1c4<>7
Grouped Discontinuous Nice Loop: 3 r9c7 -3- r9c6 =3= r7c6 =2= r7c4 -2- r1c4 -9- r1c7 =9= r3c8 =3= r79c8 -3- r9c7 => r9c7<>3
Forcing Chain Contradiction in r9 => r3c3<>6
r3c3=6 r6c3<>6 r6c3=5 r5c1<>5 r5c1=8 r9c1<>8
r3c3=6 r3c4<>6 r9c4=6 r9c4<>8
r3c3=6 r6c3<>6 r6c3=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r9c8<>8
Forcing Chain Contradiction in c8 => r3c8<>1
r3c8=1 r3c8<>3
r3c8=1 r3c8<>9 r7c8=9 r7c8<>3
r3c8=1 r3c8<>9 r3c4=9 r1c4<>9 r1c4=2 r7c4<>2 r7c6=2 r7c6<>3 r9c6=3 r9c8<>3
Forcing Chain Contradiction in c8 => r3c8<>4
r3c8=4 r3c8<>3
r3c8=4 r3c8<>9 r7c8=9 r7c8<>3
r3c8=4 r3c8<>9 r3c4=9 r1c4<>9 r1c4=2 r7c4<>2 r7c6=2 r7c6<>3 r9c6=3 r9c8<>3
Forcing Chain Contradiction in r7c4 => r6c8<>7
r6c8=7 r46c7<>7 r7c7=7 r7c7<>9 r1c7=9 r1c4<>9 r1c4=2 r7c4<>2
r6c8=7 r8c8<>7 r8c4=7 r7c4<>7
r6c8=7 r6c2<>7 r4c2=7 r4c2<>8 r7c2=8 r7c4<>8
Forcing Chain Contradiction in b9 => r7c7<>3
r7c7=3 r7c7<>7
r7c7=3 r7c7<>9 r7c8=9 r7c8<>7
r7c7=3 r5c7<>3 r5c9=3 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in b9 => r7c7<>5
r7c7=5 r7c7<>7
r7c7=5 r7c7<>9 r7c8=9 r7c8<>7
r7c7=5 r7c23<>5 r89c1=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in b9 => r7c8<>5
r7c8=5 r7c8<>9 r7c7=9 r7c7<>7
r7c8=5 r7c8<>7
r7c8=5 r7c23<>5 r89c1=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in r9 => r9c8<>5
r9c8=5 r8c89<>5 r8c1=5 r5c1<>5 r5c1=8 r9c1<>8
r9c8=5 r9c8<>3 r9c6=3 r9c6<>6 r9c4=6 r9c4<>8
r9c8=5 r9c8<>8
Forcing Net Contradiction in r7c7 => r3c3=2
r3c3<>2 r3c4=2 (r7c4<>2 r7c6=2 r7c6<>3) (r3c4<>6 r3c2=6 r3c2<>3) r3c4<>9 r3c8=9 r3c8<>3 r3c9=3 r7c9<>3 r7c8=3 (r7c8<>8) (r7c8<>7) r7c8<>9 r7c7=9 r7c7<>7 r8c8=7 r8c4<>7 r8c4=8 r7c4<>8 r7c2=8 (r9c1<>8) r4c2<>8 r4c8=8 r9c8<>8 r9c4=8 r9c4<>6 r3c4=6 r3c4<>2 r3c3=2
Forcing Chain Contradiction in r9 => r2c7<>1
r2c7=1 r2c3<>1 r7c3=1 r9c1<>1
r2c7=1 r4c7<>1 r4c7=7 r4c2<>7 r4c2=8 r5c1<>8 r5c1=5 r89c1<>5 r7c23=5 r7c5<>5 r9c5=5 r9c5<>1
r2c7=1 r2c7<>2 r2c6=2 r2c6<>6 r9c6=6 r9c6<>1
r2c7=1 r9c7<>1
r2c7=1 r4c7<>1 r4c8=1 r9c8<>1
Forcing Chain Verity => r7c4<>7
r7c2=8 r4c2<>8 r4c8=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r7c4<>7
r7c4=8 r7c4<>7
r7c8=8 r7c8<>9 r7c7=9 r1c7<>9 r1c4=9 r1c4<>2 r7c4=2 r7c4<>7
Almost Locked Set XY-Wing: A=r7c234569 {1234578}, B=r124569c7 {1234579}, C=r1c456,r2c6,r3c5 {124679}, X,Y=7,9, Z=1,4 => r7c7<>1, r7c7<>4
Forcing Chain Verity => r7c8<>4
r7c2=8 r4c2<>8 r4c2=7 r6c2<>7 r6c7=7 r6c7<>4 r6c8=4 r7c8<>4
r7c4=8 r7c4<>2 r1c4=2 r1c4<>9 r1c7=9 r7c7<>9 r7c8=9 r7c8<>4
r7c8=8 r7c8<>4
Forcing Net Verity => r5c7=3
r8c1=5 (r7c3<>5 r7c3=1 r9c1<>1 r9c1=4 r9c7<>4) r5c1<>5 r5c1=8 r4c2<>8 r4c2=7 r4c7<>7 r4c7=1 r9c7<>1 r9c7=5 r5c7<>5 r5c7=3
r8c8=5 (r2c8<>5) r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 (r1c9<>1) (r3c9<>1) r2c3<>1 r7c3=1 r7c9<>1 r8c9=1 r8c9<>8 r5c9=8 r5c9<>3 r5c7=3
r8c9=5 r8c9<>8 r5c9=8 r5c9<>3 r5c7=3
Empty Rectangle: 5 in b7 (r5c19) => r7c9<>5
Forcing Net Contradiction in r7c5 => r1c4=9
r1c4<>9 r1c7=9 (r1c7<>5) r3c8<>9 r3c8=3 r1c9<>3 r1c2=3 r1c2<>5 r1c9=5 (r2c8<>5) (r8c9<>5) r5c9<>5 r5c1=5 (r1c1<>5) r8c1<>5 r8c8=5 r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 r2c3<>1 r7c3=1 r7c5<>1
r1c4<>9 r1c7=9 (r1c7<>5) r3c8<>9 r3c8=3 r1c9<>3 r1c2=3 r1c2<>5 r1c9=5 (r1c9<>1) (r2c8<>5) (r8c9<>5) r5c9<>5 r5c1=5 (r1c1<>5) r8c1<>5 r8c8=5 r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 (r3c9<>1) r2c3<>1 r7c3=1 r7c9<>1 r8c9=1 r8c6<>1 r8c6=4 r7c5<>4
r1c4<>9 r1c4=2 r7c4<>2 r7c4=8 r7c2<>8 r4c2=8 r5c1<>8 r5c1=5 r89c1<>5 r7c23=5 r7c5<>5
r1c4<>9 r1c4=2 r7c4<>2 r7c4=8 r8c4<>8 r8c4=7 r7c5<>7
Hidden Single: r7c7=9
Hidden Single: r3c8=9
Hidden Single: r7c4=2
Locked Candidates Type 1 (Pointing): 3 in b3 => r7c9<>3
Locked Candidates Type 1 (Pointing): 7 in b9 => r4c8<>7
X-Wing: 8 r47 c28 => r89c8<>8
Sue de Coq: r8c89 - {14578} (r8c4 - {78}, r7c9,r9c7 - {145}) => r79c8<>1, r9c8<>4, r8c1<>8
Naked Single: r9c8=3
Hidden Single: r7c6=3
Discontinuous Nice Loop: 4 r8c8 -4- r6c8 -5- r5c9 -8- r8c9 =8= r8c4 =7= r8c8 => r8c8<>4
Grouped Discontinuous Nice Loop: 4 r1c1 -4- r89c1 =4= r7c2 =8= r7c8 =7= r7c5 -7- r1c5 =7= r1c1 => r1c1<>4
Almost Locked Set XZ-Rule: A=r7c39 {145}, B=r8c16 {145}, X=5, Z=4 => r8c9<>4
Almost Locked Set XY-Wing: A=r8c16 {145}, B=r1357c9 {13458}, C=r5c1 {58}, X,Y=5,8, Z=1 => r8c9<>1
Naked Pair: 5,8 in r58c9 => r1c9<>5
Sashimi X-Wing: 1 c39 r27 fr1c9 fr3c9 => r2c8<>1
Naked Pair: 4,5 in r26c8 => r8c8<>5
X-Wing: 5 r58 c19 => r19c1<>5
2-String Kite: 5 in r1c2,r6c8 (connected by r1c7,r2c8) => r6c2<>5
Continuous Nice Loop: 4/5 5= r1c2 =3= r3c2 =6= r3c4 =7= r8c4 =8= r8c9 =5= r9c7 -5- r1c7 =5= r1c2 =3 => r13c2<>4, r26c7<>5
2-String Kite: 4 in r2c2,r8c6 (connected by r7c2,r8c1) => r2c6<>4
Turbot Fish: 4 r2c2 =4= r7c2 -4- r7c9 =4= r9c7 => r2c7<>4
Naked Single: r2c7=2
Hidden Single: r1c6=2
Locked Candidates Type 1 (Pointing): 4 in b2 => r79c5<>4
Skyscraper: 4 in r2c8,r7c9 (connected by r27c2) => r13c9<>4
Hidden Single: r7c9=4
Hidden Single: r2c2=4
Naked Single: r2c8=5
Naked Single: r6c8=4
Naked Single: r6c7=7
Naked Single: r4c7=1
Naked Single: r6c2=6
Full House: r6c3=5
Naked Single: r1c7=4
Full House: r9c7=5
Naked Single: r4c8=8
Full House: r4c2=7
Full House: r5c1=8
Full House: r5c9=5
Naked Single: r3c2=3
Naked Single: r7c3=1
Full House: r2c3=6
Full House: r2c6=1
Naked Single: r8c9=8
Naked Single: r9c5=1
Naked Single: r7c8=7
Full House: r8c8=1
Naked Single: r1c2=5
Full House: r7c2=8
Full House: r7c5=5
Naked Single: r3c9=1
Full House: r1c9=3
Naked Single: r9c1=4
Full House: r8c1=5
Naked Single: r1c5=7
Full House: r1c1=1
Full House: r3c1=7
Full House: r3c5=4
Full House: r3c4=6
Naked Single: r8c6=4
Full House: r8c4=7
Full House: r9c6=6
Full House: r9c4=8
|
sudoku_normal_extremely_hard_140
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8....6.9..38...7.....58..2...3...6.1.4...2.3..12...96.........23.9.6...97.....2
|
158972463946381257732645891274539186819467325365128749681253974523794618497816532
|
. . 8 . . . . 6 .
9 . . 3 8 . . . 7
. . . . . 5 8 . .
2 . . . 3 . . . 6
. 1 . 4 . . . 2 .
3 . . 1 2 . . . 9
6 . . . . . . . .
. 2 3 . 9 . 6 . .
. 9 7 . . . . . 2
|
1 5 8 9 7 2 4 6 3
9 4 6 3 8 1 2 5 7
7 3 2 6 4 5 8 9 1
2 7 4 5 3 9 1 8 6
8 1 9 4 6 7 3 2 5
3 6 5 1 2 8 7 4 9
6 8 1 2 5 3 9 7 4
5 2 3 7 9 4 6 1 8
4 9 7 8 1 6 5 3 2
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7032_hard
|
158972463946381257732645891274539186819467325365128749681253974523794618497816532 #1 Extreme (33160) bf
Brute Force: r5c5=6
Hidden Single: r4c4=5
Locked Candidates Type 1 (Pointing): 7 in b5 => r178c6<>7
Locked Candidates Type 1 (Pointing): 8 in b5 => r789c6<>8
Locked Candidates Type 1 (Pointing): 9 in b5 => r1c6<>9
Forcing Net Contradiction in r7c2 => r3c3<>4
r3c3=4 r13c1<>4 r89c1=4 r7c2<>4
r3c3=4 (r2c2<>4) (r3c3<>6) r3c3<>2 r3c4=2 r3c4<>6 r3c2=6 r2c2<>6 r2c2=5 r7c2<>5
r3c3=4 (r4c3<>4 r4c3=9 r5c3<>9 r5c3=5 r5c9<>5) r3c3<>2 r3c4=2 (r3c4<>6 r3c2=6 r3c2<>3) r3c4<>9 r3c8=9 r3c8<>3 r3c9=3 r5c9<>3 r5c9=8 r5c1<>8 r89c1=8 r7c2<>8
Brute Force: r5c6=7
Naked Single: r6c6=8
Full House: r4c6=9
Naked Single: r4c3=4
Hidden Single: r5c3=9
Locked Candidates Type 1 (Pointing): 7 in b4 => r13c2<>7
2-String Kite: 8 in r5c9,r7c2 (connected by r4c2,r5c1) => r7c9<>8
Forcing Chain Verity => r1c4<>7
r7c2=8 r4c2<>8 r4c8=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r1c4<>7
r7c4=8 r8c4<>8 r8c4=7 r1c4<>7
r7c8=8 r7c8<>9 r7c7=9 r1c7<>9 r1c4=9 r1c4<>7
Grouped Discontinuous Nice Loop: 3 r9c7 -3- r9c6 =3= r7c6 =2= r7c4 -2- r1c4 -9- r1c7 =9= r3c8 =3= r79c8 -3- r9c7 => r9c7<>3
Forcing Chain Contradiction in r9 => r3c3<>6
r3c3=6 r6c3<>6 r6c3=5 r5c1<>5 r5c1=8 r9c1<>8
r3c3=6 r3c4<>6 r9c4=6 r9c4<>8
r3c3=6 r6c3<>6 r6c3=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r9c8<>8
Forcing Chain Contradiction in c8 => r3c8<>1
r3c8=1 r3c8<>3
r3c8=1 r3c8<>9 r7c8=9 r7c8<>3
r3c8=1 r3c8<>9 r3c4=9 r1c4<>9 r1c4=2 r7c4<>2 r7c6=2 r7c6<>3 r9c6=3 r9c8<>3
Forcing Chain Contradiction in c8 => r3c8<>4
r3c8=4 r3c8<>3
r3c8=4 r3c8<>9 r7c8=9 r7c8<>3
r3c8=4 r3c8<>9 r3c4=9 r1c4<>9 r1c4=2 r7c4<>2 r7c6=2 r7c6<>3 r9c6=3 r9c8<>3
Forcing Chain Contradiction in r7c4 => r6c8<>7
r6c8=7 r46c7<>7 r7c7=7 r7c7<>9 r1c7=9 r1c4<>9 r1c4=2 r7c4<>2
r6c8=7 r8c8<>7 r8c4=7 r7c4<>7
r6c8=7 r6c2<>7 r4c2=7 r4c2<>8 r7c2=8 r7c4<>8
Forcing Chain Contradiction in b9 => r7c7<>3
r7c7=3 r7c7<>7
r7c7=3 r7c7<>9 r7c8=9 r7c8<>7
r7c7=3 r5c7<>3 r5c9=3 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in b9 => r7c7<>5
r7c7=5 r7c7<>7
r7c7=5 r7c7<>9 r7c8=9 r7c8<>7
r7c7=5 r7c23<>5 r89c1=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in b9 => r7c8<>5
r7c8=5 r7c8<>9 r7c7=9 r7c7<>7
r7c8=5 r7c8<>7
r7c8=5 r7c23<>5 r89c1=5 r5c1<>5 r5c1=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r8c8<>7
Forcing Chain Contradiction in r9 => r9c8<>5
r9c8=5 r8c89<>5 r8c1=5 r5c1<>5 r5c1=8 r9c1<>8
r9c8=5 r9c8<>3 r9c6=3 r9c6<>6 r9c4=6 r9c4<>8
r9c8=5 r9c8<>8
Forcing Net Contradiction in r7c7 => r3c3=2
r3c3<>2 r3c4=2 (r7c4<>2 r7c6=2 r7c6<>3) (r3c4<>6 r3c2=6 r3c2<>3) r3c4<>9 r3c8=9 r3c8<>3 r3c9=3 r7c9<>3 r7c8=3 (r7c8<>8) (r7c8<>7) r7c8<>9 r7c7=9 r7c7<>7 r8c8=7 r8c4<>7 r8c4=8 r7c4<>8 r7c2=8 (r9c1<>8) r4c2<>8 r4c8=8 r9c8<>8 r9c4=8 r9c4<>6 r3c4=6 r3c4<>2 r3c3=2
Forcing Chain Contradiction in r9 => r2c7<>1
r2c7=1 r2c3<>1 r7c3=1 r9c1<>1
r2c7=1 r4c7<>1 r4c7=7 r4c2<>7 r4c2=8 r5c1<>8 r5c1=5 r89c1<>5 r7c23=5 r7c5<>5 r9c5=5 r9c5<>1
r2c7=1 r2c7<>2 r2c6=2 r2c6<>6 r9c6=6 r9c6<>1
r2c7=1 r9c7<>1
r2c7=1 r4c7<>1 r4c8=1 r9c8<>1
Forcing Chain Verity => r7c4<>7
r7c2=8 r4c2<>8 r4c8=8 r5c9<>8 r8c9=8 r8c4<>8 r8c4=7 r7c4<>7
r7c4=8 r7c4<>7
r7c8=8 r7c8<>9 r7c7=9 r1c7<>9 r1c4=9 r1c4<>2 r7c4=2 r7c4<>7
Almost Locked Set XY-Wing: A=r7c234569 {1234578}, B=r124569c7 {1234579}, C=r1c456,r2c6,r3c5 {124679}, X,Y=7,9, Z=1,4 => r7c7<>1, r7c7<>4
Forcing Chain Verity => r7c8<>4
r7c2=8 r4c2<>8 r4c2=7 r6c2<>7 r6c7=7 r6c7<>4 r6c8=4 r7c8<>4
r7c4=8 r7c4<>2 r1c4=2 r1c4<>9 r1c7=9 r7c7<>9 r7c8=9 r7c8<>4
r7c8=8 r7c8<>4
Forcing Net Verity => r5c7=3
r8c1=5 (r7c3<>5 r7c3=1 r9c1<>1 r9c1=4 r9c7<>4) r5c1<>5 r5c1=8 r4c2<>8 r4c2=7 r4c7<>7 r4c7=1 r9c7<>1 r9c7=5 r5c7<>5 r5c7=3
r8c8=5 (r2c8<>5) r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 (r1c9<>1) (r3c9<>1) r2c3<>1 r7c3=1 r7c9<>1 r8c9=1 r8c9<>8 r5c9=8 r5c9<>3 r5c7=3
r8c9=5 r8c9<>8 r5c9=8 r5c9<>3 r5c7=3
Empty Rectangle: 5 in b7 (r5c19) => r7c9<>5
Forcing Net Contradiction in r7c5 => r1c4=9
r1c4<>9 r1c7=9 (r1c7<>5) r3c8<>9 r3c8=3 r1c9<>3 r1c2=3 r1c2<>5 r1c9=5 (r2c8<>5) (r8c9<>5) r5c9<>5 r5c1=5 (r1c1<>5) r8c1<>5 r8c8=5 r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 r2c3<>1 r7c3=1 r7c5<>1
r1c4<>9 r1c7=9 (r1c7<>5) r3c8<>9 r3c8=3 r1c9<>3 r1c2=3 r1c2<>5 r1c9=5 (r1c9<>1) (r2c8<>5) (r8c9<>5) r5c9<>5 r5c1=5 (r1c1<>5) r8c1<>5 r8c8=5 r6c8<>5 r6c8=4 r2c8<>4 r2c8=1 (r3c9<>1) r2c3<>1 r7c3=1 r7c9<>1 r8c9=1 r8c6<>1 r8c6=4 r7c5<>4
r1c4<>9 r1c4=2 r7c4<>2 r7c4=8 r7c2<>8 r4c2=8 r5c1<>8 r5c1=5 r89c1<>5 r7c23=5 r7c5<>5
r1c4<>9 r1c4=2 r7c4<>2 r7c4=8 r8c4<>8 r8c4=7 r7c5<>7
Hidden Single: r7c7=9
Hidden Single: r3c8=9
Hidden Single: r7c4=2
Locked Candidates Type 1 (Pointing): 3 in b3 => r7c9<>3
Locked Candidates Type 1 (Pointing): 7 in b9 => r4c8<>7
X-Wing: 8 r47 c28 => r89c8<>8
Sue de Coq: r8c89 - {14578} (r8c4 - {78}, r7c9,r9c7 - {145}) => r79c8<>1, r9c8<>4, r8c1<>8
Naked Single: r9c8=3
Hidden Single: r7c6=3
Discontinuous Nice Loop: 4 r8c8 -4- r6c8 -5- r5c9 -8- r8c9 =8= r8c4 =7= r8c8 => r8c8<>4
Grouped Discontinuous Nice Loop: 4 r1c1 -4- r89c1 =4= r7c2 =8= r7c8 =7= r7c5 -7- r1c5 =7= r1c1 => r1c1<>4
Almost Locked Set XZ-Rule: A=r7c39 {145}, B=r8c16 {145}, X=5, Z=4 => r8c9<>4
Almost Locked Set XY-Wing: A=r8c16 {145}, B=r1357c9 {13458}, C=r5c1 {58}, X,Y=5,8, Z=1 => r8c9<>1
Naked Pair: 5,8 in r58c9 => r1c9<>5
Sashimi X-Wing: 1 c39 r27 fr1c9 fr3c9 => r2c8<>1
Naked Pair: 4,5 in r26c8 => r8c8<>5
X-Wing: 5 r58 c19 => r19c1<>5
2-String Kite: 5 in r1c2,r6c8 (connected by r1c7,r2c8) => r6c2<>5
Continuous Nice Loop: 4/5 5= r1c2 =3= r3c2 =6= r3c4 =7= r8c4 =8= r8c9 =5= r9c7 -5- r1c7 =5= r1c2 =3 => r13c2<>4, r26c7<>5
2-String Kite: 4 in r2c2,r8c6 (connected by r7c2,r8c1) => r2c6<>4
Turbot Fish: 4 r2c2 =4= r7c2 -4- r7c9 =4= r9c7 => r2c7<>4
Naked Single: r2c7=2
Hidden Single: r1c6=2
Locked Candidates Type 1 (Pointing): 4 in b2 => r79c5<>4
Skyscraper: 4 in r2c8,r7c9 (connected by r27c2) => r13c9<>4
Hidden Single: r7c9=4
Hidden Single: r2c2=4
Naked Single: r2c8=5
Naked Single: r6c8=4
Naked Single: r6c7=7
Naked Single: r4c7=1
Naked Single: r6c2=6
Full House: r6c3=5
Naked Single: r1c7=4
Full House: r9c7=5
Naked Single: r4c8=8
Full House: r4c2=7
Full House: r5c1=8
Full House: r5c9=5
Naked Single: r3c2=3
Naked Single: r7c3=1
Full House: r2c3=6
Full House: r2c6=1
Naked Single: r8c9=8
Naked Single: r9c5=1
Naked Single: r7c8=7
Full House: r8c8=1
Naked Single: r1c2=5
Full House: r7c2=8
Full House: r7c5=5
Naked Single: r3c9=1
Full House: r1c9=3
Naked Single: r9c1=4
Full House: r8c1=5
Naked Single: r1c5=7
Full House: r1c1=1
Full House: r3c1=7
Full House: r3c5=4
Full House: r3c4=6
Naked Single: r8c6=4
Full House: r8c4=7
Full House: r9c6=6
Full House: r9c4=8
|
sudoku_normal_hard_141
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7..2..6....8.36.......7..5..7...2.45..97.5..12...4.7..31.4....9.8.......6....34..
|
745281693928536174163974258876312945439765821251849736317428569584697312692153487
|
7 . . 2 . . 6 . .
. . 8 . 3 6 . . .
. . . . 7 . . 5 .
. 7 . . . 2 . 4 5
. . 9 7 . 5 . . 1
2 . . . 4 . 7 . .
3 1 . 4 . . . . 9
. 8 . . . . . . .
6 . . . . 3 4 . .
|
7 4 5 2 8 1 6 9 3
9 2 8 5 3 6 1 7 4
1 6 3 9 7 4 2 5 8
8 7 6 3 1 2 9 4 5
4 3 9 7 6 5 8 2 1
2 5 1 8 4 9 7 3 6
3 1 7 4 2 8 5 6 9
5 8 4 6 9 7 3 1 2
6 9 2 1 5 3 4 8 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4076_hard
|
745281693928536174163974258876312945439765821251849736317428569584697312692153487 #1 Extreme (22156) bf
Brute Force: r5c6=5
Hidden Single: r5c4=7
Turbot Fish: 5 r1c5 =5= r2c4 -5- r2c1 =5= r8c1 => r8c5<>5
Finned Swordfish: 5 r169 c235 fr9c4 => r7c5<>5
Forcing Chain Contradiction in r4 => r4c4<>8
r4c4=8 r5c5<>8 r5c5=6 r4c45<>6 r4c3=6 r4c3<>3
r4c4=8 r4c4<>3
r4c4=8 r4c1<>8 r5c1=8 r5c1<>4 r5c2=4 r5c2<>3 r5c78=3 r4c7<>3
Forcing Net Contradiction in r8c1 => r7c7<>8
r7c7=8 (r7c5<>8) (r7c6<>8) (r9c8<>8) (r9c9<>8) r7c7<>5 r7c3=5 (r9c2<>5) (r9c3<>5) (r1c3<>5) r6c3<>5 r6c2=5 r1c2<>5 r1c5=5 r9c5<>5 r9c4=5 r9c4<>8 r9c5=8 (r4c5<>8) r5c5<>8 r5c5=6 r7c5<>6 r7c8=6 r7c8<>8 r7c7=8 (r7c5<>8) (r7c6<>8) (r9c8<>8) (r9c9<>8) r4c7<>8 r4c1=8 r5c1<>8 r5c1=4 r8c1<>4
r7c7=8 r7c7<>5 r7c3=5 r8c1<>5
r7c7=8 (r7c6<>8 r7c6=7 r7c3<>7) (r7c5<>8) (r9c8<>8) (r9c9<>8) r7c7<>5 r7c3=5 (r9c2<>5) (r9c2<>5) (r9c3<>5) (r1c3<>5) r6c3<>5 r6c2=5 r1c2<>5 r1c5=5 (r9c5<>5) r9c5<>5 r9c4=5 r9c4<>8 r9c5=8 (r9c5<>9) r5c5<>8 r5c5=6 r7c5<>6 r7c5=2 r7c3<>2 r7c3=5 (r9c2<>5) (r9c2<>5) (r9c3<>5) (r1c3<>5) r9c3<>5 r9c4=5 r9c4<>9 r9c2=9 r8c1<>9
Almost Locked Set XZ-Rule: A=r5c5 {68}, B=r7c3567 {25678}, X=6, Z=8 => r9c5<>8
Finned Franken Swordfish: 8 c47b9 r369 fr4c7 fr5c7 fr7c8 => r6c8<>8
Grouped Continuous Nice Loop: 3/6/8 6= r6c9 =8= r6c46 -8- r5c5 -6- r7c5 =6= r7c8 -6- r8c9 =6= r6c9 =8 => r6c9<>3, r48c5,r8c8<>6, r4c5<>8
Forcing Chain Contradiction in r1 => r3c2<>4
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r5c5<>6 r5c5=8 r1c5<>8
r3c2=4 r3c6<>4 r1c6=4 r1c6<>8
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r8c4<>6 r8c9=6 r6c9<>6 r6c9=8 r9c9<>8 r79c8=8 r1c8<>8
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r8c4<>6 r8c9=6 r6c9<>6 r6c9=8 r1c9<>8
Forcing Chain Contradiction in r1 => r3c3<>4
r3c3=4 r8c3<>4 r8c1=4 r8c1<>9 r9c2=9 r1c2<>9
r3c3=4 r8c3<>4 r8c1=4 r8c1<>5 r2c1=5 r2c4<>5 r1c5=5 r1c5<>9
r3c3=4 r3c6<>4 r1c6=4 r1c6<>9
r3c3=4 r8c3<>4 r8c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Forcing Chain Verity => r7c8<>2
r3c4=8 r3c7<>8 r45c7=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>2
r6c4=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>2
r9c4=8 r7c56<>8 r7c8=8 r7c8<>2
Forcing Chain Verity => r7c8<>7
r3c4=8 r3c7<>8 r45c7=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>7
r6c4=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>7
r9c4=8 r7c6<>8 r7c6=7 r7c8<>7
Forcing Chain Contradiction in r9 => r9c2<>5
r9c2=5 r9c2<>9
r9c2=5 r9c45<>5 r8c4=5 r8c4<>6 r8c9=6 r7c8<>6 r7c8=8 r7c56<>8 r9c4=8 r9c4<>9
r9c2=5 r6c2<>5 r6c3=5 r6c3<>1 r4c13=1 r4c5<>1 r4c5=9 r9c5<>9
Almost Locked Set XZ-Rule: A=r9c2 {29}, B=r1c23,r2c12,r3c1 {123459}, X=2, Z=9 => r3c2<>9
Forcing Chain Contradiction in c3 => r8c4<>5
r8c4=5 r8c4<>6 r8c9=6 r7c8<>6 r7c8=8 r7c6<>8 r7c6=7 r7c3<>7
r8c4=5 r8c4<>6 r7c5=6 r5c5<>6 r5c5=8 r5c1<>8 r5c1=4 r8c1<>4 r8c3=4 r8c3<>7
r8c4=5 r9c45<>5 r9c3=5 r9c3<>7
Locked Candidates Type 1 (Pointing): 5 in b8 => r9c3<>5
Discontinuous Nice Loop: 9 r9c4 -9- r9c2 =9= r8c1 =5= r2c1 -5- r2c4 =5= r9c4 => r9c4<>9
Forcing Chain Contradiction in c2 => r2c2<>5
r2c2=5 r2c2<>2
r2c2=5 r2c4<>5 r9c4=5 r9c4<>8 r7c56=8 r7c8<>8 r7c8=6 r7c5<>6 r5c5=6 r4c4<>6 r4c3=6 r3c3<>6 r3c2=6 r3c2<>2
r2c2=5 r2c1<>5 r8c1=5 r8c1<>9 r9c2=9 r9c2<>2
Forcing Chain Contradiction in r1 => r3c1<>4
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r9c5<>9 r9c2=9 r1c2<>9
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r1c5<>9
r3c1=4 r3c6<>4 r1c6=4 r1c6<>9
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Forcing Chain Verity => r2c1<>4
r2c4=9 r2c4<>5 r2c1=5 r2c1<>4
r3c4=9 r3c1<>9 r3c1=1 r4c1<>1 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r4c4=9 r4c5<>9 r4c5=1 r4c1<>1 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r6c4=9 r6c8<>9 r4c7=9 r4c7<>8 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r8c4=9 r8c4<>6 r7c5=6 r5c5<>6 r5c5=8 r5c1<>8 r5c1=4 r2c1<>4
Grouped Discontinuous Nice Loop: 1 r1c3 -1- r23c1 =1= r4c1 =8= r5c1 =4= r5c2 -4- r12c2 =4= r1c3 => r1c3<>1
Almost Locked Set XY-Wing: A=r2c147 {1259}, B=r79c3,r9c2 {2579}, C=r7c7 {25}, X,Y=2,5, Z=9 => r2c2<>9
Forcing Chain Contradiction in r9 => r3c4<>1
r3c4=1 r9c4<>1
r3c4=1 r3c13<>1 r2c1=1 r2c1<>5 r2c4=5 r9c4<>5 r9c5=5 r9c5<>1
r3c4=1 r1c56<>1 r1c8=1 r9c8<>1
Grouped Discontinuous Nice Loop: 9 r8c4 -9- r3c4 -8- r3c7 =8= r45c7 -8- r6c9 -6- r8c9 =6= r8c4 => r8c4<>9
Forcing Chain Contradiction in r1 => r4c1=8
r4c1<>8 r4c1=1 r3c1<>1 r3c1=9 r1c2<>9
r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r1c5<>9
r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r46c4<>9 r23c4=9 r1c6<>9
r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Naked Single: r5c1=4
Hidden Single: r8c3=4
Locked Candidates Type 1 (Pointing): 1 in b4 => r3c3<>1
Hidden Rectangle: 3/5 in r1c23,r6c23 => r6c2<>3
AIC: 1/3 1- r6c3 =1= r4c3 =6= r4c4 =3= r6c4 -3 => r6c4<>1, r6c3<>3
Continuous Nice Loop: 1/2 9= r9c5 =5= r9c4 -5- r2c4 =5= r2c1 -5- r8c1 -9- r9c2 =9= r9c5 =5 => r9c5<>1, r9c5<>2
Sashimi X-Wing: 1 r19 c48 fr1c5 fr1c6 => r2c4<>1
Grouped Discontinuous Nice Loop: 1 r8c6 -1- r89c4 =1= r4c4 -1- r4c5 -9- r89c5 =9= r8c6 => r8c6<>1
AIC: 5 5- r7c7 =5= r7c3 =7= r7c6 -7- r8c6 -9- r8c1 -5 => r7c3,r8c7<>5
Hidden Single: r7c7=5
Hidden Single: r8c1=5
Hidden Single: r2c4=5
Hidden Single: r9c2=9
Naked Single: r9c5=5
Locked Candidates Type 1 (Pointing): 2 in b7 => r3c3<>2
Finned Swordfish: 9 r168 c568 fr6c4 => r4c5<>9
Naked Single: r4c5=1
Hidden Single: r6c3=1
Hidden Single: r6c2=5
Hidden Single: r1c3=5
Naked Pair: 8,9 in r1c5,r3c4 => r13c6<>8, r13c6<>9
Turbot Fish: 8 r1c5 =8= r3c4 -8- r3c7 =8= r5c7 => r5c5<>8
Naked Single: r5c5=6
Naked Single: r5c2=3
Full House: r4c3=6
Naked Single: r1c2=4
Naked Single: r3c3=3
Naked Single: r1c6=1
Naked Single: r2c2=2
Full House: r3c2=6
Naked Single: r3c6=4
Hidden Single: r8c4=6
Hidden Single: r7c8=6
Hidden Single: r2c9=4
Hidden Single: r6c9=6
Hidden Single: r9c4=1
Hidden Single: r2c8=7
Hidden Single: r8c8=1
Naked Pair: 2,8 in r59c8 => r1c8<>8
Swordfish: 9 r234 c147 => r6c4<>9
Uniqueness Test 1: 1/9 in r2c17,r3c17 => r3c7<>1, r3c7<>9
Hidden Single: r3c1=1
Full House: r2c1=9
Full House: r2c7=1
Hidden Single: r3c4=9
Full House: r1c5=8
Naked Single: r4c4=3
Full House: r4c7=9
Full House: r6c4=8
Full House: r6c6=9
Full House: r6c8=3
Naked Single: r1c9=3
Full House: r1c8=9
Naked Single: r7c5=2
Full House: r8c5=9
Naked Single: r8c6=7
Full House: r7c6=8
Full House: r7c3=7
Full House: r9c3=2
Naked Single: r8c9=2
Full House: r8c7=3
Naked Single: r9c8=8
Full House: r5c8=2
Full House: r9c9=7
Full House: r3c9=8
Full House: r5c7=8
Full House: r3c7=2
|
sudoku_normal_extremely_hard_141
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
7..2..6....8.36.......7..5..7...2.45..9.....12...4.7..31.4....9.8.......6....34..
|
745281693928536174163974258876312945439765821251849736317428569584697312692153487
|
7 . . 2 . . 6 . .
. . 8 . 3 6 . . .
. . . . 7 . . 5 .
. 7 . . . 2 . 4 5
. . 9 . . . . . 1
2 . . . 4 . 7 . .
3 1 . 4 . . . . 9
. 8 . . . . . . .
6 . . . . 3 4 . .
|
7 4 5 2 8 1 6 9 3
9 2 8 5 3 6 1 7 4
1 6 3 9 7 4 2 5 8
8 7 6 3 1 2 9 4 5
4 3 9 7 6 5 8 2 1
2 5 1 8 4 9 7 3 6
3 1 7 4 2 8 5 6 9
5 8 4 6 9 7 3 1 2
6 9 2 1 5 3 4 8 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4076_hard
|
745281693928536174163974258876312945439765821251849736317428569584697312692153487 #1 Extreme (22156) bf
Brute Force: r5c6=5
Hidden Single: r5c4=7
Turbot Fish: 5 r1c5 =5= r2c4 -5- r2c1 =5= r8c1 => r8c5<>5
Finned Swordfish: 5 r169 c235 fr9c4 => r7c5<>5
Forcing Chain Contradiction in r4 => r4c4<>8
r4c4=8 r5c5<>8 r5c5=6 r4c45<>6 r4c3=6 r4c3<>3
r4c4=8 r4c4<>3
r4c4=8 r4c1<>8 r5c1=8 r5c1<>4 r5c2=4 r5c2<>3 r5c78=3 r4c7<>3
Forcing Net Contradiction in r8c1 => r7c7<>8
r7c7=8 (r7c5<>8) (r7c6<>8) (r9c8<>8) (r9c9<>8) r7c7<>5 r7c3=5 (r9c2<>5) (r9c3<>5) (r1c3<>5) r6c3<>5 r6c2=5 r1c2<>5 r1c5=5 r9c5<>5 r9c4=5 r9c4<>8 r9c5=8 (r4c5<>8) r5c5<>8 r5c5=6 r7c5<>6 r7c8=6 r7c8<>8 r7c7=8 (r7c5<>8) (r7c6<>8) (r9c8<>8) (r9c9<>8) r4c7<>8 r4c1=8 r5c1<>8 r5c1=4 r8c1<>4
r7c7=8 r7c7<>5 r7c3=5 r8c1<>5
r7c7=8 (r7c6<>8 r7c6=7 r7c3<>7) (r7c5<>8) (r9c8<>8) (r9c9<>8) r7c7<>5 r7c3=5 (r9c2<>5) (r9c2<>5) (r9c3<>5) (r1c3<>5) r6c3<>5 r6c2=5 r1c2<>5 r1c5=5 (r9c5<>5) r9c5<>5 r9c4=5 r9c4<>8 r9c5=8 (r9c5<>9) r5c5<>8 r5c5=6 r7c5<>6 r7c5=2 r7c3<>2 r7c3=5 (r9c2<>5) (r9c2<>5) (r9c3<>5) (r1c3<>5) r9c3<>5 r9c4=5 r9c4<>9 r9c2=9 r8c1<>9
Almost Locked Set XZ-Rule: A=r5c5 {68}, B=r7c3567 {25678}, X=6, Z=8 => r9c5<>8
Finned Franken Swordfish: 8 c47b9 r369 fr4c7 fr5c7 fr7c8 => r6c8<>8
Grouped Continuous Nice Loop: 3/6/8 6= r6c9 =8= r6c46 -8- r5c5 -6- r7c5 =6= r7c8 -6- r8c9 =6= r6c9 =8 => r6c9<>3, r48c5,r8c8<>6, r4c5<>8
Forcing Chain Contradiction in r1 => r3c2<>4
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r5c5<>6 r5c5=8 r1c5<>8
r3c2=4 r3c6<>4 r1c6=4 r1c6<>8
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r8c4<>6 r8c9=6 r6c9<>6 r6c9=8 r9c9<>8 r79c8=8 r1c8<>8
r3c2=4 r3c2<>6 r3c3=6 r4c3<>6 r4c4=6 r8c4<>6 r8c9=6 r6c9<>6 r6c9=8 r1c9<>8
Forcing Chain Contradiction in r1 => r3c3<>4
r3c3=4 r8c3<>4 r8c1=4 r8c1<>9 r9c2=9 r1c2<>9
r3c3=4 r8c3<>4 r8c1=4 r8c1<>5 r2c1=5 r2c4<>5 r1c5=5 r1c5<>9
r3c3=4 r3c6<>4 r1c6=4 r1c6<>9
r3c3=4 r8c3<>4 r8c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Forcing Chain Verity => r7c8<>2
r3c4=8 r3c7<>8 r45c7=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>2
r6c4=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>2
r9c4=8 r7c56<>8 r7c8=8 r7c8<>2
Forcing Chain Verity => r7c8<>7
r3c4=8 r3c7<>8 r45c7=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>7
r6c4=8 r6c9<>8 r6c9=6 r8c9<>6 r7c8=6 r7c8<>7
r9c4=8 r7c6<>8 r7c6=7 r7c8<>7
Forcing Chain Contradiction in r9 => r9c2<>5
r9c2=5 r9c2<>9
r9c2=5 r9c45<>5 r8c4=5 r8c4<>6 r8c9=6 r7c8<>6 r7c8=8 r7c56<>8 r9c4=8 r9c4<>9
r9c2=5 r6c2<>5 r6c3=5 r6c3<>1 r4c13=1 r4c5<>1 r4c5=9 r9c5<>9
Almost Locked Set XZ-Rule: A=r9c2 {29}, B=r1c23,r2c12,r3c1 {123459}, X=2, Z=9 => r3c2<>9
Forcing Chain Contradiction in c3 => r8c4<>5
r8c4=5 r8c4<>6 r8c9=6 r7c8<>6 r7c8=8 r7c6<>8 r7c6=7 r7c3<>7
r8c4=5 r8c4<>6 r7c5=6 r5c5<>6 r5c5=8 r5c1<>8 r5c1=4 r8c1<>4 r8c3=4 r8c3<>7
r8c4=5 r9c45<>5 r9c3=5 r9c3<>7
Locked Candidates Type 1 (Pointing): 5 in b8 => r9c3<>5
Discontinuous Nice Loop: 9 r9c4 -9- r9c2 =9= r8c1 =5= r2c1 -5- r2c4 =5= r9c4 => r9c4<>9
Forcing Chain Contradiction in c2 => r2c2<>5
r2c2=5 r2c2<>2
r2c2=5 r2c4<>5 r9c4=5 r9c4<>8 r7c56=8 r7c8<>8 r7c8=6 r7c5<>6 r5c5=6 r4c4<>6 r4c3=6 r3c3<>6 r3c2=6 r3c2<>2
r2c2=5 r2c1<>5 r8c1=5 r8c1<>9 r9c2=9 r9c2<>2
Forcing Chain Contradiction in r1 => r3c1<>4
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r9c5<>9 r9c2=9 r1c2<>9
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r1c5<>9
r3c1=4 r3c6<>4 r1c6=4 r1c6<>9
r3c1=4 r5c1<>4 r5c1=8 r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Forcing Chain Verity => r2c1<>4
r2c4=9 r2c4<>5 r2c1=5 r2c1<>4
r3c4=9 r3c1<>9 r3c1=1 r4c1<>1 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r4c4=9 r4c5<>9 r4c5=1 r4c1<>1 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r6c4=9 r6c8<>9 r4c7=9 r4c7<>8 r4c1=8 r5c1<>8 r5c1=4 r2c1<>4
r8c4=9 r8c4<>6 r7c5=6 r5c5<>6 r5c5=8 r5c1<>8 r5c1=4 r2c1<>4
Grouped Discontinuous Nice Loop: 1 r1c3 -1- r23c1 =1= r4c1 =8= r5c1 =4= r5c2 -4- r12c2 =4= r1c3 => r1c3<>1
Almost Locked Set XY-Wing: A=r2c147 {1259}, B=r79c3,r9c2 {2579}, C=r7c7 {25}, X,Y=2,5, Z=9 => r2c2<>9
Forcing Chain Contradiction in r9 => r3c4<>1
r3c4=1 r9c4<>1
r3c4=1 r3c13<>1 r2c1=1 r2c1<>5 r2c4=5 r9c4<>5 r9c5=5 r9c5<>1
r3c4=1 r1c56<>1 r1c8=1 r9c8<>1
Grouped Discontinuous Nice Loop: 9 r8c4 -9- r3c4 -8- r3c7 =8= r45c7 -8- r6c9 -6- r8c9 =6= r8c4 => r8c4<>9
Forcing Chain Contradiction in r1 => r4c1=8
r4c1<>8 r4c1=1 r3c1<>1 r3c1=9 r1c2<>9
r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r1c5<>9
r4c1<>8 r4c1=1 r4c5<>1 r4c5=9 r46c4<>9 r23c4=9 r1c6<>9
r4c1<>8 r4c7=8 r4c7<>9 r6c8=9 r1c8<>9
Naked Single: r5c1=4
Hidden Single: r8c3=4
Locked Candidates Type 1 (Pointing): 1 in b4 => r3c3<>1
Hidden Rectangle: 3/5 in r1c23,r6c23 => r6c2<>3
AIC: 1/3 1- r6c3 =1= r4c3 =6= r4c4 =3= r6c4 -3 => r6c4<>1, r6c3<>3
Continuous Nice Loop: 1/2 9= r9c5 =5= r9c4 -5- r2c4 =5= r2c1 -5- r8c1 -9- r9c2 =9= r9c5 =5 => r9c5<>1, r9c5<>2
Sashimi X-Wing: 1 r19 c48 fr1c5 fr1c6 => r2c4<>1
Grouped Discontinuous Nice Loop: 1 r8c6 -1- r89c4 =1= r4c4 -1- r4c5 -9- r89c5 =9= r8c6 => r8c6<>1
AIC: 5 5- r7c7 =5= r7c3 =7= r7c6 -7- r8c6 -9- r8c1 -5 => r7c3,r8c7<>5
Hidden Single: r7c7=5
Hidden Single: r8c1=5
Hidden Single: r2c4=5
Hidden Single: r9c2=9
Naked Single: r9c5=5
Locked Candidates Type 1 (Pointing): 2 in b7 => r3c3<>2
Finned Swordfish: 9 r168 c568 fr6c4 => r4c5<>9
Naked Single: r4c5=1
Hidden Single: r6c3=1
Hidden Single: r6c2=5
Hidden Single: r1c3=5
Naked Pair: 8,9 in r1c5,r3c4 => r13c6<>8, r13c6<>9
Turbot Fish: 8 r1c5 =8= r3c4 -8- r3c7 =8= r5c7 => r5c5<>8
Naked Single: r5c5=6
Naked Single: r5c2=3
Full House: r4c3=6
Naked Single: r1c2=4
Naked Single: r3c3=3
Naked Single: r1c6=1
Naked Single: r2c2=2
Full House: r3c2=6
Naked Single: r3c6=4
Hidden Single: r8c4=6
Hidden Single: r7c8=6
Hidden Single: r2c9=4
Hidden Single: r6c9=6
Hidden Single: r9c4=1
Hidden Single: r2c8=7
Hidden Single: r8c8=1
Naked Pair: 2,8 in r59c8 => r1c8<>8
Swordfish: 9 r234 c147 => r6c4<>9
Uniqueness Test 1: 1/9 in r2c17,r3c17 => r3c7<>1, r3c7<>9
Hidden Single: r3c1=1
Full House: r2c1=9
Full House: r2c7=1
Hidden Single: r3c4=9
Full House: r1c5=8
Naked Single: r4c4=3
Full House: r4c7=9
Full House: r6c4=8
Full House: r6c6=9
Full House: r6c8=3
Naked Single: r1c9=3
Full House: r1c8=9
Naked Single: r7c5=2
Full House: r8c5=9
Naked Single: r8c6=7
Full House: r7c6=8
Full House: r7c3=7
Full House: r9c3=2
Naked Single: r8c9=2
Full House: r8c7=3
Naked Single: r9c8=8
Full House: r5c8=2
Full House: r9c9=7
Full House: r3c9=8
Full House: r5c7=8
Full House: r3c7=2
|
sudoku_normal_hard_142
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2.1...6.7.4.6..2....2..7...6..1.4..3718456924.56.2......4.1.36.....8.49.4..261..
|
928174365714563928653289714862917453371845692495632871287491536136758249549326187
|
. 2 . 1 . . . 6 .
7 . 4 . 6 . . 2 .
. . . 2 . . 7 . .
. 6 . . 1 . 4 . .
3 7 1 8 4 5 6 9 2
4 . 5 6 . 2 . . .
. . . 4 . 1 . 3 6
. . . . . 8 . 4 9
. 4 . . 2 6 1 . .
|
9 2 8 1 7 4 3 6 5
7 1 4 5 6 3 9 2 8
6 5 3 2 8 9 7 1 4
8 6 2 9 1 7 4 5 3
3 7 1 8 4 5 6 9 2
4 9 5 6 3 2 8 7 1
2 8 7 4 9 1 5 3 6
1 3 6 7 5 8 2 4 9
5 4 9 3 2 6 1 8 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7371_hard
|
928174365714563928653289714862917453371845692495632871287491536136758249549326187 #1 Extreme (25816) bf
Hidden Single: r6c1=4
Hidden Single: r8c8=4
Hidden Single: r7c6=1
Turbot Fish: 1 r2c9 =1= r2c2 -1- r6c2 =1= r5c3 => r5c9<>1
Brute Force: r5c8=9
Hidden Single: r5c3=1
Locked Candidates Type 1 (Pointing): 2 in b4 => r4c69<>2
Forcing Net Contradiction in r2 => r7c9<>5
r7c9=5 (r7c2<>5) (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r7c2<>8 r7c2=9 r6c2<>9 r6c2=8 r2c2<>8
r7c9=5 (r7c2<>5) (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r7c2<>8 r7c2=9 r6c2<>9 r6c2=8 r6c5<>8 r456c4=8 r2c4<>8
r7c9=5 (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r2c7<>8
r7c9=5 (r5c9<>5) (r8c7<>5 r8c7=2 r6c7<>2) r7c9<>6 r9c9=6 r9c6<>6 r6c6=6 r6c6<>2 r6c9=2 r5c9<>2 r5c9=8 r2c9<>8
Brute Force: r5c9=2
Naked Single: r5c6=5
Full House: r5c4=8
Hidden Single: r6c6=2
Hidden Single: r6c4=6
Hidden Single: r9c6=6
Hidden Single: r7c9=6
Locked Candidates Type 1 (Pointing): 7 in b9 => r9c34<>7
Hidden Pair: 1,6 in r38c1 => r38c1<>5, r3c1<>8, r3c1<>9, r8c1<>2
Forcing Chain Contradiction in r1 => r2c4<>3
r2c4=3 r9c4<>3 r9c3=3 r1c3<>3
r2c4=3 r1c5<>3
r2c4=3 r1c6<>3
r2c4=3 r2c6<>3 r2c6=9 r2c7<>9 r1c7=9 r1c7<>3
r2c4=3 r123c6<>3 r4c6=3 r4c6<>7 r1c6=7 r1c6<>4 r1c9=4 r1c9<>3
Forcing Chain Contradiction in r1 => r9c4<>5
r9c4=5 r9c4<>3 r9c3=3 r1c3<>3
r9c4=5 r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r1c5<>3
r9c4=5 r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r1c6<>3
r9c4=5 r2c4<>5 r2c4=9 r2c7<>9 r1c7=9 r1c7<>3
r9c4=5 r2c4<>5 r2c4=9 r123c6<>9 r4c6=9 r4c6<>7 r1c6=7 r1c6<>4 r1c9=4 r1c9<>3
Forcing Chain Verity => r2c9<>5
r1c1=9 r1c7<>9 r2c7=9 r2c4<>9 r2c4=5 r2c9<>5
r4c1=9 r4c6<>9 r123c6=9 r2c4<>9 r2c4=5 r2c9<>5
r7c1=9 r7c5<>9 r9c4=9 r2c4<>9 r2c4=5 r2c9<>5
r9c1=9 r9c1<>5 r9c89=5 r78c7<>5 r12c7=5 r2c9<>5
Forcing Chain Contradiction in c7 => r8c2<>5
r8c2=5 r79c1<>5 r1c1=5 r1c7<>5
r8c2=5 r8c4<>5 r2c4=5 r2c7<>5
r8c2=5 r9c1<>5 r9c89=5 r7c7<>5
r8c2=5 r8c7<>5
Forcing Chain Verity => r1c5<>9
r3c2=9 r6c2<>9 r6c5=9 r1c5<>9
r3c3=9 r3c3<>6 r3c1=6 r3c1<>1 r8c1=1 r8c2<>1 r8c2=3 r9c3<>3 r9c4=3 r9c4<>9 r7c5=9 r1c5<>9
r3c5=9 r1c5<>9
r3c6=9 r1c5<>9
Forcing Chain Verity => r3c3<>8
r3c2=9 r6c2<>9 r6c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r8c1=6 r8c3<>6 r3c3=6 r3c3<>8
r3c3=9 r3c3<>8
r3c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r8c1=6 r8c3<>6 r3c3=6 r3c3<>8
r3c6=9 r3c6<>4 r1c6=4 r1c6<>7 r1c5=7 r1c5<>8 r3c5=8 r3c3<>8
Forcing Chain Contradiction in r3c8 => r4c9<>8
r4c9=8 r4c13<>8 r6c2=8 r6c2<>9 r6c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r3c1=1 r3c8<>1
r4c9=8 r4c9<>5 r4c8=5 r3c8<>5
r4c9=8 r4c13<>8 r6c2=8 r2c2<>8 r2c79=8 r3c8<>8
Forcing Net Contradiction in c7 => r2c4=5
r2c4<>5 r2c4=9 r2c7<>9 r1c7=9 r1c7<>3
r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r2c7<>3
r2c4<>5 r2c4=9 (r2c6<>9 r2c6=3 r4c6<>3) r9c4<>9 r9c4=3 r4c4<>3 r4c9=3 r6c7<>3
Finned Swordfish: 5 r149 c189 fr1c7 => r3c89<>5
Hidden Single: r3c2=5
Naked Pair: 8,9 in r67c2 => r2c2<>8, r2c2<>9
Locked Candidates Type 1 (Pointing): 8 in b1 => r1c579<>8
Hidden Single: r3c5=8
Naked Single: r3c8=1
Naked Single: r3c1=6
Naked Single: r8c1=1
Naked Single: r8c2=3
Naked Single: r2c2=1
Naked Single: r8c4=7
Naked Single: r8c5=5
Naked Single: r7c5=9
Full House: r9c4=3
Full House: r4c4=9
Naked Single: r8c7=2
Full House: r8c3=6
Naked Single: r7c2=8
Full House: r6c2=9
Naked Single: r7c7=5
Naked Single: r9c3=9
Naked Single: r7c1=2
Full House: r7c3=7
Full House: r9c1=5
Naked Single: r3c3=3
Naked Single: r4c1=8
Full House: r1c1=9
Full House: r1c3=8
Full House: r4c3=2
Naked Single: r3c9=4
Full House: r3c6=9
Naked Single: r1c7=3
Naked Single: r2c6=3
Naked Single: r1c5=7
Full House: r1c6=4
Full House: r1c9=5
Full House: r4c6=7
Full House: r6c5=3
Naked Single: r2c9=8
Full House: r2c7=9
Full House: r6c7=8
Naked Single: r4c8=5
Full House: r4c9=3
Naked Single: r9c9=7
Full House: r6c9=1
Full House: r6c8=7
Full House: r9c8=8
|
sudoku_normal_extremely_hard_142
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
.2.1...6.7.4.6..2....2..7...6..1.4..37..4.6....5.........4...3......8..9.4..2.1..
|
928174365714563928653289714862917453371845692495632871287491536136758249549326187
|
. 2 . 1 . . . 6 .
7 . 4 . 6 . . 2 .
. . . 2 . . 7 . .
. 6 . . 1 . 4 . .
3 7 . . 4 . 6 . .
. . 5 . . . . . .
. . . 4 . . . 3 .
. . . . . 8 . . 9
. 4 . . 2 . 1 . .
|
9 2 8 1 7 4 3 6 5
7 1 4 5 6 3 9 2 8
6 5 3 2 8 9 7 1 4
8 6 2 9 1 7 4 5 3
3 7 1 8 4 5 6 9 2
4 9 5 6 3 2 8 7 1
2 8 7 4 9 1 5 3 6
1 3 6 7 5 8 2 4 9
5 4 9 3 2 6 1 8 7
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_7371_hard
|
928174365714563928653289714862917453371845692495632871287491536136758249549326187 #1 Extreme (25816) bf
Hidden Single: r6c1=4
Hidden Single: r8c8=4
Hidden Single: r7c6=1
Turbot Fish: 1 r2c9 =1= r2c2 -1- r6c2 =1= r5c3 => r5c9<>1
Brute Force: r5c8=9
Hidden Single: r5c3=1
Locked Candidates Type 1 (Pointing): 2 in b4 => r4c69<>2
Forcing Net Contradiction in r2 => r7c9<>5
r7c9=5 (r7c2<>5) (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r7c2<>8 r7c2=9 r6c2<>9 r6c2=8 r2c2<>8
r7c9=5 (r7c2<>5) (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r7c2<>8 r7c2=9 r6c2<>9 r6c2=8 r6c5<>8 r456c4=8 r2c4<>8
r7c9=5 (r7c7<>5) r8c7<>5 r8c7=2 r7c7<>2 r7c7=8 r2c7<>8
r7c9=5 (r5c9<>5) (r8c7<>5 r8c7=2 r6c7<>2) r7c9<>6 r9c9=6 r9c6<>6 r6c6=6 r6c6<>2 r6c9=2 r5c9<>2 r5c9=8 r2c9<>8
Brute Force: r5c9=2
Naked Single: r5c6=5
Full House: r5c4=8
Hidden Single: r6c6=2
Hidden Single: r6c4=6
Hidden Single: r9c6=6
Hidden Single: r7c9=6
Locked Candidates Type 1 (Pointing): 7 in b9 => r9c34<>7
Hidden Pair: 1,6 in r38c1 => r38c1<>5, r3c1<>8, r3c1<>9, r8c1<>2
Forcing Chain Contradiction in r1 => r2c4<>3
r2c4=3 r9c4<>3 r9c3=3 r1c3<>3
r2c4=3 r1c5<>3
r2c4=3 r1c6<>3
r2c4=3 r2c6<>3 r2c6=9 r2c7<>9 r1c7=9 r1c7<>3
r2c4=3 r123c6<>3 r4c6=3 r4c6<>7 r1c6=7 r1c6<>4 r1c9=4 r1c9<>3
Forcing Chain Contradiction in r1 => r9c4<>5
r9c4=5 r9c4<>3 r9c3=3 r1c3<>3
r9c4=5 r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r1c5<>3
r9c4=5 r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r1c6<>3
r9c4=5 r2c4<>5 r2c4=9 r2c7<>9 r1c7=9 r1c7<>3
r9c4=5 r2c4<>5 r2c4=9 r123c6<>9 r4c6=9 r4c6<>7 r1c6=7 r1c6<>4 r1c9=4 r1c9<>3
Forcing Chain Verity => r2c9<>5
r1c1=9 r1c7<>9 r2c7=9 r2c4<>9 r2c4=5 r2c9<>5
r4c1=9 r4c6<>9 r123c6=9 r2c4<>9 r2c4=5 r2c9<>5
r7c1=9 r7c5<>9 r9c4=9 r2c4<>9 r2c4=5 r2c9<>5
r9c1=9 r9c1<>5 r9c89=5 r78c7<>5 r12c7=5 r2c9<>5
Forcing Chain Contradiction in c7 => r8c2<>5
r8c2=5 r79c1<>5 r1c1=5 r1c7<>5
r8c2=5 r8c4<>5 r2c4=5 r2c7<>5
r8c2=5 r9c1<>5 r9c89=5 r7c7<>5
r8c2=5 r8c7<>5
Forcing Chain Verity => r1c5<>9
r3c2=9 r6c2<>9 r6c5=9 r1c5<>9
r3c3=9 r3c3<>6 r3c1=6 r3c1<>1 r8c1=1 r8c2<>1 r8c2=3 r9c3<>3 r9c4=3 r9c4<>9 r7c5=9 r1c5<>9
r3c5=9 r1c5<>9
r3c6=9 r1c5<>9
Forcing Chain Verity => r3c3<>8
r3c2=9 r6c2<>9 r6c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r8c1=6 r8c3<>6 r3c3=6 r3c3<>8
r3c3=9 r3c3<>8
r3c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r8c1=6 r8c3<>6 r3c3=6 r3c3<>8
r3c6=9 r3c6<>4 r1c6=4 r1c6<>7 r1c5=7 r1c5<>8 r3c5=8 r3c3<>8
Forcing Chain Contradiction in r3c8 => r4c9<>8
r4c9=8 r4c13<>8 r6c2=8 r6c2<>9 r6c5=9 r7c5<>9 r9c4=9 r9c4<>3 r9c3=3 r8c2<>3 r8c2=1 r8c1<>1 r3c1=1 r3c8<>1
r4c9=8 r4c9<>5 r4c8=5 r3c8<>5
r4c9=8 r4c13<>8 r6c2=8 r2c2<>8 r2c79=8 r3c8<>8
Forcing Net Contradiction in c7 => r2c4=5
r2c4<>5 r2c4=9 r2c7<>9 r1c7=9 r1c7<>3
r2c4<>5 r2c4=9 r2c6<>9 r2c6=3 r2c7<>3
r2c4<>5 r2c4=9 (r2c6<>9 r2c6=3 r4c6<>3) r9c4<>9 r9c4=3 r4c4<>3 r4c9=3 r6c7<>3
Finned Swordfish: 5 r149 c189 fr1c7 => r3c89<>5
Hidden Single: r3c2=5
Naked Pair: 8,9 in r67c2 => r2c2<>8, r2c2<>9
Locked Candidates Type 1 (Pointing): 8 in b1 => r1c579<>8
Hidden Single: r3c5=8
Naked Single: r3c8=1
Naked Single: r3c1=6
Naked Single: r8c1=1
Naked Single: r8c2=3
Naked Single: r2c2=1
Naked Single: r8c4=7
Naked Single: r8c5=5
Naked Single: r7c5=9
Full House: r9c4=3
Full House: r4c4=9
Naked Single: r8c7=2
Full House: r8c3=6
Naked Single: r7c2=8
Full House: r6c2=9
Naked Single: r7c7=5
Naked Single: r9c3=9
Naked Single: r7c1=2
Full House: r7c3=7
Full House: r9c1=5
Naked Single: r3c3=3
Naked Single: r4c1=8
Full House: r1c1=9
Full House: r1c3=8
Full House: r4c3=2
Naked Single: r3c9=4
Full House: r3c6=9
Naked Single: r1c7=3
Naked Single: r2c6=3
Naked Single: r1c5=7
Full House: r1c6=4
Full House: r1c9=5
Full House: r4c6=7
Full House: r6c5=3
Naked Single: r2c9=8
Full House: r2c7=9
Full House: r6c7=8
Naked Single: r4c8=5
Full House: r4c9=3
Naked Single: r9c9=7
Full House: r6c9=1
Full House: r6c8=7
Full House: r9c8=8
|
sudoku_normal_hard_143
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
1...8......9..76..65.2.....8..1.....32.458.....4..6..37......19.....43.8..3...7..
|
147689532239547681658231974875193246326458197914726853782365419561974328493812765
|
1 . . . 8 . . . .
. . 9 . . 7 6 . .
6 5 . 2 . . . . .
8 . . 1 . . . . .
3 2 . 4 5 8 . . .
. . 4 . . 6 . . 3
7 . . . . . . 1 9
. . . . . 4 3 . 8
. . 3 . . . 7 . .
|
1 4 7 6 8 9 5 3 2
2 3 9 5 4 7 6 8 1
6 5 8 2 3 1 9 7 4
8 7 5 1 9 3 2 4 6
3 2 6 4 5 8 1 9 7
9 1 4 7 2 6 8 5 3
7 8 2 3 6 5 4 1 9
5 6 1 9 7 4 3 2 8
4 9 3 8 1 2 7 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5980_hard
|
147689532239547681658231974875193246326458197914726853782365419561974328493812765 #1 Extreme (31762) bf
Brute Force: r5c4=4
Finned X-Wing: 4 r17 c27 fr1c8 fr1c9 => r3c7<>4
Forcing Chain Contradiction in c1 => r8c4<>6
r8c4=6 r1c4<>6 r3c5=6 r3c1<>6
r8c4=6 r8c4<>7 r6c4=7 r6c4<>8 r5c6=8 r5c6<>3 r5c1=3 r5c1<>6
r8c4=6 r8c1<>6
r8c4=6 r8c8<>6 r9c89=6 r9c1<>6
Brute Force: r5c6=8
Hidden Single: r5c1=3
Locked Candidates Type 2 (Claiming): 9 in r5 => r4c78,r6c78<>9
Grouped Discontinuous Nice Loop: 4 r2c8 -4- r1c789 =4= r1c2 =3= r2c2 =8= r2c8 => r2c8<>4
Grouped Discontinuous Nice Loop: 6 r9c4 -6- r1c4 =6= r3c5 -6- r3c1 =6= r89c1 -6- r7c23 =6= r7c45 -6- r9c4 => r9c4<>6
Forcing Chain Contradiction in c2 => r3c3<>6
r3c3=6 r3c3<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>7
r3c3=6 r45c3<>6 r4c2=6 r4c2<>7
r3c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Chain Contradiction in c2 => r8c3<>6
r8c3=6 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r3c7=8 r3c3<>8 r3c3=7 r1c2<>7
r8c3=6 r45c3<>6 r4c2=6 r4c2<>7
r8c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Chain Contradiction in r3c9 => r8c5<>1
r8c5=1 r2c5<>1 r2c9=1 r3c9<>1
r8c5=1 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r6c8=8 r2c8<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>4 r1c789=4 r3c9<>4
r8c5=1 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r3c7=8 r3c3<>8 r3c3=7 r3c9<>7
Locked Candidates Type 1 (Pointing): 1 in b8 => r9c2<>1
Forcing Net Verity => r1c2<>6
r8c2=1 r6c2<>1 r6c7=1 r6c7<>8 r6c8=8 r2c8<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>6
r8c2=6 r1c2<>6
r8c2=9 (r8c4<>9) (r8c1<>9) r9c1<>9 r6c1=9 r6c4<>9 r6c4=7 r8c4<>7 r8c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>6
Forcing Chain Contradiction in c2 => r1c4<>5
r1c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7
r1c4=5 r1c4<>6 r1c3=6 r45c3<>6 r4c2=6 r4c2<>7
r1c4=5 r1c4<>6 r1c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Net Verity => r1c4=6
r8c2=1 r6c2<>1 r6c7=1 (r6c7<>5) r6c7<>8 (r3c7=8 r3c3<>8 r3c3=7 r4c3<>7) r6c8=8 r6c8<>5 r6c1=5 r4c3<>5 r4c3=6 r1c3<>6 r1c4=6
r8c2=6 (r8c1<>6) r9c1<>6 r3c1=6 r1c3<>6 r1c4=6
r8c2=9 (r8c2<>1 r6c2=1 r6c2<>7) (r8c4<>9) (r8c1<>9) r9c1<>9 r6c1=9 r6c4<>9 r6c4=7 r8c4<>7 r8c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7 r4c2=7 r4c2<>6 r45c3=6 r1c3<>6 r1c4=6
Hidden Single: r3c1=6
Discontinuous Nice Loop: 2 r8c3 -2- r1c3 -7- r3c3 -8- r3c7 =8= r6c7 =1= r6c2 -1- r8c2 =1= r8c3 => r8c3<>2
Forcing Chain Contradiction in r3c7 => r3c5<>9
r3c5=9 r3c5<>4 r2c5=4 r2c5<>1 r2c9=1 r3c7<>1
r3c5=9 r3c5<>4 r2c5=4 r2c1<>4 r2c1=2 r1c3<>2 r1c3=7 r3c3<>7 r3c3=8 r3c7<>8
r3c5=9 r3c7<>9
Locked Candidates Type 1 (Pointing): 9 in b2 => r49c6<>9
Forcing Chain Contradiction in c5 => r6c8<>7
r6c8=7 r5c89<>7 r5c3=7 r46c2<>7 r1c2=7 r1c2<>3 r2c2=3 r2c5<>3
r6c8=7 r5c89<>7 r5c3=7 r1c3<>7 r1c3=2 r2c1<>2 r2c1=4 r2c5<>4 r3c5=4 r3c5<>3
r6c8=7 r6c45<>7 r4c5=7 r4c5<>3
r6c8=7 r5c89<>7 r5c3=7 r46c2<>7 r1c2=7 r1c2<>3 r2c2=3 r2c4<>3 r7c4=3 r7c5<>3
Forcing Chain Contradiction in c2 => r7c6<>3
r7c6=3 r7c4<>3 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7
r7c6=3 r4c6<>3 r4c5=3 r4c5<>9 r4c2=9 r4c2<>7
r7c6=3 r4c6<>3 r4c5=3 r4c5<>7 r6c45=7 r6c2<>7
Forcing Chain Contradiction in r2c2 => r9c4=8
r9c4<>8 r7c4=8 r7c4<>3 r2c4=3 r2c2<>3
r9c4<>8 r7c4=8 r7c4<>3 r2c4=3 r2c4<>5 r1c6=5 r7c6<>5 r7c6=2 r7c3<>2 r1c3=2 r2c1<>2 r2c1=4 r2c2<>4
r9c4<>8 r9c2=8 r2c2<>8
Naked Pair: 3,5 in r27c4 => r8c4<>5
2-String Kite: 9 in r4c2,r8c4 (connected by r4c5,r6c4) => r8c2<>9
Discontinuous Nice Loop: 6 r7c3 -6- r8c2 -1- r6c2 =1= r6c7 =8= r3c7 -8- r3c3 =8= r7c3 => r7c3<>6
Locked Candidates Type 1 (Pointing): 6 in b7 => r4c2<>6
Almost Locked Set XY-Wing: A=r6c1245 {12579}, B=r7c23467 {234568}, C=r8c2 {16}, X,Y=1,6, Z=2 => r7c5<>2
Forcing Chain Contradiction in r1c7 => r2c4=5
r2c4<>5 r7c4=5 r7c6<>5 r7c6=2 r7c3<>2 r1c3=2 r1c7<>2
r2c4<>5 r2c4=3 r7c4<>3 r7c5=3 r7c5<>6 r7c2=6 r7c2<>4 r7c7=4 r1c7<>4
r2c4<>5 r1c6=5 r1c7<>5
r2c4<>5 r2c4=3 r7c4<>3 r7c5=3 r7c5<>6 r7c2=6 r8c2<>6 r8c2=1 r8c3<>1 r5c3=1 r5c7<>1 r5c7=9 r1c7<>9
Naked Single: r7c4=3
Naked Single: r7c5=6
Uniqueness Test 2: 7/9 in r6c45,r8c45 => r49c5<>2
Discontinuous Nice Loop: 9 r6c5 -9- r6c4 -7- r8c4 =7= r8c5 =2= r6c5 => r6c5<>9
Almost Locked Set XY-Wing: A=r1c6 {39}, B=r35c7 {189}, C=r1c23,r2c1,r3c3 {23478}, X,Y=3,8, Z=9 => r1c7<>9
Naked Triple: 2,4,5 in r147c7 => r6c7<>2, r6c7<>5
Finned X-Wing: 5 r68 c18 fr8c3 => r9c1<>5
Finned Swordfish: 2 r268 c158 fr2c9 => r1c8<>2
Almost Locked Set XY-Wing: A=r4c25 {379}, B=r137c3 {2578}, C=r47c6 {235}, X,Y=3,5, Z=7 => r4c3<>7
Forcing Chain Contradiction in r8c8 => r1c6=9
r1c6<>9 r1c6=3 r4c6<>3 r4c6=2 r6c5<>2 r6c8=2 r8c8<>2
r1c6<>9 r3c6=9 r3c6<>1 r9c6=1 r9c6<>5 r9c89=5 r8c8<>5
r1c6<>9 r1c6=3 r1c2<>3 r2c2=3 r2c2<>8 r2c8=8 r6c8<>8 r6c7=8 r6c7<>1 r6c2=1 r8c2<>1 r8c2=6 r8c8<>6
Almost Locked Set Chain: 2- r2c1259 {12348} -8- r3c3 {78} -7- r1c23,r2c1 {2347} -3- r1c789,r23c9 {123457} -2 => r2c8<>2
AIC: 8 8- r2c8 =8= r2c2 -8- r7c2 -4- r9c1 =4= r2c1 =2= r2c9 =1= r2c5 -1- r3c6 -3- r4c6 -2- r6c5 =2= r6c8 =8= r6c7 -8 => r3c7,r6c8<>8
Hidden Single: r6c7=8
Hidden Single: r6c2=1
Naked Single: r8c2=6
Hidden Single: r8c3=1
Locked Candidates Type 2 (Claiming): 7 in r6 => r4c5<>7
Naked Pair: 2,5 in r68c8 => r149c8<>5, r49c8<>2
Hidden Pair: 2,7 in r68c5 => r8c5<>9
X-Wing: 2 c58 r68 => r8c1<>2
Naked Pair: 5,9 in r68c1 => r9c1<>9
W-Wing: 2/5 in r7c6,r8c8 connected by 5 in r9c69 => r7c7,r8c5<>2
Naked Single: r8c5=7
Naked Single: r6c5=2
Naked Single: r8c4=9
Full House: r6c4=7
Naked Single: r4c6=3
Full House: r4c5=9
Naked Single: r6c8=5
Full House: r6c1=9
Naked Single: r8c1=5
Full House: r8c8=2
Naked Single: r9c5=1
Naked Single: r3c6=1
Naked Single: r4c2=7
Naked Single: r3c7=9
Naked Single: r5c3=6
Full House: r4c3=5
Naked Single: r5c7=1
Naked Single: r5c9=7
Full House: r5c8=9
Naked Single: r3c9=4
Naked Single: r3c5=3
Full House: r2c5=4
Naked Single: r2c1=2
Full House: r9c1=4
Naked Single: r1c3=7
Naked Single: r2c9=1
Naked Single: r7c2=8
Naked Single: r9c2=9
Full House: r7c3=2
Full House: r3c3=8
Full House: r3c8=7
Naked Single: r9c8=6
Naked Single: r1c8=3
Naked Single: r2c2=3
Full House: r1c2=4
Full House: r2c8=8
Full House: r4c8=4
Naked Single: r7c6=5
Full House: r7c7=4
Full House: r9c9=5
Full House: r9c6=2
Naked Single: r4c7=2
Full House: r1c7=5
Full House: r1c9=2
Full House: r4c9=6
|
sudoku_normal_extremely_hard_143
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
1...8......9..76...5.2.....8..1......2..5......4..6..37......19.....43.8..3...7..
|
147689532239547681658231974875193246326458197914726853782365419561974328493812765
|
1 . . . 8 . . . .
. . 9 . . 7 6 . .
. 5 . 2 . . . . .
8 . . 1 . . . . .
. 2 . . 5 . . . .
. . 4 . . 6 . . 3
7 . . . . . . 1 9
. . . . . 4 3 . 8
. . 3 . . . 7 . .
|
1 4 7 6 8 9 5 3 2
2 3 9 5 4 7 6 8 1
6 5 8 2 3 1 9 7 4
8 7 5 1 9 3 2 4 6
3 2 6 4 5 8 1 9 7
9 1 4 7 2 6 8 5 3
7 8 2 3 6 5 4 1 9
5 6 1 9 7 4 3 2 8
4 9 3 8 1 2 7 6 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5980_hard
|
147689532239547681658231974875193246326458197914726853782365419561974328493812765 #1 Extreme (31762) bf
Brute Force: r5c4=4
Finned X-Wing: 4 r17 c27 fr1c8 fr1c9 => r3c7<>4
Forcing Chain Contradiction in c1 => r8c4<>6
r8c4=6 r1c4<>6 r3c5=6 r3c1<>6
r8c4=6 r8c4<>7 r6c4=7 r6c4<>8 r5c6=8 r5c6<>3 r5c1=3 r5c1<>6
r8c4=6 r8c1<>6
r8c4=6 r8c8<>6 r9c89=6 r9c1<>6
Brute Force: r5c6=8
Hidden Single: r5c1=3
Locked Candidates Type 2 (Claiming): 9 in r5 => r4c78,r6c78<>9
Grouped Discontinuous Nice Loop: 4 r2c8 -4- r1c789 =4= r1c2 =3= r2c2 =8= r2c8 => r2c8<>4
Grouped Discontinuous Nice Loop: 6 r9c4 -6- r1c4 =6= r3c5 -6- r3c1 =6= r89c1 -6- r7c23 =6= r7c45 -6- r9c4 => r9c4<>6
Forcing Chain Contradiction in c2 => r3c3<>6
r3c3=6 r3c3<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>7
r3c3=6 r45c3<>6 r4c2=6 r4c2<>7
r3c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Chain Contradiction in c2 => r8c3<>6
r8c3=6 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r3c7=8 r3c3<>8 r3c3=7 r1c2<>7
r8c3=6 r45c3<>6 r4c2=6 r4c2<>7
r8c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Chain Contradiction in r3c9 => r8c5<>1
r8c5=1 r2c5<>1 r2c9=1 r3c9<>1
r8c5=1 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r6c8=8 r2c8<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>4 r1c789=4 r3c9<>4
r8c5=1 r8c3<>1 r5c3=1 r6c2<>1 r6c7=1 r6c7<>8 r3c7=8 r3c3<>8 r3c3=7 r3c9<>7
Locked Candidates Type 1 (Pointing): 1 in b8 => r9c2<>1
Forcing Net Verity => r1c2<>6
r8c2=1 r6c2<>1 r6c7=1 r6c7<>8 r6c8=8 r2c8<>8 r2c2=8 r2c2<>3 r1c2=3 r1c2<>6
r8c2=6 r1c2<>6
r8c2=9 (r8c4<>9) (r8c1<>9) r9c1<>9 r6c1=9 r6c4<>9 r6c4=7 r8c4<>7 r8c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>6
Forcing Chain Contradiction in c2 => r1c4<>5
r1c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7
r1c4=5 r1c4<>6 r1c3=6 r45c3<>6 r4c2=6 r4c2<>7
r1c4=5 r1c4<>6 r1c3=6 r45c3<>6 r4c2=6 r4c2<>9 r4c56=9 r6c4<>9 r6c4=7 r6c2<>7
Forcing Net Verity => r1c4=6
r8c2=1 r6c2<>1 r6c7=1 (r6c7<>5) r6c7<>8 (r3c7=8 r3c3<>8 r3c3=7 r4c3<>7) r6c8=8 r6c8<>5 r6c1=5 r4c3<>5 r4c3=6 r1c3<>6 r1c4=6
r8c2=6 (r8c1<>6) r9c1<>6 r3c1=6 r1c3<>6 r1c4=6
r8c2=9 (r8c2<>1 r6c2=1 r6c2<>7) (r8c4<>9) (r8c1<>9) r9c1<>9 r6c1=9 r6c4<>9 r6c4=7 r8c4<>7 r8c4=5 r2c4<>5 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7 r4c2=7 r4c2<>6 r45c3=6 r1c3<>6 r1c4=6
Hidden Single: r3c1=6
Discontinuous Nice Loop: 2 r8c3 -2- r1c3 -7- r3c3 -8- r3c7 =8= r6c7 =1= r6c2 -1- r8c2 =1= r8c3 => r8c3<>2
Forcing Chain Contradiction in r3c7 => r3c5<>9
r3c5=9 r3c5<>4 r2c5=4 r2c5<>1 r2c9=1 r3c7<>1
r3c5=9 r3c5<>4 r2c5=4 r2c1<>4 r2c1=2 r1c3<>2 r1c3=7 r3c3<>7 r3c3=8 r3c7<>8
r3c5=9 r3c7<>9
Locked Candidates Type 1 (Pointing): 9 in b2 => r49c6<>9
Forcing Chain Contradiction in c5 => r6c8<>7
r6c8=7 r5c89<>7 r5c3=7 r46c2<>7 r1c2=7 r1c2<>3 r2c2=3 r2c5<>3
r6c8=7 r5c89<>7 r5c3=7 r1c3<>7 r1c3=2 r2c1<>2 r2c1=4 r2c5<>4 r3c5=4 r3c5<>3
r6c8=7 r6c45<>7 r4c5=7 r4c5<>3
r6c8=7 r5c89<>7 r5c3=7 r46c2<>7 r1c2=7 r1c2<>3 r2c2=3 r2c4<>3 r7c4=3 r7c5<>3
Forcing Chain Contradiction in c2 => r7c6<>3
r7c6=3 r7c4<>3 r2c4=3 r2c2<>3 r1c2=3 r1c2<>7
r7c6=3 r4c6<>3 r4c5=3 r4c5<>9 r4c2=9 r4c2<>7
r7c6=3 r4c6<>3 r4c5=3 r4c5<>7 r6c45=7 r6c2<>7
Forcing Chain Contradiction in r2c2 => r9c4=8
r9c4<>8 r7c4=8 r7c4<>3 r2c4=3 r2c2<>3
r9c4<>8 r7c4=8 r7c4<>3 r2c4=3 r2c4<>5 r1c6=5 r7c6<>5 r7c6=2 r7c3<>2 r1c3=2 r2c1<>2 r2c1=4 r2c2<>4
r9c4<>8 r9c2=8 r2c2<>8
Naked Pair: 3,5 in r27c4 => r8c4<>5
2-String Kite: 9 in r4c2,r8c4 (connected by r4c5,r6c4) => r8c2<>9
Discontinuous Nice Loop: 6 r7c3 -6- r8c2 -1- r6c2 =1= r6c7 =8= r3c7 -8- r3c3 =8= r7c3 => r7c3<>6
Locked Candidates Type 1 (Pointing): 6 in b7 => r4c2<>6
Almost Locked Set XY-Wing: A=r6c1245 {12579}, B=r7c23467 {234568}, C=r8c2 {16}, X,Y=1,6, Z=2 => r7c5<>2
Forcing Chain Contradiction in r1c7 => r2c4=5
r2c4<>5 r7c4=5 r7c6<>5 r7c6=2 r7c3<>2 r1c3=2 r1c7<>2
r2c4<>5 r2c4=3 r7c4<>3 r7c5=3 r7c5<>6 r7c2=6 r7c2<>4 r7c7=4 r1c7<>4
r2c4<>5 r1c6=5 r1c7<>5
r2c4<>5 r2c4=3 r7c4<>3 r7c5=3 r7c5<>6 r7c2=6 r8c2<>6 r8c2=1 r8c3<>1 r5c3=1 r5c7<>1 r5c7=9 r1c7<>9
Naked Single: r7c4=3
Naked Single: r7c5=6
Uniqueness Test 2: 7/9 in r6c45,r8c45 => r49c5<>2
Discontinuous Nice Loop: 9 r6c5 -9- r6c4 -7- r8c4 =7= r8c5 =2= r6c5 => r6c5<>9
Almost Locked Set XY-Wing: A=r1c6 {39}, B=r35c7 {189}, C=r1c23,r2c1,r3c3 {23478}, X,Y=3,8, Z=9 => r1c7<>9
Naked Triple: 2,4,5 in r147c7 => r6c7<>2, r6c7<>5
Finned X-Wing: 5 r68 c18 fr8c3 => r9c1<>5
Finned Swordfish: 2 r268 c158 fr2c9 => r1c8<>2
Almost Locked Set XY-Wing: A=r4c25 {379}, B=r137c3 {2578}, C=r47c6 {235}, X,Y=3,5, Z=7 => r4c3<>7
Forcing Chain Contradiction in r8c8 => r1c6=9
r1c6<>9 r1c6=3 r4c6<>3 r4c6=2 r6c5<>2 r6c8=2 r8c8<>2
r1c6<>9 r3c6=9 r3c6<>1 r9c6=1 r9c6<>5 r9c89=5 r8c8<>5
r1c6<>9 r1c6=3 r1c2<>3 r2c2=3 r2c2<>8 r2c8=8 r6c8<>8 r6c7=8 r6c7<>1 r6c2=1 r8c2<>1 r8c2=6 r8c8<>6
Almost Locked Set Chain: 2- r2c1259 {12348} -8- r3c3 {78} -7- r1c23,r2c1 {2347} -3- r1c789,r23c9 {123457} -2 => r2c8<>2
AIC: 8 8- r2c8 =8= r2c2 -8- r7c2 -4- r9c1 =4= r2c1 =2= r2c9 =1= r2c5 -1- r3c6 -3- r4c6 -2- r6c5 =2= r6c8 =8= r6c7 -8 => r3c7,r6c8<>8
Hidden Single: r6c7=8
Hidden Single: r6c2=1
Naked Single: r8c2=6
Hidden Single: r8c3=1
Locked Candidates Type 2 (Claiming): 7 in r6 => r4c5<>7
Naked Pair: 2,5 in r68c8 => r149c8<>5, r49c8<>2
Hidden Pair: 2,7 in r68c5 => r8c5<>9
X-Wing: 2 c58 r68 => r8c1<>2
Naked Pair: 5,9 in r68c1 => r9c1<>9
W-Wing: 2/5 in r7c6,r8c8 connected by 5 in r9c69 => r7c7,r8c5<>2
Naked Single: r8c5=7
Naked Single: r6c5=2
Naked Single: r8c4=9
Full House: r6c4=7
Naked Single: r4c6=3
Full House: r4c5=9
Naked Single: r6c8=5
Full House: r6c1=9
Naked Single: r8c1=5
Full House: r8c8=2
Naked Single: r9c5=1
Naked Single: r3c6=1
Naked Single: r4c2=7
Naked Single: r3c7=9
Naked Single: r5c3=6
Full House: r4c3=5
Naked Single: r5c7=1
Naked Single: r5c9=7
Full House: r5c8=9
Naked Single: r3c9=4
Naked Single: r3c5=3
Full House: r2c5=4
Naked Single: r2c1=2
Full House: r9c1=4
Naked Single: r1c3=7
Naked Single: r2c9=1
Naked Single: r7c2=8
Naked Single: r9c2=9
Full House: r7c3=2
Full House: r3c3=8
Full House: r3c8=7
Naked Single: r9c8=6
Naked Single: r1c8=3
Naked Single: r2c2=3
Full House: r1c2=4
Full House: r2c8=8
Full House: r4c8=4
Naked Single: r7c6=5
Full House: r7c7=4
Full House: r9c9=5
Full House: r9c6=2
Naked Single: r4c7=2
Full House: r1c7=5
Full House: r1c9=2
Full House: r4c9=6
|
sudoku_normal_hard_144
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
2.8.6...419.8.4..2.....2.8.78.24.5.6...35847..4.7.6.28...42...7..7.8.24....6.7..5
|
278963154195874632436512789783241596962358471541796328319425867657189243824637915
|
2 . 8 . 6 . . . 4
1 9 . 8 . 4 . . 2
. . . . . 2 . 8 .
7 8 . 2 4 . 5 . 6
. . . 3 5 8 4 7 .
. 4 . 7 . 6 . 2 8
. . . 4 2 . . . 7
. . 7 . 8 . 2 4 .
. . . 6 . 7 . . 5
|
2 7 8 9 6 3 1 5 4
1 9 5 8 7 4 6 3 2
4 3 6 5 1 2 7 8 9
7 8 3 2 4 1 5 9 6
9 6 2 3 5 8 4 7 1
5 4 1 7 9 6 3 2 8
3 1 9 4 2 5 8 6 7
6 5 7 1 8 9 2 4 3
8 2 4 6 3 7 9 1 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4137_hard
|
278963154195874632436512789783241596962358471541796328319425867657189243824637915 #1 Extreme (15614) bf
Hidden Single: r1c3=8
Hidden Single: r3c6=2
Hidden Single: r5c6=8
Hidden Single: r2c9=2
Hidden Single: r4c5=4
Hidden Single: r5c7=4
Hidden Single: r6c9=8
Hidden Single: r7c4=4
Hidden Single: r5c8=7
Locked Candidates Type 1 (Pointing): 6 in b9 => r7c123<>6
Brute Force: r5c4=3
Forcing Net Contradiction in r2c5 => r6c1<>9
r6c1=9 (r6c1<>5 r6c3=5 r2c3<>5 r2c8=5 r2c8<>3) (r6c7<>9) r6c5<>9 r6c5=1 r6c7<>1 r6c7=3 (r2c7<>3) r4c8<>3 r4c3=3 r2c3<>3 r2c5=3
r6c1=9 (r6c5<>9) (r8c1<>9) (r4c3<>9) (r5c1<>9) r5c3<>9 r5c9=9 (r8c9<>9) r4c8<>9 r4c6=9 r8c6<>9 r8c4=9 r9c5<>9 r3c5=9 r3c5<>7 r2c5=7
Forcing Net Contradiction in r2 => r7c8<>3
r7c8=3 (r4c8<>3 r4c3=3 r6c3<>3 r6c7=3 r2c7<>3) r7c8<>6 r7c7=6 r2c7<>6 r2c7=7 r3c7<>7 r3c2=7 r3c5<>7 r2c5=7
r7c8=3 (r4c8<>3 r4c3=3 r6c3<>3 r6c7=3 r2c7<>3) r7c8<>6 r7c7=6 r2c7<>6 r2c7=7
Forcing Net Contradiction in r8c1 => r3c5<>9
r3c5=9 (r3c5<>7 r2c5=7 r2c5<>3) (r6c5<>9 r6c5=1 r6c7<>1) (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 (r8c6<>9 r4c6=9 r4c3<>9) r8c9<>9 r5c9=9 (r6c7<>9 r6c7=3 r2c7<>3) r5c9<>1 r4c8=1 r4c3<>1 r4c3=3 r2c3<>3 r2c8=3 r3c9<>3 r8c9=3 r8c1<>3
r3c5=9 (r6c5<>9 r6c5=1 r6c7<>1) (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 r8c9<>9 r5c9=9 r6c7<>9 r6c7=3 r6c1<>3 r6c1=5 r8c1<>5
r3c5=9 (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 r8c9<>9 r5c9=9 r5c1<>9 r5c1=6 r8c1<>6
r3c5=9 (r1c4<>9) r3c4<>9 r8c4=9 r8c1<>9
Forcing Net Verity => r8c9=3
r1c2=3 (r1c6<>3) r1c2<>7 r1c7=7 r2c7<>7 r2c5=7 r2c5<>3 r3c5=3 r3c9<>3 r8c9=3
r1c6=3 (r2c5<>3) (r3c5<>3 r9c5=3 r9c5<>9 r6c5=9 r4c6<>9 r4c6=1 r4c3<>1) (r3c5<>3 r9c5=3 r9c5<>9 r6c5=9 r6c7<>9) (r3c5<>3) r2c5<>3 r2c5=7 r3c5<>7 r3c5=1 (r3c9<>1) (r1c4<>1) r3c4<>1 r8c4=1 r8c9<>1 r5c9=1 (r6c7<>1 r6c7=3 r2c7<>3) r5c9<>9 r4c8=9 r4c3<>9 r4c3=3 r2c3<>3 r2c8=3 r3c9<>3 r8c9=3
r1c7=3 r3c9<>3 r8c9=3
r1c8=3 r3c9<>3 r8c9=3
W-Wing: 1/9 in r4c6,r9c8 connected by 9 in r69c5 => r4c8<>1
Discontinuous Nice Loop: 1 r7c6 -1- r4c6 -9- r6c5 =9= r9c5 =3= r7c6 => r7c6<>1
Grouped Discontinuous Nice Loop: 9 r6c3 -9- r6c5 -1- r6c7 =1= r5c9 =9= r5c13 -9- r6c3 => r6c3<>9
Forcing Chain Contradiction in c5 => r3c9=9
r3c9<>9 r3c9=1 r3c5<>1
r3c9<>9 r3c9=1 r5c9<>1 r6c7=1 r6c5<>1
r3c9<>9 r5c9=9 r5c1<>9 r5c1=6 r8c1<>6 r8c2=6 r8c2<>1 r8c46=1 r9c5<>1
Full House: r5c9=1
Locked Candidates Type 1 (Pointing): 1 in b4 => r79c3<>1
Locked Candidates Type 2 (Claiming): 9 in r5 => r4c3<>9
2-String Kite: 9 in r4c8,r9c5 (connected by r4c6,r6c5) => r9c8<>9
Naked Single: r9c8=1
Hidden Single: r7c2=1
Hidden Rectangle: 8/9 in r7c17,r9c17 => r7c1<>9
XY-Chain: 5 5- r1c8 -3- r4c8 -9- r4c6 -1- r6c5 -9- r9c5 -3- r9c2 -2- r5c2 -6- r8c2 -5 => r1c2<>5
XY-Chain: 9 9- r5c1 -6- r5c2 -2- r9c2 -3- r9c5 -9 => r9c1<>9
AIC: 5 5- r2c3 =5= r2c8 =6= r7c8 =9= r4c8 -9- r4c6 -1- r8c6 =1= r8c4 -1- r3c4 -5 => r3c123<>5
Hidden Single: r8c2=5
Hidden Single: r3c4=5
Hidden Single: r2c3=5
Hidden Single: r7c6=5
Hidden Single: r6c1=5
Hidden Single: r8c1=6
Naked Single: r5c1=9
Hidden Single: r1c8=5
Hidden Single: r1c6=3
Naked Single: r1c2=7
Naked Single: r2c5=7
Naked Single: r1c7=1
Full House: r1c4=9
Full House: r3c5=1
Full House: r8c4=1
Full House: r8c6=9
Full House: r4c6=1
Full House: r6c5=9
Full House: r9c5=3
Naked Single: r4c3=3
Full House: r4c8=9
Full House: r6c7=3
Full House: r6c3=1
Naked Single: r9c2=2
Naked Single: r7c3=9
Naked Single: r7c8=6
Full House: r2c8=3
Full House: r2c7=6
Full House: r3c7=7
Naked Single: r5c2=6
Full House: r3c2=3
Full House: r5c3=2
Naked Single: r9c3=4
Full House: r3c3=6
Full House: r3c1=4
Naked Single: r7c7=8
Full House: r7c1=3
Full House: r9c1=8
Full House: r9c7=9
|
sudoku_normal_extremely_hard_144
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
2...6...419.8.4..........8.78.2..5.6....5.....4.7.6.2.....2...7..7.8.24....6.7..5
|
278963154195874632436512789783241596962358471541796328319425867657189243824637915
|
2 . . . 6 . . . 4
1 9 . 8 . 4 . . .
. . . . . . . 8 .
7 8 . 2 . . 5 . 6
. . . . 5 . . . .
. 4 . 7 . 6 . 2 .
. . . . 2 . . . 7
. . 7 . 8 . 2 4 .
. . . 6 . 7 . . 5
|
2 7 8 9 6 3 1 5 4
1 9 5 8 7 4 6 3 2
4 3 6 5 1 2 7 8 9
7 8 3 2 4 1 5 9 6
9 6 2 3 5 8 4 7 1
5 4 1 7 9 6 3 2 8
3 1 9 4 2 5 8 6 7
6 5 7 1 8 9 2 4 3
8 2 4 6 3 7 9 1 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4137_hard
|
278963154195874632436512789783241596962358471541796328319425867657189243824637915 #1 Extreme (15614) bf
Hidden Single: r1c3=8
Hidden Single: r3c6=2
Hidden Single: r5c6=8
Hidden Single: r2c9=2
Hidden Single: r4c5=4
Hidden Single: r5c7=4
Hidden Single: r6c9=8
Hidden Single: r7c4=4
Hidden Single: r5c8=7
Locked Candidates Type 1 (Pointing): 6 in b9 => r7c123<>6
Brute Force: r5c4=3
Forcing Net Contradiction in r2c5 => r6c1<>9
r6c1=9 (r6c1<>5 r6c3=5 r2c3<>5 r2c8=5 r2c8<>3) (r6c7<>9) r6c5<>9 r6c5=1 r6c7<>1 r6c7=3 (r2c7<>3) r4c8<>3 r4c3=3 r2c3<>3 r2c5=3
r6c1=9 (r6c5<>9) (r8c1<>9) (r4c3<>9) (r5c1<>9) r5c3<>9 r5c9=9 (r8c9<>9) r4c8<>9 r4c6=9 r8c6<>9 r8c4=9 r9c5<>9 r3c5=9 r3c5<>7 r2c5=7
Forcing Net Contradiction in r2 => r7c8<>3
r7c8=3 (r4c8<>3 r4c3=3 r6c3<>3 r6c7=3 r2c7<>3) r7c8<>6 r7c7=6 r2c7<>6 r2c7=7 r3c7<>7 r3c2=7 r3c5<>7 r2c5=7
r7c8=3 (r4c8<>3 r4c3=3 r6c3<>3 r6c7=3 r2c7<>3) r7c8<>6 r7c7=6 r2c7<>6 r2c7=7
Forcing Net Contradiction in r8c1 => r3c5<>9
r3c5=9 (r3c5<>7 r2c5=7 r2c5<>3) (r6c5<>9 r6c5=1 r6c7<>1) (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 (r8c6<>9 r4c6=9 r4c3<>9) r8c9<>9 r5c9=9 (r6c7<>9 r6c7=3 r2c7<>3) r5c9<>1 r4c8=1 r4c3<>1 r4c3=3 r2c3<>3 r2c8=3 r3c9<>3 r8c9=3 r8c1<>3
r3c5=9 (r6c5<>9 r6c5=1 r6c7<>1) (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 r8c9<>9 r5c9=9 r6c7<>9 r6c7=3 r6c1<>3 r6c1=5 r8c1<>5
r3c5=9 (r3c9<>9) (r1c4<>9) r3c4<>9 r8c4=9 r8c9<>9 r5c9=9 r5c1<>9 r5c1=6 r8c1<>6
r3c5=9 (r1c4<>9) r3c4<>9 r8c4=9 r8c1<>9
Forcing Net Verity => r8c9=3
r1c2=3 (r1c6<>3) r1c2<>7 r1c7=7 r2c7<>7 r2c5=7 r2c5<>3 r3c5=3 r3c9<>3 r8c9=3
r1c6=3 (r2c5<>3) (r3c5<>3 r9c5=3 r9c5<>9 r6c5=9 r4c6<>9 r4c6=1 r4c3<>1) (r3c5<>3 r9c5=3 r9c5<>9 r6c5=9 r6c7<>9) (r3c5<>3) r2c5<>3 r2c5=7 r3c5<>7 r3c5=1 (r3c9<>1) (r1c4<>1) r3c4<>1 r8c4=1 r8c9<>1 r5c9=1 (r6c7<>1 r6c7=3 r2c7<>3) r5c9<>9 r4c8=9 r4c3<>9 r4c3=3 r2c3<>3 r2c8=3 r3c9<>3 r8c9=3
r1c7=3 r3c9<>3 r8c9=3
r1c8=3 r3c9<>3 r8c9=3
W-Wing: 1/9 in r4c6,r9c8 connected by 9 in r69c5 => r4c8<>1
Discontinuous Nice Loop: 1 r7c6 -1- r4c6 -9- r6c5 =9= r9c5 =3= r7c6 => r7c6<>1
Grouped Discontinuous Nice Loop: 9 r6c3 -9- r6c5 -1- r6c7 =1= r5c9 =9= r5c13 -9- r6c3 => r6c3<>9
Forcing Chain Contradiction in c5 => r3c9=9
r3c9<>9 r3c9=1 r3c5<>1
r3c9<>9 r3c9=1 r5c9<>1 r6c7=1 r6c5<>1
r3c9<>9 r5c9=9 r5c1<>9 r5c1=6 r8c1<>6 r8c2=6 r8c2<>1 r8c46=1 r9c5<>1
Full House: r5c9=1
Locked Candidates Type 1 (Pointing): 1 in b4 => r79c3<>1
Locked Candidates Type 2 (Claiming): 9 in r5 => r4c3<>9
2-String Kite: 9 in r4c8,r9c5 (connected by r4c6,r6c5) => r9c8<>9
Naked Single: r9c8=1
Hidden Single: r7c2=1
Hidden Rectangle: 8/9 in r7c17,r9c17 => r7c1<>9
XY-Chain: 5 5- r1c8 -3- r4c8 -9- r4c6 -1- r6c5 -9- r9c5 -3- r9c2 -2- r5c2 -6- r8c2 -5 => r1c2<>5
XY-Chain: 9 9- r5c1 -6- r5c2 -2- r9c2 -3- r9c5 -9 => r9c1<>9
AIC: 5 5- r2c3 =5= r2c8 =6= r7c8 =9= r4c8 -9- r4c6 -1- r8c6 =1= r8c4 -1- r3c4 -5 => r3c123<>5
Hidden Single: r8c2=5
Hidden Single: r3c4=5
Hidden Single: r2c3=5
Hidden Single: r7c6=5
Hidden Single: r6c1=5
Hidden Single: r8c1=6
Naked Single: r5c1=9
Hidden Single: r1c8=5
Hidden Single: r1c6=3
Naked Single: r1c2=7
Naked Single: r2c5=7
Naked Single: r1c7=1
Full House: r1c4=9
Full House: r3c5=1
Full House: r8c4=1
Full House: r8c6=9
Full House: r4c6=1
Full House: r6c5=9
Full House: r9c5=3
Naked Single: r4c3=3
Full House: r4c8=9
Full House: r6c7=3
Full House: r6c3=1
Naked Single: r9c2=2
Naked Single: r7c3=9
Naked Single: r7c8=6
Full House: r2c8=3
Full House: r2c7=6
Full House: r3c7=7
Naked Single: r5c2=6
Full House: r3c2=3
Full House: r5c3=2
Naked Single: r9c3=4
Full House: r3c3=6
Full House: r3c1=4
Naked Single: r7c7=8
Full House: r7c1=3
Full House: r9c1=8
Full House: r9c7=9
|
sudoku_normal_hard_145
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8..6..32..35......5.4..1....2..7.1.6.4198.55.1.7..4.1...9...7..9...1.4.5.....9.
|
948126573216357489375948612894265731763419825521873946182594367639782154457631298
|
. . 8 . . 6 . . 3
2 . . 3 5 . . . .
. . 5 . 4 . . 1 .
. . . 2 . . 7 . 1
. 6 . 4 1 9 8 . 5
5 . 1 . 7 . . 4 .
1 . . . 9 . . . 7
. . 9 . . . 1 . 4
. 5 . . . . . 9 .
|
9 4 8 1 2 6 5 7 3
2 1 6 3 5 7 4 8 9
3 7 5 9 4 8 6 1 2
8 9 4 2 6 5 7 3 1
7 6 3 4 1 9 8 2 5
5 2 1 8 7 3 9 4 6
1 8 2 5 9 4 3 6 7
6 3 9 7 8 2 1 5 4
4 5 7 6 3 1 2 9 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4365_hard
|
948126573216357489375948612894265731763419825521873946182594367639782154457631298 #1 Extreme (38294) bf
Brute Force: r5c5=1
Hidden Single: r4c9=1
Forcing Net Contradiction in c8 => r7c6<>5
r7c6=5 (r8c6<>5 r8c8=5 r1c8<>5) (r4c6<>5) r5c6<>5 r4c5=5 r1c5<>5 r1c5=2 r1c8<>2 r1c8=7
r7c6=5 (r8c6<>5 r8c8=5 r2c8<>5) (r4c6<>5) r5c6<>5 r4c5=5 (r2c5<>5 r2c5=8 r2c8<>8) r4c5<>6 r4c8=6 r2c8<>6 r2c8=7
Brute Force: r5c6=9
Locked Candidates Type 1 (Pointing): 5 in b5 => r4c8<>5
Locked Candidates Type 1 (Pointing): 9 in b6 => r6c2<>9
Forcing Net Contradiction in c2 => r1c2<>7
r1c2=7 r1c2<>4
r1c2=7 r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4
r1c2=7 (r1c2<>9) r1c2<>1 r1c4=1 (r2c6<>1 r2c2=1 r2c2<>9) r1c4<>9 r3c4=9 r3c2<>9 r4c2=9 r4c2<>4
r1c2=7 r1c2<>1 r1c4=1 r9c4<>1 r9c6=1 r9c6<>4 r7c6=4 r7c2<>4
Forcing Net Contradiction in r2c8 => r2c3<>4
r2c3=4 (r1c2<>4 r1c7=4 r1c7<>5) (r4c3<>4 r4c3=3 r7c3<>3) (r4c3<>4 r4c3=3 r4c6<>3 r6c6=3 r7c6<>3) (r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r7c8<>3) r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r7c2<>3 r7c7=3 r7c7<>5 r2c7=5 r2c8<>5
r2c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
r2c3=4 (r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r3c2<>7) (r2c3<>7) r4c3<>4 r4c3=3 r5c1<>3 r5c1=7 r5c3<>7 r9c3=7 r8c2<>7 r2c2=7 r2c8<>7
r2c3=4 (r1c2<>4 r1c7=4 r1c7<>5) (r4c3<>4 r4c3=3 r7c3<>3) (r4c3<>4 r4c3=3 r4c6<>3 r6c6=3 r7c6<>3) (r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r7c8<>3) r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r7c2<>3 r7c7=3 r7c7<>5 r2c7=5 r2c5<>5 r2c5=8 r2c8<>8
Forcing Net Contradiction in r2 => r1c2<>9
r1c2=9 (r1c2<>4) r1c2<>1 r1c4=1 (r9c4<>1 r9c6=1 r9c6<>4) r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r1c7<>4 r1c1=4 r9c1<>4 r9c3=4 (r9c3<>7) r4c3<>4 r4c3=3 r5c1<>3 r5c1=7 r5c3<>7 r2c3=7 r2c3<>6
r1c2=9 r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6
r1c2=9 (r1c2<>4) r1c2<>1 r1c4=1 (r9c4<>1 r9c6=1 r9c6<>4) r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r1c7<>4 r1c1=4 r9c1<>4 r9c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
r1c2=9 (r2c2<>9) r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6
Forcing Net Contradiction in r9c4 => r1c4<>5
r1c4=5 (r2c5<>5 r2c5=8 r3c6<>8 r3c6=7 r3c2<>7) (r1c4<>7) (r1c4<>1 r9c4=1 r9c4<>7) r1c4<>9 r3c4=9 r3c4<>7 r8c4=7 r8c2<>7 r2c2=7 (r2c2<>9) r2c2<>4 r2c7=4 (r1c7<>4 r1c1=4 r1c1<>9) r2c7<>9 r2c9=9 r1c7<>9 r1c4=9 r1c4<>5
Locked Candidates Type 2 (Claiming): 5 in c4 => r8c56<>5
Hidden Rectangle: 5/8 in r2c56,r4c56 => r4c6<>8
Forcing Net Contradiction in r4 => r4c6=5
r4c6<>5 r4c5=5 r4c1=9
r4c6<>5 r2c6=5 r2c6<>1 r2c2=1 (r2c2<>9) r1c2<>1 r1c4=1 r1c4<>9 r3c4=9 r3c2<>9 r4c2=9
Forcing Net Contradiction in c2 => r2c6<>8
r2c6=8 r2c6<>1 r2c2=1 (r2c2<>9) r1c2<>1 r1c4=1 r1c4<>9 r3c4=9 r3c2<>9 r4c2=9 r4c2<>8
r2c6=8 (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6) (r3c6<>8 r3c9=8 r3c9<>6) (r3c6<>8 r3c9=8 r3c9<>2) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c7=2 r3c7<>6 r3c1=6 r2c3<>6 r2c8=6 r4c8<>6 r4c5=6 r6c4<>6 r6c4=8 r6c2<>8
r2c6=8 (r2c8<>8) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6) (r3c6<>8 r3c9=8 r3c9<>6) (r3c6<>8 r3c9=8 r3c9<>2) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c7=2 r3c7<>6 r3c1=6 (r8c1<>6) r2c3<>6 r2c8=6 (r8c8<>6) r4c8<>6 r4c5=6 r8c5<>6 r8c4=6 r8c4<>5 r8c8=5 r8c8<>8 r7c8=8 r7c2<>8
r2c6=8 (r2c6<>1 r2c2=1 r2c2<>7) (r3c6<>8) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c6=7 r3c2<>7 r8c2=7 r8c2<>8
Forcing Net Contradiction in r7 => r2c7<>5
r2c7=5 (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r1c8<>7 r2c8=7 r2c3<>7 r2c3=6 r7c3<>6
r2c7=5 (r2c9<>5 r5c9=5 r5c8<>5) (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r2c2<>9 r2c9=9 r3c7<>9 r3c7=6 r6c7<>6) (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r5c8<>2 r5c8=3 r4c8<>3 r4c8=6 r6c9<>6 r6c4=6 r7c4<>6
r2c7=5 (r1c8<>5 r1c5=5 r1c5<>2 r3c6=2 r3c7<>2) (r2c7<>9) r2c7<>4 r2c2=4 r2c2<>9 r2c9=9 r3c7<>9 r3c7=6 r7c7<>6
r2c7=5 (r2c9<>5 r5c9=5 r5c8<>5) (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r5c8<>2 r5c8=3 r4c8<>3 r4c8=6 r7c8<>6
Forcing Net Contradiction in r7c7 => r2c7<>6
r2c7=6 r2c3<>6 r2c3=7 (r1c1<>7) (r2c6<>7 r2c6=1 r1c4<>1) r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r2c2<>4 r2c7=4 r2c7<>6
Forcing Net Contradiction in r3c9 => r2c8<>6
r2c8=6 r2c3<>6 r2c3=7 (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 (r1c4<>1 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
Forcing Chain Contradiction in r7 => r9c9<>6
r9c9=6 r2c9<>6 r2c3=6 r7c3<>6
r9c9=6 r78c8<>6 r4c8=6 r4c5<>6 r6c4=6 r7c4<>6
r9c9=6 r7c7<>6
r9c9=6 r7c8<>6
Grouped Discontinuous Nice Loop: 5 r2c9 -5- r2c5 -8- r2c8 =8= r78c8 -8- r9c9 -2- r5c9 -5- r2c9 => r2c9<>5
Hidden Single: r5c9=5
Discontinuous Nice Loop: 2 r1c8 -2- r1c5 -5- r2c5 =5= r2c8 =7= r1c8 => r1c8<>2
Grouped Discontinuous Nice Loop: 2 r9c5 -2- r9c9 -8- r3c9 =8= r2c89 -8- r2c5 -5- r1c5 -2- r9c5 => r9c5<>2
Forcing Chain Verity => r7c3<>4
r9c3=2 r5c3<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
r9c6=2 r9c6<>4 r7c6=4 r7c3<>4
r9c7=2 r78c8<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
r9c9=2 r78c8<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
Forcing Net Verity => r1c5=2
r9c5=3 (r9c7<>3) (r7c6<>3) (r8c6<>3) r9c6<>3 r6c6=3 r6c7<>3 r7c7=3 r7c7<>5 r1c7=5 r1c5<>5 r1c5=2
r9c5=6 (r7c4<>6) (r8c4<>6) (r8c5<>6) r4c5<>6 r4c8=6 (r7c8<>6) r8c8<>6 r8c1=6 r7c3<>6 r7c7=6 r7c7<>5 r1c7=5 r1c5<>5 r1c5=2
r9c5=8 r2c5<>8 r2c5=5 r1c5<>5 r1c5=2
Hidden Single: r2c5=5
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c9<>8
Discontinuous Nice Loop: 8 r9c4 -8- r9c9 =8= r2c9 -8- r2c8 -7- r2c6 -1- r9c6 =1= r9c4 => r9c4<>8
Grouped Discontinuous Nice Loop: 8 r9c6 -8- r9c9 -2- r78c8 =2= r5c8 -2- r5c3 =2= r6c2 =8= r4c12 -8- r4c5 =8= r89c5 -8- r9c6 => r9c6<>8
Forcing Chain Contradiction in r9 => r7c6<>8
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r9c3<>2
r7c6=8 r7c6<>4 r9c6=4 r9c6<>2
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c7<>2
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c9<>2
Forcing Chain Contradiction in c1 => r8c4<>8
r8c4=8 r89c5<>8 r4c5=8 r4c1<>8
r8c4=8 r8c1<>8
r8c4=8 r8c4<>5 r8c8=5 r1c8<>5 r1c8=7 r2c8<>7 r2c8=8 r2c9<>8 r9c9=8 r9c1<>8
Forcing Chain Contradiction in c1 => r8c6<>8
r8c6=8 r89c5<>8 r4c5=8 r4c1<>8
r8c6=8 r8c1<>8
r8c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c9<>2 r9c9=8 r9c1<>8
Forcing Chain Contradiction in r7c4 => r8c8<>3
r8c8=3 r8c8<>5 r8c4=5 r7c4<>5
r8c8=3 r4c8<>3 r4c8=6 r4c5<>6 r6c4=6 r7c4<>6
r8c8=3 r79c7<>3 r6c7=3 r6c6<>3 r6c6=8 r3c6<>8 r3c4=8 r7c4<>8
Forcing Chain Contradiction in r6 => r7c6<>3
r7c6=3 r8c56<>3 r8c12=3 r79c3<>3 r45c3=3 r6c2<>3
r7c6=3 r6c6<>3
r7c6=3 r7c8<>3 r79c7=3 r6c7<>3
Forcing Net Contradiction in r9 => r2c3=6
r2c3<>6 r2c3=7 (r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r9c3<>2
r2c3<>6 r2c3=7 (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>2
r2c3<>6 r2c3=7 (r5c3<>7 r5c1=7 r5c1<>3) (r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r5c8<>2 r78c8=2 r9c7<>2
r2c3<>6 r2c3=7 r2c8<>7 r2c8=8 r2c9<>8 r9c9=8 r9c9<>2
Hidden Pair: 2,6 in r3c79 => r3c79<>9
XYZ-Wing: 2/3/7 in r5c13,r7c3 => r4c3<>3
Naked Single: r4c3=4
Finned Swordfish: 6 r367 c479 fr7c8 => r9c7<>6
AIC: 3 3- r4c8 -6- r6c9 =6= r3c9 =2= r3c7 -2- r9c7 -3 => r6c7,r7c8<>3
Finned Swordfish: 3 r368 c126 fr8c5 => r9c6<>3
Discontinuous Nice Loop: 2 r6c7 -2- r3c7 -6- r3c9 =6= r6c9 =9= r6c7 => r6c7<>2
Discontinuous Nice Loop: 3 r8c1 -3- r7c3 -2- r7c6 -4- r7c2 =4= r9c1 =6= r8c1 => r8c1<>3
Discontinuous Nice Loop: 3 r9c1 -3- r7c3 -2- r7c6 -4- r7c2 =4= r9c1 => r9c1<>3
Almost Locked Set XZ-Rule: A=r9c13579 {234678}, B=r1345c1 {34789}, X=4, Z=7 => r8c1<>7
Almost Locked Set XY-Wing: A=r9c579 {2368}, B=r12478c8 {235678}, C=r4c125 {3689}, X,Y=3,6, Z=2 => r7c7<>2
Empty Rectangle: 2 in b9 (r5c38) => r9c3<>2
Discontinuous Nice Loop: 7 r1c1 -7- r1c8 -5- r1c7 =5= r7c7 =3= r9c7 -3- r9c3 -7- r5c3 =7= r5c1 -7- r1c1 => r1c1<>7
AIC: 9 9- r1c1 -4- r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 =2= r6c9 =9= r2c9 -9 => r1c7,r2c2<>9
Discontinuous Nice Loop: 6 r8c4 -6- r8c1 =6= r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 -3- r4c8 -6- r4c5 =6= r6c4 -6- r8c4 => r8c4<>6
Discontinuous Nice Loop: 6 r8c8 -6- r8c1 =6= r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 -3- r4c8 -6- r8c8 => r8c8<>6
Locked Candidates Type 1 (Pointing): 6 in b9 => r7c4<>6
XY-Chain: 7 7- r1c8 -5- r1c7 -4- r2c7 -9- r6c7 -6- r6c4 -8- r7c4 -5- r8c4 -7 => r1c4<>7
Hidden Single: r1c8=7
Naked Single: r2c8=8
Naked Single: r2c9=9
Naked Single: r2c7=4
Naked Single: r1c7=5
Hidden Single: r9c9=8
Hidden Single: r6c7=9
X-Wing: 8 c15 r48 => r48c2<>8
Naked Triple: 2,3,7 in r79c3,r8c2 => r7c2<>2, r7c2<>3, r9c1<>7
Hidden Pair: 6,8 in r8c15 => r8c5<>3
X-Wing: 3 r68 c26 => r34c2<>3
Naked Single: r4c2=9
Naked Single: r3c2=7
Naked Single: r2c2=1
Full House: r2c6=7
Naked Single: r3c6=8
Naked Single: r1c2=4
Naked Single: r3c4=9
Full House: r1c4=1
Full House: r1c1=9
Full House: r3c1=3
Naked Single: r6c6=3
Naked Single: r7c2=8
Naked Single: r4c1=8
Naked Single: r5c1=7
Naked Single: r8c6=2
Naked Single: r6c2=2
Full House: r8c2=3
Full House: r5c3=3
Full House: r5c8=2
Naked Single: r7c4=5
Naked Single: r8c1=6
Full House: r9c1=4
Naked Single: r4c5=6
Full House: r4c8=3
Full House: r6c9=6
Full House: r6c4=8
Full House: r3c9=2
Full House: r3c7=6
Naked Single: r7c6=4
Full House: r9c6=1
Naked Single: r8c8=5
Full House: r7c8=6
Naked Single: r7c3=2
Full House: r9c3=7
Full House: r7c7=3
Full House: r9c7=2
Naked Single: r8c4=7
Full House: r8c5=8
Full House: r9c5=3
Full House: r9c4=6
|
sudoku_normal_extremely_hard_145
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
..8..6..32..3.......5.4..1....2..7...6.4..8..5.1.7..4.1...9...7..9...1.4.5.....9.
|
948126573216357489375948612894265731763419825521873946182594367639782154457631298
|
. . 8 . . 6 . . 3
2 . . 3 . . . . .
. . 5 . 4 . . 1 .
. . . 2 . . 7 . .
. 6 . 4 . . 8 . .
5 . 1 . 7 . . 4 .
1 . . . 9 . . . 7
. . 9 . . . 1 . 4
. 5 . . . . . 9 .
|
9 4 8 1 2 6 5 7 3
2 1 6 3 5 7 4 8 9
3 7 5 9 4 8 6 1 2
8 9 4 2 6 5 7 3 1
7 6 3 4 1 9 8 2 5
5 2 1 8 7 3 9 4 6
1 8 2 5 9 4 3 6 7
6 3 9 7 8 2 1 5 4
4 5 7 6 3 1 2 9 8
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4365_hard
|
948126573216357489375948612894265731763419825521873946182594367639782154457631298 #1 Extreme (38294) bf
Brute Force: r5c5=1
Hidden Single: r4c9=1
Forcing Net Contradiction in c8 => r7c6<>5
r7c6=5 (r8c6<>5 r8c8=5 r1c8<>5) (r4c6<>5) r5c6<>5 r4c5=5 r1c5<>5 r1c5=2 r1c8<>2 r1c8=7
r7c6=5 (r8c6<>5 r8c8=5 r2c8<>5) (r4c6<>5) r5c6<>5 r4c5=5 (r2c5<>5 r2c5=8 r2c8<>8) r4c5<>6 r4c8=6 r2c8<>6 r2c8=7
Brute Force: r5c6=9
Locked Candidates Type 1 (Pointing): 5 in b5 => r4c8<>5
Locked Candidates Type 1 (Pointing): 9 in b6 => r6c2<>9
Forcing Net Contradiction in c2 => r1c2<>7
r1c2=7 r1c2<>4
r1c2=7 r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4
r1c2=7 (r1c2<>9) r1c2<>1 r1c4=1 (r2c6<>1 r2c2=1 r2c2<>9) r1c4<>9 r3c4=9 r3c2<>9 r4c2=9 r4c2<>4
r1c2=7 r1c2<>1 r1c4=1 r9c4<>1 r9c6=1 r9c6<>4 r7c6=4 r7c2<>4
Forcing Net Contradiction in r2c8 => r2c3<>4
r2c3=4 (r1c2<>4 r1c7=4 r1c7<>5) (r4c3<>4 r4c3=3 r7c3<>3) (r4c3<>4 r4c3=3 r4c6<>3 r6c6=3 r7c6<>3) (r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r7c8<>3) r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r7c2<>3 r7c7=3 r7c7<>5 r2c7=5 r2c8<>5
r2c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
r2c3=4 (r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r3c2<>7) (r2c3<>7) r4c3<>4 r4c3=3 r5c1<>3 r5c1=7 r5c3<>7 r9c3=7 r8c2<>7 r2c2=7 r2c8<>7
r2c3=4 (r1c2<>4 r1c7=4 r1c7<>5) (r4c3<>4 r4c3=3 r7c3<>3) (r4c3<>4 r4c3=3 r4c6<>3 r6c6=3 r7c6<>3) (r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r7c8<>3) r2c3<>6 r3c1=6 r3c1<>3 r3c2=3 r7c2<>3 r7c7=3 r7c7<>5 r2c7=5 r2c5<>5 r2c5=8 r2c8<>8
Forcing Net Contradiction in r2 => r1c2<>9
r1c2=9 (r1c2<>4) r1c2<>1 r1c4=1 (r9c4<>1 r9c6=1 r9c6<>4) r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r1c7<>4 r1c1=4 r9c1<>4 r9c3=4 (r9c3<>7) r4c3<>4 r4c3=3 r5c1<>3 r5c1=7 r5c3<>7 r2c3=7 r2c3<>6
r1c2=9 r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6
r1c2=9 (r1c2<>4) r1c2<>1 r1c4=1 (r9c4<>1 r9c6=1 r9c6<>4) r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r1c7<>4 r1c1=4 r9c1<>4 r9c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
r1c2=9 (r2c2<>9) r1c2<>1 r1c4=1 r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6
Forcing Net Contradiction in r9c4 => r1c4<>5
r1c4=5 (r2c5<>5 r2c5=8 r3c6<>8 r3c6=7 r3c2<>7) (r1c4<>7) (r1c4<>1 r9c4=1 r9c4<>7) r1c4<>9 r3c4=9 r3c4<>7 r8c4=7 r8c2<>7 r2c2=7 (r2c2<>9) r2c2<>4 r2c7=4 (r1c7<>4 r1c1=4 r1c1<>9) r2c7<>9 r2c9=9 r1c7<>9 r1c4=9 r1c4<>5
Locked Candidates Type 2 (Claiming): 5 in c4 => r8c56<>5
Hidden Rectangle: 5/8 in r2c56,r4c56 => r4c6<>8
Forcing Net Contradiction in r4 => r4c6=5
r4c6<>5 r4c5=5 r4c1=9
r4c6<>5 r2c6=5 r2c6<>1 r2c2=1 (r2c2<>9) r1c2<>1 r1c4=1 r1c4<>9 r3c4=9 r3c2<>9 r4c2=9
Forcing Net Contradiction in c2 => r2c6<>8
r2c6=8 r2c6<>1 r2c2=1 (r2c2<>9) r1c2<>1 r1c4=1 r1c4<>9 r3c4=9 r3c2<>9 r4c2=9 r4c2<>8
r2c6=8 (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6) (r3c6<>8 r3c9=8 r3c9<>6) (r3c6<>8 r3c9=8 r3c9<>2) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c7=2 r3c7<>6 r3c1=6 r2c3<>6 r2c8=6 r4c8<>6 r4c5=6 r6c4<>6 r6c4=8 r6c2<>8
r2c6=8 (r2c8<>8) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>6) (r2c6<>1 r2c2=1 r2c2<>4 r2c7=4 r2c7<>9 r2c9=9 r2c9<>6) (r3c6<>8 r3c9=8 r3c9<>6) (r3c6<>8 r3c9=8 r3c9<>2) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c7=2 r3c7<>6 r3c1=6 (r8c1<>6) r2c3<>6 r2c8=6 (r8c8<>6) r4c8<>6 r4c5=6 r8c5<>6 r8c4=6 r8c4<>5 r8c8=5 r8c8<>8 r7c8=8 r7c2<>8
r2c6=8 (r2c6<>1 r2c2=1 r2c2<>7) (r3c6<>8) r2c5<>8 r2c5=5 r1c5<>5 r1c5=2 r3c6<>2 r3c6=7 r3c2<>7 r8c2=7 r8c2<>8
Forcing Net Contradiction in r7 => r2c7<>5
r2c7=5 (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r1c8<>7 r2c8=7 r2c3<>7 r2c3=6 r7c3<>6
r2c7=5 (r2c9<>5 r5c9=5 r5c8<>5) (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r2c2<>9 r2c9=9 r3c7<>9 r3c7=6 r6c7<>6) (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r5c8<>2 r5c8=3 r4c8<>3 r4c8=6 r6c9<>6 r6c4=6 r7c4<>6
r2c7=5 (r1c8<>5 r1c5=5 r1c5<>2 r3c6=2 r3c7<>2) (r2c7<>9) r2c7<>4 r2c2=4 r2c2<>9 r2c9=9 r3c7<>9 r3c7=6 r7c7<>6
r2c7=5 (r2c9<>5 r5c9=5 r5c8<>5) (r1c8<>5 r1c5=5 r1c5<>2) r2c7<>4 r2c2=4 (r1c1<>4) r1c2<>4 r1c7=4 r1c7<>2 r1c8=2 r5c8<>2 r5c8=3 r4c8<>3 r4c8=6 r7c8<>6
Forcing Net Contradiction in r7c7 => r2c7<>6
r2c7=6 r2c3<>6 r2c3=7 (r1c1<>7) (r2c6<>7 r2c6=1 r1c4<>1) r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r2c2<>4 r2c7=4 r2c7<>6
Forcing Net Contradiction in r3c9 => r2c8<>6
r2c8=6 r2c3<>6 r2c3=7 (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 (r1c4<>1 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r4c3<>4 r4c3=3 r4c8<>3 r4c8=6 r2c8<>6
Forcing Chain Contradiction in r7 => r9c9<>6
r9c9=6 r2c9<>6 r2c3=6 r7c3<>6
r9c9=6 r78c8<>6 r4c8=6 r4c5<>6 r6c4=6 r7c4<>6
r9c9=6 r7c7<>6
r9c9=6 r7c8<>6
Grouped Discontinuous Nice Loop: 5 r2c9 -5- r2c5 -8- r2c8 =8= r78c8 -8- r9c9 -2- r5c9 -5- r2c9 => r2c9<>5
Hidden Single: r5c9=5
Discontinuous Nice Loop: 2 r1c8 -2- r1c5 -5- r2c5 =5= r2c8 =7= r1c8 => r1c8<>2
Grouped Discontinuous Nice Loop: 2 r9c5 -2- r9c9 -8- r3c9 =8= r2c89 -8- r2c5 -5- r1c5 -2- r9c5 => r9c5<>2
Forcing Chain Verity => r7c3<>4
r9c3=2 r5c3<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
r9c6=2 r9c6<>4 r7c6=4 r7c3<>4
r9c7=2 r78c8<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
r9c9=2 r78c8<>2 r5c8=2 r5c8<>3 r5c13=3 r4c3<>3 r4c3=4 r7c3<>4
Forcing Net Verity => r1c5=2
r9c5=3 (r9c7<>3) (r7c6<>3) (r8c6<>3) r9c6<>3 r6c6=3 r6c7<>3 r7c7=3 r7c7<>5 r1c7=5 r1c5<>5 r1c5=2
r9c5=6 (r7c4<>6) (r8c4<>6) (r8c5<>6) r4c5<>6 r4c8=6 (r7c8<>6) r8c8<>6 r8c1=6 r7c3<>6 r7c7=6 r7c7<>5 r1c7=5 r1c5<>5 r1c5=2
r9c5=8 r2c5<>8 r2c5=5 r1c5<>5 r1c5=2
Hidden Single: r2c5=5
Locked Candidates Type 1 (Pointing): 8 in b2 => r3c9<>8
Discontinuous Nice Loop: 8 r9c4 -8- r9c9 =8= r2c9 -8- r2c8 -7- r2c6 -1- r9c6 =1= r9c4 => r9c4<>8
Grouped Discontinuous Nice Loop: 8 r9c6 -8- r9c9 -2- r78c8 =2= r5c8 -2- r5c3 =2= r6c2 =8= r4c12 -8- r4c5 =8= r89c5 -8- r9c6 => r9c6<>8
Forcing Chain Contradiction in r9 => r7c6<>8
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r9c3<>2
r7c6=8 r7c6<>4 r9c6=4 r9c6<>2
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c7<>2
r7c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c9<>2
Forcing Chain Contradiction in c1 => r8c4<>8
r8c4=8 r89c5<>8 r4c5=8 r4c1<>8
r8c4=8 r8c1<>8
r8c4=8 r8c4<>5 r8c8=5 r1c8<>5 r1c8=7 r2c8<>7 r2c8=8 r2c9<>8 r9c9=8 r9c1<>8
Forcing Chain Contradiction in c1 => r8c6<>8
r8c6=8 r89c5<>8 r4c5=8 r4c1<>8
r8c6=8 r8c1<>8
r8c6=8 r89c5<>8 r4c5=8 r4c12<>8 r6c2=8 r6c2<>2 r5c3=2 r5c8<>2 r78c8=2 r9c9<>2 r9c9=8 r9c1<>8
Forcing Chain Contradiction in r7c4 => r8c8<>3
r8c8=3 r8c8<>5 r8c4=5 r7c4<>5
r8c8=3 r4c8<>3 r4c8=6 r4c5<>6 r6c4=6 r7c4<>6
r8c8=3 r79c7<>3 r6c7=3 r6c6<>3 r6c6=8 r3c6<>8 r3c4=8 r7c4<>8
Forcing Chain Contradiction in r6 => r7c6<>3
r7c6=3 r8c56<>3 r8c12=3 r79c3<>3 r45c3=3 r6c2<>3
r7c6=3 r6c6<>3
r7c6=3 r7c8<>3 r79c7=3 r6c7<>3
Forcing Net Contradiction in r9 => r2c3=6
r2c3<>6 r2c3=7 (r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r9c3<>2
r2c3<>6 r2c3=7 (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>2
r2c3<>6 r2c3=7 (r5c3<>7 r5c1=7 r5c1<>3) (r2c8<>7 r1c8=7 r1c4<>7 r1c4=9 r1c1<>9 r1c1=4 r9c1<>4) (r9c3<>7) (r3c2<>7 r8c2=7 r9c1<>7) r2c6<>7 r2c6=1 r9c6<>1 r9c4=1 r9c4<>7 r9c6=7 r9c6<>4 r9c3=4 r4c3<>4 r4c3=3 r5c3<>3 r5c8=3 r5c8<>2 r78c8=2 r9c7<>2
r2c3<>6 r2c3=7 r2c8<>7 r2c8=8 r2c9<>8 r9c9=8 r9c9<>2
Hidden Pair: 2,6 in r3c79 => r3c79<>9
XYZ-Wing: 2/3/7 in r5c13,r7c3 => r4c3<>3
Naked Single: r4c3=4
Finned Swordfish: 6 r367 c479 fr7c8 => r9c7<>6
AIC: 3 3- r4c8 -6- r6c9 =6= r3c9 =2= r3c7 -2- r9c7 -3 => r6c7,r7c8<>3
Finned Swordfish: 3 r368 c126 fr8c5 => r9c6<>3
Discontinuous Nice Loop: 2 r6c7 -2- r3c7 -6- r3c9 =6= r6c9 =9= r6c7 => r6c7<>2
Discontinuous Nice Loop: 3 r8c1 -3- r7c3 -2- r7c6 -4- r7c2 =4= r9c1 =6= r8c1 => r8c1<>3
Discontinuous Nice Loop: 3 r9c1 -3- r7c3 -2- r7c6 -4- r7c2 =4= r9c1 => r9c1<>3
Almost Locked Set XZ-Rule: A=r9c13579 {234678}, B=r1345c1 {34789}, X=4, Z=7 => r8c1<>7
Almost Locked Set XY-Wing: A=r9c579 {2368}, B=r12478c8 {235678}, C=r4c125 {3689}, X,Y=3,6, Z=2 => r7c7<>2
Empty Rectangle: 2 in b9 (r5c38) => r9c3<>2
Discontinuous Nice Loop: 7 r1c1 -7- r1c8 -5- r1c7 =5= r7c7 =3= r9c7 -3- r9c3 -7- r5c3 =7= r5c1 -7- r1c1 => r1c1<>7
AIC: 9 9- r1c1 -4- r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 =2= r6c9 =9= r2c9 -9 => r1c7,r2c2<>9
Discontinuous Nice Loop: 6 r8c4 -6- r8c1 =6= r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 -3- r4c8 -6- r4c5 =6= r6c4 -6- r8c4 => r8c4<>6
Discontinuous Nice Loop: 6 r8c8 -6- r8c1 =6= r9c1 =4= r9c6 -4- r7c6 -2- r7c3 =2= r5c3 -2- r5c8 -3- r4c8 -6- r8c8 => r8c8<>6
Locked Candidates Type 1 (Pointing): 6 in b9 => r7c4<>6
XY-Chain: 7 7- r1c8 -5- r1c7 -4- r2c7 -9- r6c7 -6- r6c4 -8- r7c4 -5- r8c4 -7 => r1c4<>7
Hidden Single: r1c8=7
Naked Single: r2c8=8
Naked Single: r2c9=9
Naked Single: r2c7=4
Naked Single: r1c7=5
Hidden Single: r9c9=8
Hidden Single: r6c7=9
X-Wing: 8 c15 r48 => r48c2<>8
Naked Triple: 2,3,7 in r79c3,r8c2 => r7c2<>2, r7c2<>3, r9c1<>7
Hidden Pair: 6,8 in r8c15 => r8c5<>3
X-Wing: 3 r68 c26 => r34c2<>3
Naked Single: r4c2=9
Naked Single: r3c2=7
Naked Single: r2c2=1
Full House: r2c6=7
Naked Single: r3c6=8
Naked Single: r1c2=4
Naked Single: r3c4=9
Full House: r1c4=1
Full House: r1c1=9
Full House: r3c1=3
Naked Single: r6c6=3
Naked Single: r7c2=8
Naked Single: r4c1=8
Naked Single: r5c1=7
Naked Single: r8c6=2
Naked Single: r6c2=2
Full House: r8c2=3
Full House: r5c3=3
Full House: r5c8=2
Naked Single: r7c4=5
Naked Single: r8c1=6
Full House: r9c1=4
Naked Single: r4c5=6
Full House: r4c8=3
Full House: r6c9=6
Full House: r6c4=8
Full House: r3c9=2
Full House: r3c7=6
Naked Single: r7c6=4
Full House: r9c6=1
Naked Single: r8c8=5
Full House: r7c8=6
Naked Single: r7c3=2
Full House: r9c3=7
Full House: r7c7=3
Full House: r9c7=2
Naked Single: r8c4=7
Full House: r8c5=8
Full House: r9c5=3
Full House: r9c4=6
|
sudoku_normal_hard_146
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
4.62..8.7..8.......3..8..6......6...641.5....9..7..4.6..4.7.1.9.791....21...29...
|
496235817518697243732481965387946521641352798925718436264573189879164352153829674
|
4 . 6 2 . . 8 . 7
. . 8 . . . . . .
. 3 . . 8 . . 6 .
. . . . . 6 . . .
6 4 1 . 5 . . . .
9 . . 7 . . 4 . 6
. . 4 . 7 . 1 . 9
. 7 9 1 . . . . 2
1 . . . 2 9 . . .
|
4 9 6 2 3 5 8 1 7
5 1 8 6 9 7 2 4 3
7 3 2 4 8 1 9 6 5
3 8 7 9 4 6 5 2 1
6 4 1 3 5 2 7 9 8
9 2 5 7 1 8 4 3 6
2 6 4 5 7 3 1 8 9
8 7 9 1 6 4 3 5 2
1 5 3 8 2 9 6 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4177_hard
|
496235817518697243732481965387946521641352798925718436264573189879164352153829674 #1 Extreme (42218) bf
Hidden Single: r8c3=9
Empty Rectangle: 9 in b5 (r3c47) => r4c7<>9
Brute Force: r5c2=4
Brute Force: r5c1=6
Brute Force: r5c3=1
Locked Candidates Type 1 (Pointing): 7 in b4 => r4c78<>7
Naked Triple: 2,5,7 in r23c1,r3c3 => r1c23,r2c2<>5, r2c2<>2
Naked Single: r1c3=6
Grouped Discontinuous Nice Loop: 4 r2c6 -4- r2c89 =4= r3c9 =1= r3c6 =7= r2c6 => r2c6<>4
Grouped Discontinuous Nice Loop: 5 r4c1 -5- r23c1 =5= r3c3 -5- r9c3 -3- r78c1 =3= r4c1 => r4c1<>5
Grouped Discontinuous Nice Loop: 5 r4c3 -5- r9c3 -3- r78c1 =3= r4c1 =7= r4c3 => r4c3<>5
Forcing Chain Contradiction in r2c4 => r1c8<>9
r1c8=9 r1c8<>3 r1c56=3 r2c4<>3
r1c8=9 r3c7<>9 r3c4=9 r45c4<>9 r4c5=9 r4c5<>4 r4c4=4 r2c4<>4
r1c8=9 r1c8<>5 r1c6=5 r2c4<>5
r1c8=9 r23c7<>9 r5c7=9 r5c7<>7 r9c7=7 r9c7<>6 r8c7=6 r8c5<>6 r2c5=6 r2c4<>6
r1c8=9 r1c2<>9 r2c2=9 r2c4<>9
Forcing Chain Contradiction in c8 => r2c5<>4
r2c5=4 r2c8<>4
r2c5=4 r3c6<>4 r8c6=4 r8c8<>4
r2c5=4 r2c5<>6 r8c5=6 r8c7<>6 r9c7=6 r9c7<>7 r9c8=7 r9c8<>4
Forcing Net Contradiction in r8 => r2c4<>4
r2c4=4 (r2c4<>5) (r3c4<>4) (r4c4<>4 r4c5=4 r4c5<>9) r2c4<>6 r2c5=6 r2c5<>9 r1c5=9 r3c4<>9 r3c4=5 (r2c6<>5) r1c6<>5 r1c8=5 (r2c7<>5) (r2c8<>5) r2c9<>5 r2c1=5 r8c1<>5
r2c4=4 r3c6<>4 r8c6=4 r8c6<>5
r2c4=4 r2c4<>6 r2c5=6 r8c5<>6 r8c7=6 r8c7<>5
r2c4=4 (r3c4<>4) (r4c4<>4 r4c5=4 r4c5<>9) r2c4<>6 r2c5=6 r2c5<>9 r1c5=9 r3c4<>9 r3c4=5 r1c6<>5 r1c8=5 r8c8<>5
Locked Candidates Type 1 (Pointing): 4 in b2 => r3c9<>4
Almost Locked Set XY-Wing: A=r4c12379 {123578}, B=r45c4,r56c6,r6c5 {123489}, C=r3c13479 {124579}, X,Y=1,4, Z=3 => r4c5<>3
Forcing Net Contradiction in r7 => r2c6<>3
r2c6=3 (r7c6<>3) (r1c5<>3) r1c6<>3 r1c8=3 (r7c8<>3) r1c8<>5 r1c6=5 r7c6<>5 r7c6=8 r7c8<>8 r7c8=5 (r8c7<>5) (r8c8<>5) r1c8<>5 r1c6=5 r8c6<>5 r8c1=5 (r8c1<>8) (r8c1<>3) r9c3<>5 r9c3=3 r7c1<>3 r4c1=3 r4c1<>8 r7c1=8
r2c6=3 (r7c6<>3) (r1c5<>3) r1c6<>3 r1c8=3 r1c8<>5 r1c6=5 r7c6<>5 r7c6=8
Forcing Net Contradiction in r3c4 => r2c8<>5
r2c8=5 (r8c8<>5) (r7c8<>5) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 (r8c8<>3) r7c8<>3 r7c8=8 r8c8<>8 r8c8=4 r8c6<>4 r3c6=4 r3c4<>4
r2c8=5 r1c8<>5 r1c6=5 r3c4<>5
r2c8=5 (r8c8<>5) (r7c8<>5) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 (r8c8<>3) r7c8<>3 r7c8=8 r8c8<>8 r8c8=4 (r8c5<>4 r4c5=4 r4c5<>9) (r8c5<>4 r4c5=4 r4c5<>1) r8c6<>4 r3c6=4 r3c6<>1 r3c9=1 r4c9<>1 r4c8=1 r4c8<>9 r4c4=9 r3c4<>9
Forcing Net Contradiction in r5c4 => r3c7<>5
r3c7=5 (r3c7<>9 r3c4=9 r1c5<>9) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 r1c5<>3 r1c5=1 r6c5<>1 r6c5=3 r5c4<>3
r3c7=5 (r2c9<>5) (r3c9<>5) (r8c7<>5) (r2c7<>5) (r2c9<>5) r1c8<>5 r1c6=5 (r8c6<>5) (r2c4<>5) r2c6<>5 r2c1=5 r8c1<>5 r8c8=5 (r7c8<>5 r7c8=8 r9c9<>8) r9c9<>5 r4c9=5 r4c9<>8 r5c9=8 r5c4<>8
r3c7=5 r3c7<>9 r3c4=9 r5c4<>9
Forcing Net Contradiction in c6 => r4c5<>1
r4c5=1 (r1c5<>1) r6c5<>1 r6c5=3 r1c5<>3 r1c5=9 r1c2<>9 r1c2=1 r1c6<>1
r4c5=1 r4c5<>4 r4c4=4 r3c4<>4 r3c6=4 r3c6<>7 r2c6=7 r2c6<>1
r4c5=1 r4c5<>4 r4c4=4 r3c4<>4 r3c6=4 r3c6<>1
r4c5=1 r6c6<>1
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c8<>1
Forcing Net Contradiction in r5 => r4c8<>8
r4c8=8 r4c8<>9 r4c45=9 r5c4<>9
r4c8=8 r4c8<>1 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r3c4=4 r3c4<>9 r3c7=9 r5c7<>9
r4c8=8 (r5c9<>8 r9c9=8 r9c9<>4) r4c8<>1 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r3c4=4 r9c4<>4 r9c8=4 r9c8<>7 r9c7=7 r5c7<>7 r5c8=7 r5c8<>9
Forcing Net Contradiction in r1 => r5c7<>2
r5c7=2 r1c5=9 r1c2<>9 r1c2=1
r5c7=2 (r6c8<>2 r2c8=2 r2c8<>1) (r5c7<>9) r5c7<>7 r5c8=7 r5c8<>9 r5c4=9 (r4c4<>9) r4c5<>9 r4c8=9 r4c8<>1 r1c8=1
Forcing Net Contradiction in r9 => r5c6<>3
r5c6=3 (r5c9<>3 r5c9=8 r6c8<>8) r5c6<>2 r6c6=2 r6c6<>8 r6c2=8 r9c2<>8
r5c6=3 (r5c9<>3 r5c9=8 r4c9<>8) (r5c9<>3 r5c9=8 r6c8<>8) r5c6<>2 r6c6=2 r6c6<>8 r6c2=8 (r4c1<>8) r4c2<>8 r4c4=8 r9c4<>8
r5c6=3 r5c6<>2 r5c8=2 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>8
r5c6=3 r5c9<>3 r5c9=8 r9c9<>8
Forcing Net Contradiction in c8 => r5c6=2
r5c6<>2 r5c8=2 (r6c8<>2) r4c7<>2 r4c7=5 r6c8<>5 r6c8=8 (r4c9<>8) r5c9<>8 (r5c9=3 r6c8<>3) (r5c9=3 r4c7<>3) r9c9=8 r9c9<>4 r2c9=4 r2c8<>4
r5c6<>2 (r5c6=8 r5c9<>8 r5c9=3 r4c9<>3) (r5c6=8 r5c9<>8 r5c9=3 r6c8<>3) (r5c6=8 r5c9<>8 r5c9=3 r4c7<>3) r5c8=2 (r6c8<>2) r4c7<>2 r4c7=5 (r4c9<>5) r6c8<>5 r6c8=8 r4c9<>8 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r8c6=4 r8c8<>4
r5c6<>2 r5c8=2 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>4
Forcing Net Contradiction in c8 => r3c3<>5
r3c3=5 (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 r4c8<>2 r2c8=2 r2c8<>4
r3c3=5 (r2c1<>5) (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 r4c8<>2 r2c8=2 r2c1<>2 r2c1=7 (r3c1<>7) r3c3<>7 r3c6=7 r3c6<>4 r8c6=4 r8c8<>4
r3c3=5 (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 (r4c8<>9) r4c8<>2 r2c8=2 r2c8<>9 r5c8=9 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>4
Locked Candidates Type 1 (Pointing): 5 in b1 => r78c1<>5
Finned X-Wing: 5 r18 c68 fr8c7 => r79c8<>5
Forcing Net Contradiction in r7c2 => r3c3=2
r3c3<>2 r23c1=2 r7c1<>2 r7c2=2
r3c3<>2 r23c1=2 r7c1<>2 r7c2=2 (r7c2<>5) r7c2<>6 r7c4=6 r7c4<>5 r7c6=5 (r8c6<>5) r1c6<>5 r1c8=5 r8c8<>5 r8c7=5 r8c7<>6 r8c5=6 r7c4<>6 r7c2=6
Naked Single: r3c7=9
Hidden Single: r4c3=7
Empty Rectangle: 3 in b5 (r69c3) => r9c4<>3
Uniqueness Test 4: 5/7 in r2c16,r3c16 => r23c6<>5
Hidden Rectangle: 3/7 in r5c78,r9c78 => r9c8<>3
Grouped AIC: 8 8- r7c8 -3- r7c46 =3= r8c56 -3- r8c1 -8 => r7c12,r8c8<>8
Almost Locked Set XZ-Rule: A=r6c356 {1358}, B=r78c1,r9c3 {2358}, X=5, Z=8 => r8c6<>8
Hidden Single: r8c1=8
Finned Jellyfish: 3 c1479 r2457 fr8c7 fr9c7 fr9c9 => r7c8<>3
Naked Single: r7c8=8
Hidden Single: r6c6=8
Hidden Single: r9c4=8
Hidden Single: r5c9=8
Hidden Single: r4c2=8
Hidden Single: r6c5=1
Locked Candidates Type 1 (Pointing): 5 in b4 => r6c8<>5
Locked Candidates Type 1 (Pointing): 3 in b5 => r27c4<>3
Locked Candidates Type 1 (Pointing): 4 in b8 => r8c8<>4
W-Wing: 3/5 in r7c6,r8c8 connected by 5 in r1c68 => r8c56<>3
Hidden Single: r7c6=3
Naked Single: r7c1=2
Naked Single: r4c1=3
Naked Single: r6c3=5
Full House: r6c2=2
Full House: r9c3=3
Full House: r6c8=3
Naked Single: r5c7=7
Naked Single: r8c8=5
Naked Single: r5c8=9
Full House: r5c4=3
Naked Single: r1c8=1
Naked Single: r8c6=4
Naked Single: r9c7=6
Naked Single: r9c9=4
Naked Single: r1c2=9
Naked Single: r1c6=5
Full House: r1c5=3
Naked Single: r3c9=5
Naked Single: r4c8=2
Naked Single: r8c5=6
Full House: r8c7=3
Full House: r9c8=7
Full House: r9c2=5
Full House: r2c8=4
Full House: r7c4=5
Full House: r7c2=6
Full House: r2c2=1
Naked Single: r3c4=4
Naked Single: r2c9=3
Full House: r4c9=1
Full House: r4c7=5
Full House: r2c7=2
Naked Single: r3c1=7
Full House: r2c1=5
Full House: r3c6=1
Full House: r2c6=7
Naked Single: r2c5=9
Full House: r2c4=6
Full House: r4c4=9
Full House: r4c5=4
|
sudoku_normal_extremely_hard_146
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
4..2..8.7..8.......3..8..6......6.......5....9..7..4.6..4.7.1.9.7.1....21...29...
|
496235817518697243732481965387946521641352798925718436264573189879164352153829674
|
4 . . 2 . . 8 . 7
. . 8 . . . . . .
. 3 . . 8 . . 6 .
. . . . . 6 . . .
. . . . 5 . . . .
9 . . 7 . . 4 . 6
. . 4 . 7 . 1 . 9
. 7 . 1 . . . . 2
1 . . . 2 9 . . .
|
4 9 6 2 3 5 8 1 7
5 1 8 6 9 7 2 4 3
7 3 2 4 8 1 9 6 5
3 8 7 9 4 6 5 2 1
6 4 1 3 5 2 7 9 8
9 2 5 7 1 8 4 3 6
2 6 4 5 7 3 1 8 9
8 7 9 1 6 4 3 5 2
1 5 3 8 2 9 6 7 4
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4177_hard
|
496235817518697243732481965387946521641352798925718436264573189879164352153829674 #1 Extreme (42218) bf
Hidden Single: r8c3=9
Empty Rectangle: 9 in b5 (r3c47) => r4c7<>9
Brute Force: r5c2=4
Brute Force: r5c1=6
Brute Force: r5c3=1
Locked Candidates Type 1 (Pointing): 7 in b4 => r4c78<>7
Naked Triple: 2,5,7 in r23c1,r3c3 => r1c23,r2c2<>5, r2c2<>2
Naked Single: r1c3=6
Grouped Discontinuous Nice Loop: 4 r2c6 -4- r2c89 =4= r3c9 =1= r3c6 =7= r2c6 => r2c6<>4
Grouped Discontinuous Nice Loop: 5 r4c1 -5- r23c1 =5= r3c3 -5- r9c3 -3- r78c1 =3= r4c1 => r4c1<>5
Grouped Discontinuous Nice Loop: 5 r4c3 -5- r9c3 -3- r78c1 =3= r4c1 =7= r4c3 => r4c3<>5
Forcing Chain Contradiction in r2c4 => r1c8<>9
r1c8=9 r1c8<>3 r1c56=3 r2c4<>3
r1c8=9 r3c7<>9 r3c4=9 r45c4<>9 r4c5=9 r4c5<>4 r4c4=4 r2c4<>4
r1c8=9 r1c8<>5 r1c6=5 r2c4<>5
r1c8=9 r23c7<>9 r5c7=9 r5c7<>7 r9c7=7 r9c7<>6 r8c7=6 r8c5<>6 r2c5=6 r2c4<>6
r1c8=9 r1c2<>9 r2c2=9 r2c4<>9
Forcing Chain Contradiction in c8 => r2c5<>4
r2c5=4 r2c8<>4
r2c5=4 r3c6<>4 r8c6=4 r8c8<>4
r2c5=4 r2c5<>6 r8c5=6 r8c7<>6 r9c7=6 r9c7<>7 r9c8=7 r9c8<>4
Forcing Net Contradiction in r8 => r2c4<>4
r2c4=4 (r2c4<>5) (r3c4<>4) (r4c4<>4 r4c5=4 r4c5<>9) r2c4<>6 r2c5=6 r2c5<>9 r1c5=9 r3c4<>9 r3c4=5 (r2c6<>5) r1c6<>5 r1c8=5 (r2c7<>5) (r2c8<>5) r2c9<>5 r2c1=5 r8c1<>5
r2c4=4 r3c6<>4 r8c6=4 r8c6<>5
r2c4=4 r2c4<>6 r2c5=6 r8c5<>6 r8c7=6 r8c7<>5
r2c4=4 (r3c4<>4) (r4c4<>4 r4c5=4 r4c5<>9) r2c4<>6 r2c5=6 r2c5<>9 r1c5=9 r3c4<>9 r3c4=5 r1c6<>5 r1c8=5 r8c8<>5
Locked Candidates Type 1 (Pointing): 4 in b2 => r3c9<>4
Almost Locked Set XY-Wing: A=r4c12379 {123578}, B=r45c4,r56c6,r6c5 {123489}, C=r3c13479 {124579}, X,Y=1,4, Z=3 => r4c5<>3
Forcing Net Contradiction in r7 => r2c6<>3
r2c6=3 (r7c6<>3) (r1c5<>3) r1c6<>3 r1c8=3 (r7c8<>3) r1c8<>5 r1c6=5 r7c6<>5 r7c6=8 r7c8<>8 r7c8=5 (r8c7<>5) (r8c8<>5) r1c8<>5 r1c6=5 r8c6<>5 r8c1=5 (r8c1<>8) (r8c1<>3) r9c3<>5 r9c3=3 r7c1<>3 r4c1=3 r4c1<>8 r7c1=8
r2c6=3 (r7c6<>3) (r1c5<>3) r1c6<>3 r1c8=3 r1c8<>5 r1c6=5 r7c6<>5 r7c6=8
Forcing Net Contradiction in r3c4 => r2c8<>5
r2c8=5 (r8c8<>5) (r7c8<>5) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 (r8c8<>3) r7c8<>3 r7c8=8 r8c8<>8 r8c8=4 r8c6<>4 r3c6=4 r3c4<>4
r2c8=5 r1c8<>5 r1c6=5 r3c4<>5
r2c8=5 (r8c8<>5) (r7c8<>5) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 (r8c8<>3) r7c8<>3 r7c8=8 r8c8<>8 r8c8=4 (r8c5<>4 r4c5=4 r4c5<>9) (r8c5<>4 r4c5=4 r4c5<>1) r8c6<>4 r3c6=4 r3c6<>1 r3c9=1 r4c9<>1 r4c8=1 r4c8<>9 r4c4=9 r3c4<>9
Forcing Net Contradiction in r5c4 => r3c7<>5
r3c7=5 (r3c7<>9 r3c4=9 r1c5<>9) (r1c8<>5) r3c9<>5 r3c9=1 r1c8<>1 r1c8=3 r1c5<>3 r1c5=1 r6c5<>1 r6c5=3 r5c4<>3
r3c7=5 (r2c9<>5) (r3c9<>5) (r8c7<>5) (r2c7<>5) (r2c9<>5) r1c8<>5 r1c6=5 (r8c6<>5) (r2c4<>5) r2c6<>5 r2c1=5 r8c1<>5 r8c8=5 (r7c8<>5 r7c8=8 r9c9<>8) r9c9<>5 r4c9=5 r4c9<>8 r5c9=8 r5c4<>8
r3c7=5 r3c7<>9 r3c4=9 r5c4<>9
Forcing Net Contradiction in c6 => r4c5<>1
r4c5=1 (r1c5<>1) r6c5<>1 r6c5=3 r1c5<>3 r1c5=9 r1c2<>9 r1c2=1 r1c6<>1
r4c5=1 r4c5<>4 r4c4=4 r3c4<>4 r3c6=4 r3c6<>7 r2c6=7 r2c6<>1
r4c5=1 r4c5<>4 r4c4=4 r3c4<>4 r3c6=4 r3c6<>1
r4c5=1 r6c6<>1
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c8<>1
Forcing Net Contradiction in r5 => r4c8<>8
r4c8=8 r4c8<>9 r4c45=9 r5c4<>9
r4c8=8 r4c8<>1 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r3c4=4 r3c4<>9 r3c7=9 r5c7<>9
r4c8=8 (r5c9<>8 r9c9=8 r9c9<>4) r4c8<>1 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r3c4=4 r9c4<>4 r9c8=4 r9c8<>7 r9c7=7 r5c7<>7 r5c8=7 r5c8<>9
Forcing Net Contradiction in r1 => r5c7<>2
r5c7=2 r1c5=9 r1c2<>9 r1c2=1
r5c7=2 (r6c8<>2 r2c8=2 r2c8<>1) (r5c7<>9) r5c7<>7 r5c8=7 r5c8<>9 r5c4=9 (r4c4<>9) r4c5<>9 r4c8=9 r4c8<>1 r1c8=1
Forcing Net Contradiction in r9 => r5c6<>3
r5c6=3 (r5c9<>3 r5c9=8 r6c8<>8) r5c6<>2 r6c6=2 r6c6<>8 r6c2=8 r9c2<>8
r5c6=3 (r5c9<>3 r5c9=8 r4c9<>8) (r5c9<>3 r5c9=8 r6c8<>8) r5c6<>2 r6c6=2 r6c6<>8 r6c2=8 (r4c1<>8) r4c2<>8 r4c4=8 r9c4<>8
r5c6=3 r5c6<>2 r5c8=2 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>8
r5c6=3 r5c9<>3 r5c9=8 r9c9<>8
Forcing Net Contradiction in c8 => r5c6=2
r5c6<>2 r5c8=2 (r6c8<>2) r4c7<>2 r4c7=5 r6c8<>5 r6c8=8 (r4c9<>8) r5c9<>8 (r5c9=3 r6c8<>3) (r5c9=3 r4c7<>3) r9c9=8 r9c9<>4 r2c9=4 r2c8<>4
r5c6<>2 (r5c6=8 r5c9<>8 r5c9=3 r4c9<>3) (r5c6=8 r5c9<>8 r5c9=3 r6c8<>3) (r5c6=8 r5c9<>8 r5c9=3 r4c7<>3) r5c8=2 (r6c8<>2) r4c7<>2 r4c7=5 (r4c9<>5) r6c8<>5 r6c8=8 r4c9<>8 r4c9=1 r3c9<>1 r3c6=1 r3c6<>4 r8c6=4 r8c8<>4
r5c6<>2 r5c8=2 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>4
Forcing Net Contradiction in c8 => r3c3<>5
r3c3=5 (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 r4c8<>2 r2c8=2 r2c8<>4
r3c3=5 (r2c1<>5) (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 r4c8<>2 r2c8=2 r2c1<>2 r2c1=7 (r3c1<>7) r3c3<>7 r3c6=7 r3c6<>4 r8c6=4 r8c8<>4
r3c3=5 (r9c3<>5 r9c3=3 r6c3<>3 r6c3=2 r6c8<>2) r3c9<>5 r3c9=1 r4c9<>1 r4c8=1 (r4c8<>9) r4c8<>2 r2c8=2 r2c8<>9 r5c8=9 r5c8<>7 r5c7=7 r9c7<>7 r9c8=7 r9c8<>4
Locked Candidates Type 1 (Pointing): 5 in b1 => r78c1<>5
Finned X-Wing: 5 r18 c68 fr8c7 => r79c8<>5
Forcing Net Contradiction in r7c2 => r3c3=2
r3c3<>2 r23c1=2 r7c1<>2 r7c2=2
r3c3<>2 r23c1=2 r7c1<>2 r7c2=2 (r7c2<>5) r7c2<>6 r7c4=6 r7c4<>5 r7c6=5 (r8c6<>5) r1c6<>5 r1c8=5 r8c8<>5 r8c7=5 r8c7<>6 r8c5=6 r7c4<>6 r7c2=6
Naked Single: r3c7=9
Hidden Single: r4c3=7
Empty Rectangle: 3 in b5 (r69c3) => r9c4<>3
Uniqueness Test 4: 5/7 in r2c16,r3c16 => r23c6<>5
Hidden Rectangle: 3/7 in r5c78,r9c78 => r9c8<>3
Grouped AIC: 8 8- r7c8 -3- r7c46 =3= r8c56 -3- r8c1 -8 => r7c12,r8c8<>8
Almost Locked Set XZ-Rule: A=r6c356 {1358}, B=r78c1,r9c3 {2358}, X=5, Z=8 => r8c6<>8
Hidden Single: r8c1=8
Finned Jellyfish: 3 c1479 r2457 fr8c7 fr9c7 fr9c9 => r7c8<>3
Naked Single: r7c8=8
Hidden Single: r6c6=8
Hidden Single: r9c4=8
Hidden Single: r5c9=8
Hidden Single: r4c2=8
Hidden Single: r6c5=1
Locked Candidates Type 1 (Pointing): 5 in b4 => r6c8<>5
Locked Candidates Type 1 (Pointing): 3 in b5 => r27c4<>3
Locked Candidates Type 1 (Pointing): 4 in b8 => r8c8<>4
W-Wing: 3/5 in r7c6,r8c8 connected by 5 in r1c68 => r8c56<>3
Hidden Single: r7c6=3
Naked Single: r7c1=2
Naked Single: r4c1=3
Naked Single: r6c3=5
Full House: r6c2=2
Full House: r9c3=3
Full House: r6c8=3
Naked Single: r5c7=7
Naked Single: r8c8=5
Naked Single: r5c8=9
Full House: r5c4=3
Naked Single: r1c8=1
Naked Single: r8c6=4
Naked Single: r9c7=6
Naked Single: r9c9=4
Naked Single: r1c2=9
Naked Single: r1c6=5
Full House: r1c5=3
Naked Single: r3c9=5
Naked Single: r4c8=2
Naked Single: r8c5=6
Full House: r8c7=3
Full House: r9c8=7
Full House: r9c2=5
Full House: r2c8=4
Full House: r7c4=5
Full House: r7c2=6
Full House: r2c2=1
Naked Single: r3c4=4
Naked Single: r2c9=3
Full House: r4c9=1
Full House: r4c7=5
Full House: r2c7=2
Naked Single: r3c1=7
Full House: r2c1=5
Full House: r3c6=1
Full House: r2c6=7
Naked Single: r2c5=9
Full House: r2c4=6
Full House: r4c4=9
Full House: r4c5=4
|
sudoku_normal_hard_147
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
....4..1....9.27.....6.......6..3.....276.9..8......5..1..5...3..3..92..4......8.
|
978345612651982734324671598146593827532768941897124356219856473783419265465237189
|
. . . . 4 . . 1 .
. . . 9 . 2 7 . .
. . . 6 . . . . .
. . 6 . . 3 . . .
. . 2 7 6 . 9 . .
8 . . . . . . 5 .
. 1 . . 5 . . . 3
. . 3 . . 9 2 . .
4 . . . . . . 8 .
|
9 7 8 3 4 5 6 1 2
6 5 1 9 8 2 7 3 4
3 2 4 6 7 1 5 9 8
1 4 6 5 9 3 8 2 7
5 3 2 7 6 8 9 4 1
8 9 7 1 2 4 3 5 6
2 1 9 8 5 6 4 7 3
7 8 3 4 1 9 2 6 5
4 6 5 2 3 7 1 8 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8325_hard
|
978345612651982734324671598146593827532768941897124356219856473783419265465237189 #1 Extreme (34946) bf
Grouped Discontinuous Nice Loop: 5 r1c1 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r1c1 => r1c1<>5
Grouped Discontinuous Nice Loop: 5 r1c2 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r1c2 => r1c2<>5
Grouped Discontinuous Nice Loop: 5 r3c1 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r3c1 => r3c1<>5
Grouped Discontinuous Nice Loop: 5 r3c2 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r3c2 => r3c2<>5
Brute Force: r5c5=6
Forcing Net Contradiction in r7 => r4c4<>2
r4c4=2 (r4c8<>2 r3c8=2 r3c8<>9 r7c8=9 r7c3<>9) (r6c4<>2) r6c5<>2 r6c9=2 (r6c9<>7) r6c9<>6 r6c7=6 r6c7<>3 r6c2=3 r6c2<>7 r6c3=7 r7c3<>7 r7c3=8
r4c4=2 (r7c4<>2) (r6c4<>2) r6c5<>2 r6c9=2 r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r7c4<>4 r7c4=8
Forcing Net Contradiction in b9 => r4c4<>4
r4c4=4 (r4c4<>5 r1c4=5 r1c4<>3 r9c4=3 r9c4<>1) (r4c4<>5 r1c4=5 r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c7<>8 r4c7=1 r9c7<>1) (r6c4<>4) r6c6<>4 r6c6=1 (r9c6<>1) r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>1 r9c9=1 r9c9<>9 r7c8=9 r7c8<>7
r4c4=4 (r4c4<>1) (r6c6<>4 r6c6=1 r6c4<>1) r4c4<>5 r1c4=5 (r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 r8c5<>8) r1c4<>3 r9c4=3 r9c4<>1 r8c4=1 r8c5<>1 r8c5=7 r8c8<>7
r4c4=4 (r4c4<>1) (r6c6<>4 r6c6=1 r6c4<>1) r4c4<>5 r1c4=5 (r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 r8c5<>8) r1c4<>3 r9c4=3 r9c4<>1 r8c4=1 r8c5<>1 r8c5=7 r8c9<>7
r4c4=4 (r4c4<>5 r1c4=5 r1c4<>3 r9c4=3 r9c4<>1) (r4c4<>5 r1c4=5 r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c7<>8 r4c7=1 r9c7<>1) (r6c4<>4) r6c6<>4 r6c6=1 (r9c6<>1) r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>1 r9c9=1 r9c9<>7
Grouped Discontinuous Nice Loop: 4 r6c2 -4- r4c2 =4= r4c789 -4- r5c8 -3- r6c7 =3= r6c2 => r6c2<>4
Forcing Net Contradiction in c4 => r2c2<>4
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r4c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r6c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c7<>4) (r6c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r5c6=4 r5c8<>4 r5c8=3 r6c7<>3 r6c7=6 r7c7<>6 r7c7=4 (r8c8<>4) r8c9<>4 r8c4=4 r8c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Forcing Net Contradiction in c4 => r3c2<>4
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r4c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r6c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c7<>4) (r6c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r5c6=4 r5c8<>4 r5c8=3 r6c7<>3 r6c7=6 r7c7<>6 r7c7=4 (r8c8<>4) r8c9<>4 r8c4=4 r8c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Locked Candidates Type 1 (Pointing): 4 in b1 => r6c3<>4
Forcing Net Contradiction in c4 => r6c7<>4
r6c7=4 r6c6<>4 r6c6=1 r4c4<>1
r6c7=4 r6c6<>4 r6c6=1 r6c4<>1
r6c7=4 (r7c7<>4 r7c7=6 r8c8<>6 r2c8=6 r2c2<>6 r2c2=8 r8c2<>8) (r5c8<>4) (r5c9<>4) (r4c7<>4) (r4c8<>4) r4c9<>4 r4c2=4 r5c2<>4 (r5c2=5 r4c1<>5 r4c4=5 r4c4<>8) r5c6=4 r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c4=8 r8c4<>1
r6c7=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Forcing Net Verity => r5c6<>4
r4c4=1 r6c6<>1 r6c6=4 r5c6<>4
r6c4=1 r6c6<>1 r6c6=4 r5c6<>4
r8c4=1 r8c4<>4 r7c46=4 r7c7<>4 r7c7=6 r6c7<>6 r6c9=6 r6c9<>4 r6c46=4 r5c6<>4
r9c4=1 (r6c4<>1) (r9c4<>2) r9c4<>3 r9c5=3 r9c5<>2 r9c2=2 r7c1<>2 r7c4=2 r6c4<>2 r6c4=4 r5c6<>4
Locked Candidates Type 1 (Pointing): 4 in b5 => r6c9<>4
Forcing Net Contradiction in c4 => r6c9<>1
r6c9=1 (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r9c4<>2 r9c4=3 r1c4<>3) (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r7c4<>2) r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r7c4<>4 r7c4=8 r1c4<>8 r1c4=5
r6c9=1 (r4c7<>1) r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r4c7<>4 r4c7=8 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5
Forcing Net Contradiction in c3 => r7c8<>4
r7c8=4 (r5c8<>4 r5c8=3 r6c7<>3 r6c2=3 r6c2<>7) r7c7<>4 r7c7=6 r6c7<>6 r6c9=6 r6c9<>7 r6c3=7
r7c8=4 (r7c8<>9 r3c8=9 r3c9<>9 r9c9=9 r9c3<>9) (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r9c7<>6) r6c7<>6 r6c7=1 r9c7<>1 r9c7=5 r9c3<>5 r9c3=7
Forcing Net Contradiction in r2c2 => r8c9<>6
r8c9=6 r6c9<>6 r6c7=6 r6c7<>3 r6c2=3 r2c2<>3
r8c9=6 (r8c1<>6) (r8c8<>6) r7c7<>6 r7c7=4 r8c8<>4 r8c8=7 r8c1<>7 r8c1=5 r9c3<>5 r123c3=5 r2c2<>5
r8c9=6 (r7c8<>6) r8c8<>6 r2c8=6 r2c2<>6
r8c9=6 (r8c2<>6) (r8c1<>6) (r8c8<>6) r7c7<>6 r7c7=4 r8c8<>4 r8c8=7 (r8c2<>7) r8c1<>7 r8c1=5 r8c2<>5 r8c2=8 r2c2<>8
Forcing Net Verity => r9c4<>1
r6c4=1 r9c4<>1
r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
r6c4=4 (r8c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r7c6=4 r7c7<>4 r7c7=6 r6c7<>6 r6c7=3 r5c8<>3 r5c8=4 r8c8<>4 r8c9=4 r8c9<>1 r8c45=1 r9c4<>1
Forcing Net Verity => r3c1<>1
r3c6=1 r3c1<>1
r5c6=1 (r6c4<>1 r8c4=1 r8c5<>1) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c5=7 r8c8<>7 r8c8=4 (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r8c8<>6) r6c7<>6 r6c7=1 r6c3<>1 r45c1=1 r3c1<>1
r6c6=1 r6c3<>1 r45c1=1 r3c1<>1
r9c6=1 (r5c6<>1) (r8c4<>1) r8c5<>1 r8c9=1 r5c9<>1 r5c1=1 r3c1<>1
Forcing Net Contradiction in r7c8 => r3c3<>5
r3c3=5 (r2c3<>5 r2c9=5 r2c9<>8) (r2c3<>5 r2c9=5 r1c7<>5 r9c7=5 r9c7<>1) (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r5c1<>1) r6c7<>1 r4c7=1 (r4c4<>1 r8c4=1 r8c4<>8) (r4c7<>8) r5c9<>1 r5c6=1 (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 (r2c5<>8) r8c5<>8 r8c2=8 r2c2<>8 r2c3=8 r2c3<>4 r3c3=4 r3c3<>5
Forcing Net Contradiction in r6 => r5c6<>1
r5c6=1 (r6c4<>1 r8c4=1 r8c4<>8) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r2c9<>8) (r4c7<>8) r4c9<>8 r4c5=8 (r2c5<>8) r8c5<>8 r8c2=8 r2c2<>8 r2c3=8 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1
r5c6=1 (r6c4<>1 r8c4=1 r8c5<>1) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c5=7 r8c8<>7 r8c8=4 (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r8c8<>6) r6c7<>6 r6c7=1
Forcing Net Contradiction in r7c8 => r1c6<>8
r1c6=8 (r1c7<>8) r5c6<>8 (r5c6=5 r4c4<>5 r1c4=5 r1c3<>5) (r5c6=5 r4c4<>5 r1c4=5 r1c7<>5) r5c9=8 r4c7<>8 r3c7=8 r3c7<>5 r9c7=5 r9c3<>5 r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 r5c1<>1 r5c9=1 r5c9<>8 r5c6=8 r1c6<>8
Forcing Net Contradiction in b4 => r1c9<>5
r1c9=5 (r1c7<>5) r3c7<>5 r9c7=5 r9c7<>1 r46c7=1 r5c9<>1 r5c1=1
r1c9=5 (r1c3<>5) (r1c7<>5) r3c7<>5 r9c7=5 r9c3<>5 r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1
Forcing Net Contradiction in c5 => r2c2<>3
r2c2=3 (r6c2<>3 r6c7=3 r1c7<>3) (r1c1<>3) (r2c1<>3) r3c1<>3 r5c1=3 (r5c8<>3 r5c8=4 r2c8<>4 r2c8=6 r1c7<>6) (r5c8<>3 r5c8=4 r4c7<>4) r5c1<>1 r5c9=1 r4c7<>1 r4c7=8 r1c7<>8 r1c7=5 r1c6<>5 r1c6=7 r3c5<>7
r2c2=3 (r2c8<>3) (r1c1<>3) (r2c1<>3) r3c1<>3 r5c1=3 r5c8<>3 r5c8=4 (r8c8<>4) r2c8<>4 r2c8=6 r8c8<>6 r8c8=7 r8c5<>7
r2c2=3 (r1c1<>3) (r1c2<>3) r6c2<>3 r6c7=3 r1c7<>3 r1c4=3 r9c4<>3 r9c5=3 r9c5<>7
Forcing Net Contradiction in r7c8 => r2c3<>8
r2c3=8 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 r5c1<>1 (r2c1=1 r2c5<>1 r2c5=3 r1c4<>3) r5c9=1 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=8 (r7c4<>8) r1c4<>5 r4c4=5 r5c6<>5 r5c6=8 r7c6<>8 r7c3=8 r2c3<>8
Forcing Net Contradiction in r7c8 => r3c3<>7
r3c3=7 (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r6c6<>1) (r6c7<>1) r5c1<>1 r5c9=1 (r5c9<>8 r5c6=8 r5c6<>5) r4c7<>1 r9c7=1 r9c6<>1 r3c6=1 r3c6<>5 r1c6=5 r1c6<>7 r1c123=7 r3c3<>7
Forcing Net Contradiction in r7c8 => r3c3<>8
r3c3=8 (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r9c4<>2 r9c4=3 r1c4<>3) r5c1<>1 r5c9=1 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=8 (r7c4<>8) r1c4<>5 r4c4=5 r5c6<>5 r5c6=8 r7c6<>8 r7c3=8 r3c3<>8
Forcing Net Contradiction in r1c7 => r1c9<>8
r1c9=8 (r1c4<>8) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=3 r1c7<>3
r1c9=8 (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>4) (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r4c4<>1 r6c4=1 (r6c6<>1) r6c4<>4 r7c4=4 r7c7<>4 r7c7=6 r7c6<>6 r9c6=6 r9c6<>1 r3c6=1 r3c6<>5 r1c46=5 r1c7<>5
r1c9=8 (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>4) (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r4c4<>1 r6c4=1 r6c4<>4 r7c4=4 r7c7<>4 r7c7=6 r1c7<>6
r1c9=8 r1c7<>8
Forcing Net Verity => r3c9<>5
r1c3=5 (r1c6<>5) r1c4<>5 r4c4=5 r5c6<>5 r3c6=5 r3c9<>5
r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 (r6c7<>1) r5c1<>1 r5c9=1 r4c7<>1 r9c7=1 r9c7<>5 r13c7=5 r3c9<>5
r9c3=5 (r8c1<>5) r8c2<>5 r8c9=5 r3c9<>5
Forcing Chain Contradiction in c7 => r7c6<>8
r7c6=8 r7c3<>8 r1c3=8 r1c7<>8
r7c6=8 r5c6<>8 r5c6=5 r3c6<>5 r3c7=5 r3c7<>8
r7c6=8 r5c6<>8 r5c9=8 r4c7<>8
Forcing Net Contradiction in r7c8 => r2c1<>1
r2c1=1 (r3c3<>1 r6c3=1 r6c6<>1 r6c6=4 r6c4<>4) (r4c1<>1) r5c1<>1 r5c9=1 (r4c7<>1 r9c7=1 r9c6<>1 r3c6=1 r3c6<>5 r3c7=5 r3c7<>4) (r4c7<>1) (r4c9<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 (r4c4<>1) r4c4<>1 r4c5=1 r6c4<>1 r8c4=1 r8c4<>4 r7c4=4 (r7c4<>8 r1c4=8 r1c7<>8 r1c7=3 r6c7<>3) r7c7<>4 r4c7=4 r7c7<>4 r7c7=6 r6c7<>6 r6c7=1 r5c9<>1 r5c1=1 r2c1<>1
Locked Candidates Type 1 (Pointing): 1 in b1 => r6c3<>1
Hidden Pair: 1,4 in r23c3 => r2c3<>5, r3c3<>9
Grouped AIC: 5 5- r9c3 =5= r1c3 -5- r2c12 =5= r2c9 -5- r13c7 =5= r9c7 -5 => r9c29<>5
Grouped Discontinuous Nice Loop: 1 r9c5 -1- r8c45 =1= r8c9 =5= r2c9 -5- r3c7 =5= r3c6 =1= r23c5 -1- r9c5 => r9c5<>1
Almost Locked Set XY-Wing: A=r7c67 {467}, B=r79c3,r8c12,r9c2 {256789}, C=r9c45 {237}, X,Y=2,7, Z=6 => r7c1<>6
Forcing Chain Contradiction in r8 => r4c4<>1
r4c4=1 r8c4<>1
r4c4=1 r4c4<>5 r5c6=5 r5c6<>8 r3c6=8 r3c6<>1 r23c5=1 r8c5<>1
r4c4=1 r4c4<>5 r1c4=5 r1c3<>5 r9c3=5 r9c7<>5 r8c9=5 r8c9<>1
Naked Pair: 5,8 in r4c4,r5c6 => r4c5<>8
Forcing Chain Contradiction in r9c7 => r4c5<>1
r4c5=1 r6c456<>1 r6c7=1 r9c7<>1
r4c5=1 r23c5<>1 r3c6=1 r3c6<>5 r3c7=5 r9c7<>5
r4c5=1 r6c4<>1 r8c4=1 r8c4<>4 r7c46=4 r7c7<>4 r7c7=6 r9c7<>6
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c7<>1
XY-Wing: 3/6/4 in r5c8,r67c7 => r4c7,r8c8<>4
Discontinuous Nice Loop: 1 r6c5 -1- r6c4 =1= r8c4 =4= r8c9 -4- r7c7 =4= r3c7 -4- r3c3 -1- r2c3 =1= r2c5 -1- r6c5 => r6c5<>1
Locked Pair: 2,9 in r46c5 => r6c4,r9c5<>2
Almost Locked Set XZ-Rule: A=r8c128 {5678}, B=r23679c3 {145789}, X=5,8 => r1c3,r8c59<>7, r1c3<>9
W-Wing: 5/8 in r1c3,r4c4 connected by 8 in r7c34 => r1c4<>5
Hidden Single: r4c4=5
Naked Single: r5c6=8
XYZ-Wing: 1/3/8 in r1c4,r28c5 => r3c5<>8
Continuous Nice Loop: 4/5/7 8= r7c4 =2= r9c4 =3= r9c5 =7= r3c5 -7- r1c6 -5- r1c3 -8- r7c3 =8= r7c4 =2 => r7c4<>4, r1c7<>5, r3c6<>7
Naked Triple: 2,3,8 in r179c4 => r8c4<>8
X-Wing: 8 c34 r17 => r1c27<>8
Naked Pair: 3,6 in r16c7 => r3c7<>3, r79c7<>6
Naked Single: r7c7=4
Hidden Single: r6c6=4
Naked Single: r6c4=1
Naked Single: r8c4=4
Naked Pair: 1,5 in r8c9,r9c7 => r9c9<>1
W-Wing: 8/5 in r1c3,r3c7 connected by 5 in r9c37 => r3c2<>8
Locked Candidates Type 2 (Claiming): 8 in r3 => r2c9<>8
XYZ-Wing: 3/4/6 in r1c7,r25c8 => r3c8<>3
XY-Chain: 4 4- r3c3 -1- r3c6 -5- r3c7 -8- r4c7 -1- r5c9 -4 => r3c9<>4
AIC: 4 4- r5c8 -3- r2c8 =3= r1c7 -3- r1c4 -8- r7c4 =8= r8c5 =1= r8c9 -1- r5c9 -4 => r4c89,r5c2<>4
Hidden Single: r4c2=4
XY-Chain: 5 5- r5c2 -3- r5c8 -4- r5c9 -1- r8c9 -5 => r8c2<>5
Continuous Nice Loop: 3/6 5= r2c9 =4= r5c9 -4- r5c8 -3- r2c8 =3= r1c7 -3- r1c4 -8- r1c3 -5- r1c6 =5= r3c6 -5- r3c7 =5= r2c9 =4 => r1c12<>3, r2c9<>6
Naked Triple: 1,4,5 in r258c9 => r4c9<>1
Discontinuous Nice Loop: 7 r9c3 -7- r9c5 =7= r3c5 -7- r1c6 -5- r1c3 =5= r9c3 => r9c3<>7
Discontinuous Nice Loop: 7 r4c1 -7- r6c3 -9- r9c3 -5- r9c7 -1- r4c7 =1= r4c1 => r4c1<>7
Locked Candidates Type 1 (Pointing): 7 in b4 => r6c9<>7
XY-Wing: 2/7/6 in r48c8,r6c9 => r9c9<>6
Locked Candidates Type 1 (Pointing): 6 in b9 => r2c8<>6
Locked Candidates Type 1 (Pointing): 6 in b3 => r1c12<>6
Naked Pair: 3,4 in r25c8 => r3c8<>4
Hidden Single: r3c3=4
Naked Single: r2c3=1
Naked Pair: 3,8 in r1c4,r2c5 => r3c5<>3
Locked Candidates Type 2 (Claiming): 3 in r3 => r2c1<>3
XYZ-Wing: 2/6/9 in r16c9,r3c8 => r3c9<>2
XY-Chain: 8 8- r1c3 -5- r9c3 -9- r9c9 -7- r9c5 -3- r2c5 -8 => r1c4,r2c2<>8
Naked Single: r1c4=3
Naked Single: r1c7=6
Naked Single: r2c5=8
Naked Single: r9c4=2
Full House: r7c4=8
Naked Single: r6c7=3
Naked Single: r8c5=1
Naked Single: r5c8=4
Naked Single: r3c5=7
Naked Single: r8c9=5
Naked Single: r2c8=3
Naked Single: r5c9=1
Naked Single: r1c6=5
Full House: r3c6=1
Naked Single: r9c5=3
Naked Single: r2c9=4
Naked Single: r9c7=1
Naked Single: r4c7=8
Full House: r3c7=5
Naked Single: r1c3=8
Hidden Single: r8c2=8
Hidden Single: r6c9=6
Hidden Single: r7c1=2
Hidden Single: r9c3=5
Hidden Single: r4c1=1
Hidden Single: r3c9=8
Hidden Single: r6c5=2
Full House: r4c5=9
Locked Candidates Type 2 (Claiming): 9 in c1 => r13c2<>9
W-Wing: 9/7 in r1c1,r9c9 connected by 7 in r8c18 => r1c9<>9
Naked Single: r1c9=2
Full House: r3c8=9
Naked Single: r1c2=7
Full House: r1c1=9
Naked Single: r4c9=7
Full House: r4c8=2
Full House: r9c9=9
Naked Single: r3c1=3
Full House: r3c2=2
Naked Single: r6c2=9
Full House: r6c3=7
Full House: r7c3=9
Naked Single: r9c2=6
Full House: r8c1=7
Full House: r9c6=7
Full House: r8c8=6
Full House: r7c6=6
Full House: r7c8=7
Naked Single: r5c1=5
Full House: r2c1=6
Full House: r2c2=5
Full House: r5c2=3
|
sudoku_normal_extremely_hard_147
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
....4..1....9.27.....6.......6..3.....27..9..8......5..1..5...3..3..92..4......8.
|
978345612651982734324671598146593827532768941897124356219856473783419265465237189
|
. . . . 4 . . 1 .
. . . 9 . 2 7 . .
. . . 6 . . . . .
. . 6 . . 3 . . .
. . 2 7 . . 9 . .
8 . . . . . . 5 .
. 1 . . 5 . . . 3
. . 3 . . 9 2 . .
4 . . . . . . 8 .
|
9 7 8 3 4 5 6 1 2
6 5 1 9 8 2 7 3 4
3 2 4 6 7 1 5 9 8
1 4 6 5 9 3 8 2 7
5 3 2 7 6 8 9 4 1
8 9 7 1 2 4 3 5 6
2 1 9 8 5 6 4 7 3
7 8 3 4 1 9 2 6 5
4 6 5 2 3 7 1 8 9
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_8325_hard
|
978345612651982734324671598146593827532768941897124356219856473783419265465237189 #1 Extreme (34946) bf
Grouped Discontinuous Nice Loop: 5 r1c1 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r1c1 => r1c1<>5
Grouped Discontinuous Nice Loop: 5 r1c2 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r1c2 => r1c2<>5
Grouped Discontinuous Nice Loop: 5 r3c1 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r3c1 => r3c1<>5
Grouped Discontinuous Nice Loop: 5 r3c2 -5- r2c123 =5= r2c9 -5- r8c9 =5= r8c12 -5- r9c3 =5= r123c3 -5- r3c2 => r3c2<>5
Brute Force: r5c5=6
Forcing Net Contradiction in r7 => r4c4<>2
r4c4=2 (r4c8<>2 r3c8=2 r3c8<>9 r7c8=9 r7c3<>9) (r6c4<>2) r6c5<>2 r6c9=2 (r6c9<>7) r6c9<>6 r6c7=6 r6c7<>3 r6c2=3 r6c2<>7 r6c3=7 r7c3<>7 r7c3=8
r4c4=2 (r7c4<>2) (r6c4<>2) r6c5<>2 r6c9=2 r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r7c4<>4 r7c4=8
Forcing Net Contradiction in b9 => r4c4<>4
r4c4=4 (r4c4<>5 r1c4=5 r1c4<>3 r9c4=3 r9c4<>1) (r4c4<>5 r1c4=5 r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c7<>8 r4c7=1 r9c7<>1) (r6c4<>4) r6c6<>4 r6c6=1 (r9c6<>1) r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>1 r9c9=1 r9c9<>9 r7c8=9 r7c8<>7
r4c4=4 (r4c4<>1) (r6c6<>4 r6c6=1 r6c4<>1) r4c4<>5 r1c4=5 (r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 r8c5<>8) r1c4<>3 r9c4=3 r9c4<>1 r8c4=1 r8c5<>1 r8c5=7 r8c8<>7
r4c4=4 (r4c4<>1) (r6c6<>4 r6c6=1 r6c4<>1) r4c4<>5 r1c4=5 (r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 r8c5<>8) r1c4<>3 r9c4=3 r9c4<>1 r8c4=1 r8c5<>1 r8c5=7 r8c9<>7
r4c4=4 (r4c4<>5 r1c4=5 r1c4<>3 r9c4=3 r9c4<>1) (r4c4<>5 r1c4=5 r3c6<>5 r5c6=5 r5c6<>8 r5c9=8 r4c7<>8 r4c7=1 r9c7<>1) (r6c4<>4) r6c6<>4 r6c6=1 (r9c6<>1) r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>1 r9c9=1 r9c9<>7
Grouped Discontinuous Nice Loop: 4 r6c2 -4- r4c2 =4= r4c789 -4- r5c8 -3- r6c7 =3= r6c2 => r6c2<>4
Forcing Net Contradiction in c4 => r2c2<>4
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r4c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r6c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c7<>4) (r6c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r5c6=4 r5c8<>4 r5c8=3 r6c7<>3 r6c7=6 r7c7<>6 r7c7=4 (r8c8<>4) r8c9<>4 r8c4=4 r8c4<>1
r2c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Forcing Net Contradiction in c4 => r3c2<>4
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r4c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 r6c6<>4 r6c6=1 r6c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c7<>4) (r6c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r5c6=4 r5c8<>4 r5c8=3 r6c7<>3 r6c7=6 r7c7<>6 r7c7=4 (r8c8<>4) r8c9<>4 r8c4=4 r8c4<>1
r3c2=4 (r2c3<>4) r3c3<>4 r6c3=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Locked Candidates Type 1 (Pointing): 4 in b1 => r6c3<>4
Forcing Net Contradiction in c4 => r6c7<>4
r6c7=4 r6c6<>4 r6c6=1 r4c4<>1
r6c7=4 r6c6<>4 r6c6=1 r6c4<>1
r6c7=4 (r7c7<>4 r7c7=6 r8c8<>6 r2c8=6 r2c2<>6 r2c2=8 r8c2<>8) (r5c8<>4) (r5c9<>4) (r4c7<>4) (r4c8<>4) r4c9<>4 r4c2=4 r5c2<>4 (r5c2=5 r4c1<>5 r4c4=5 r4c4<>8) r5c6=4 r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c4=8 r8c4<>1
r6c7=4 (r6c4<>4) r6c6<>4 r6c6=1 r6c4<>1 r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
Forcing Net Verity => r5c6<>4
r4c4=1 r6c6<>1 r6c6=4 r5c6<>4
r6c4=1 r6c6<>1 r6c6=4 r5c6<>4
r8c4=1 r8c4<>4 r7c46=4 r7c7<>4 r7c7=6 r6c7<>6 r6c9=6 r6c9<>4 r6c46=4 r5c6<>4
r9c4=1 (r6c4<>1) (r9c4<>2) r9c4<>3 r9c5=3 r9c5<>2 r9c2=2 r7c1<>2 r7c4=2 r6c4<>2 r6c4=4 r5c6<>4
Locked Candidates Type 1 (Pointing): 4 in b5 => r6c9<>4
Forcing Net Contradiction in c4 => r6c9<>1
r6c9=1 (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r9c4<>2 r9c4=3 r1c4<>3) (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r7c4<>2) r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r7c4<>4 r7c4=8 r1c4<>8 r1c4=5
r6c9=1 (r4c7<>1) r6c9<>6 r6c7=6 r7c7<>6 r7c7=4 r4c7<>4 r4c7=8 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5
Forcing Net Contradiction in c3 => r7c8<>4
r7c8=4 (r5c8<>4 r5c8=3 r6c7<>3 r6c2=3 r6c2<>7) r7c7<>4 r7c7=6 r6c7<>6 r6c9=6 r6c9<>7 r6c3=7
r7c8=4 (r7c8<>9 r3c8=9 r3c9<>9 r9c9=9 r9c3<>9) (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r9c7<>6) r6c7<>6 r6c7=1 r9c7<>1 r9c7=5 r9c3<>5 r9c3=7
Forcing Net Contradiction in r2c2 => r8c9<>6
r8c9=6 r6c9<>6 r6c7=6 r6c7<>3 r6c2=3 r2c2<>3
r8c9=6 (r8c1<>6) (r8c8<>6) r7c7<>6 r7c7=4 r8c8<>4 r8c8=7 r8c1<>7 r8c1=5 r9c3<>5 r123c3=5 r2c2<>5
r8c9=6 (r7c8<>6) r8c8<>6 r2c8=6 r2c2<>6
r8c9=6 (r8c2<>6) (r8c1<>6) (r8c8<>6) r7c7<>6 r7c7=4 r8c8<>4 r8c8=7 (r8c2<>7) r8c1<>7 r8c1=5 r8c2<>5 r8c2=8 r2c2<>8
Forcing Net Verity => r9c4<>1
r6c4=1 r9c4<>1
r6c4=2 (r4c5<>2) r6c5<>2 r9c5=2 r9c5<>3 r9c4=3 r9c4<>1
r6c4=4 (r8c4<>4) r6c6<>4 (r6c6=1 r6c7<>1) r7c6=4 r7c7<>4 r7c7=6 r6c7<>6 r6c7=3 r5c8<>3 r5c8=4 r8c8<>4 r8c9=4 r8c9<>1 r8c45=1 r9c4<>1
Forcing Net Verity => r3c1<>1
r3c6=1 r3c1<>1
r5c6=1 (r6c4<>1 r8c4=1 r8c5<>1) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c5=7 r8c8<>7 r8c8=4 (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r8c8<>6) r6c7<>6 r6c7=1 r6c3<>1 r45c1=1 r3c1<>1
r6c6=1 r6c3<>1 r45c1=1 r3c1<>1
r9c6=1 (r5c6<>1) (r8c4<>1) r8c5<>1 r8c9=1 r5c9<>1 r5c1=1 r3c1<>1
Forcing Net Contradiction in r7c8 => r3c3<>5
r3c3=5 (r2c3<>5 r2c9=5 r2c9<>8) (r2c3<>5 r2c9=5 r1c7<>5 r9c7=5 r9c7<>1) (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r5c1<>1) r6c7<>1 r4c7=1 (r4c4<>1 r8c4=1 r8c4<>8) (r4c7<>8) r5c9<>1 r5c6=1 (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 r4c9<>8 r4c5=8 (r2c5<>8) r8c5<>8 r8c2=8 r2c2<>8 r2c3=8 r2c3<>4 r3c3=4 r3c3<>5
Forcing Net Contradiction in r6 => r5c6<>1
r5c6=1 (r6c4<>1 r8c4=1 r8c4<>8) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r2c9<>8) (r4c7<>8) r4c9<>8 r4c5=8 (r2c5<>8) r8c5<>8 r8c2=8 r2c2<>8 r2c3=8 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1
r5c6=1 (r6c4<>1 r8c4=1 r8c5<>1) (r5c6<>5 r4c4=5 r4c4<>8) r5c6<>8 r5c9=8 (r4c7<>8) r4c9<>8 r4c5=8 r8c5<>8 r8c5=7 r8c8<>7 r8c8=4 (r5c8<>4 r5c8=3 r6c7<>3) r7c7<>4 r7c7=6 (r8c8<>6) r6c7<>6 r6c7=1
Forcing Net Contradiction in r7c8 => r1c6<>8
r1c6=8 (r1c7<>8) r5c6<>8 (r5c6=5 r4c4<>5 r1c4=5 r1c3<>5) (r5c6=5 r4c4<>5 r1c4=5 r1c7<>5) r5c9=8 r4c7<>8 r3c7=8 r3c7<>5 r9c7=5 r9c3<>5 r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 r5c1<>1 r5c9=1 r5c9<>8 r5c6=8 r1c6<>8
Forcing Net Contradiction in b4 => r1c9<>5
r1c9=5 (r1c7<>5) r3c7<>5 r9c7=5 r9c7<>1 r46c7=1 r5c9<>1 r5c1=1
r1c9=5 (r1c3<>5) (r1c7<>5) r3c7<>5 r9c7=5 r9c3<>5 r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1
Forcing Net Contradiction in c5 => r2c2<>3
r2c2=3 (r6c2<>3 r6c7=3 r1c7<>3) (r1c1<>3) (r2c1<>3) r3c1<>3 r5c1=3 (r5c8<>3 r5c8=4 r2c8<>4 r2c8=6 r1c7<>6) (r5c8<>3 r5c8=4 r4c7<>4) r5c1<>1 r5c9=1 r4c7<>1 r4c7=8 r1c7<>8 r1c7=5 r1c6<>5 r1c6=7 r3c5<>7
r2c2=3 (r2c8<>3) (r1c1<>3) (r2c1<>3) r3c1<>3 r5c1=3 r5c8<>3 r5c8=4 (r8c8<>4) r2c8<>4 r2c8=6 r8c8<>6 r8c8=7 r8c5<>7
r2c2=3 (r1c1<>3) (r1c2<>3) r6c2<>3 r6c7=3 r1c7<>3 r1c4=3 r9c4<>3 r9c5=3 r9c5<>7
Forcing Net Contradiction in r7c8 => r2c3<>8
r2c3=8 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 r5c1<>1 (r2c1=1 r2c5<>1 r2c5=3 r1c4<>3) r5c9=1 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=8 (r7c4<>8) r1c4<>5 r4c4=5 r5c6<>5 r5c6=8 r7c6<>8 r7c3=8 r2c3<>8
Forcing Net Contradiction in r7c8 => r3c3<>7
r3c3=7 (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r6c6<>1) (r6c7<>1) r5c1<>1 r5c9=1 (r5c9<>8 r5c6=8 r5c6<>5) r4c7<>1 r9c7=1 r9c6<>1 r3c6=1 r3c6<>5 r1c6=5 r1c6<>7 r1c123=7 r3c3<>7
Forcing Net Contradiction in r7c8 => r3c3<>8
r3c3=8 (r3c3<>1) r3c3<>4 r2c3=4 r2c3<>1 r6c3=1 (r6c6<>1 r6c6=4 r6c4<>4 r6c4=2 r9c4<>2 r9c4=3 r1c4<>3) r5c1<>1 r5c9=1 r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=8 (r7c4<>8) r1c4<>5 r4c4=5 r5c6<>5 r5c6=8 r7c6<>8 r7c3=8 r3c3<>8
Forcing Net Contradiction in r1c7 => r1c9<>8
r1c9=8 (r1c4<>8) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r1c4<>5 r1c4=3 r1c7<>3
r1c9=8 (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>4) (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r4c4<>1 r6c4=1 (r6c6<>1) r6c4<>4 r7c4=4 r7c7<>4 r7c7=6 r7c6<>6 r9c6=6 r9c6<>1 r3c6=1 r3c6<>5 r1c46=5 r1c7<>5
r1c9=8 (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>4) (r3c7<>8 r4c7=8 r4c4<>8 r8c4=8 r8c4<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 r4c4<>1 r6c4=1 r6c4<>4 r7c4=4 r7c7<>4 r7c7=6 r1c7<>6
r1c9=8 r1c7<>8
Forcing Net Verity => r3c9<>5
r1c3=5 (r1c6<>5) r1c4<>5 r4c4=5 r5c6<>5 r3c6=5 r3c9<>5
r2c3=5 (r2c3<>1) r2c3<>4 r3c3=4 r3c3<>1 r6c3=1 (r6c7<>1) r5c1<>1 r5c9=1 r4c7<>1 r9c7=1 r9c7<>5 r13c7=5 r3c9<>5
r9c3=5 (r8c1<>5) r8c2<>5 r8c9=5 r3c9<>5
Forcing Chain Contradiction in c7 => r7c6<>8
r7c6=8 r7c3<>8 r1c3=8 r1c7<>8
r7c6=8 r5c6<>8 r5c6=5 r3c6<>5 r3c7=5 r3c7<>8
r7c6=8 r5c6<>8 r5c9=8 r4c7<>8
Forcing Net Contradiction in r7c8 => r2c1<>1
r2c1=1 (r3c3<>1 r6c3=1 r6c6<>1 r6c6=4 r6c4<>4) (r4c1<>1) r5c1<>1 r5c9=1 (r4c7<>1 r9c7=1 r9c6<>1 r3c6=1 r3c6<>5 r3c7=5 r3c7<>4) (r4c7<>1) (r4c9<>1) r5c9<>8 r5c6=8 r5c6<>5 r4c4=5 (r4c4<>1) r4c4<>1 r4c5=1 r6c4<>1 r8c4=1 r8c4<>4 r7c4=4 (r7c4<>8 r1c4=8 r1c7<>8 r1c7=3 r6c7<>3) r7c7<>4 r4c7=4 r7c7<>4 r7c7=6 r6c7<>6 r6c7=1 r5c9<>1 r5c1=1 r2c1<>1
Locked Candidates Type 1 (Pointing): 1 in b1 => r6c3<>1
Hidden Pair: 1,4 in r23c3 => r2c3<>5, r3c3<>9
Grouped AIC: 5 5- r9c3 =5= r1c3 -5- r2c12 =5= r2c9 -5- r13c7 =5= r9c7 -5 => r9c29<>5
Grouped Discontinuous Nice Loop: 1 r9c5 -1- r8c45 =1= r8c9 =5= r2c9 -5- r3c7 =5= r3c6 =1= r23c5 -1- r9c5 => r9c5<>1
Almost Locked Set XY-Wing: A=r7c67 {467}, B=r79c3,r8c12,r9c2 {256789}, C=r9c45 {237}, X,Y=2,7, Z=6 => r7c1<>6
Forcing Chain Contradiction in r8 => r4c4<>1
r4c4=1 r8c4<>1
r4c4=1 r4c4<>5 r5c6=5 r5c6<>8 r3c6=8 r3c6<>1 r23c5=1 r8c5<>1
r4c4=1 r4c4<>5 r1c4=5 r1c3<>5 r9c3=5 r9c7<>5 r8c9=5 r8c9<>1
Naked Pair: 5,8 in r4c4,r5c6 => r4c5<>8
Forcing Chain Contradiction in r9c7 => r4c5<>1
r4c5=1 r6c456<>1 r6c7=1 r9c7<>1
r4c5=1 r23c5<>1 r3c6=1 r3c6<>5 r3c7=5 r9c7<>5
r4c5=1 r6c4<>1 r8c4=1 r8c4<>4 r7c46=4 r7c7<>4 r7c7=6 r9c7<>6
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c7<>1
XY-Wing: 3/6/4 in r5c8,r67c7 => r4c7,r8c8<>4
Discontinuous Nice Loop: 1 r6c5 -1- r6c4 =1= r8c4 =4= r8c9 -4- r7c7 =4= r3c7 -4- r3c3 -1- r2c3 =1= r2c5 -1- r6c5 => r6c5<>1
Locked Pair: 2,9 in r46c5 => r6c4,r9c5<>2
Almost Locked Set XZ-Rule: A=r8c128 {5678}, B=r23679c3 {145789}, X=5,8 => r1c3,r8c59<>7, r1c3<>9
W-Wing: 5/8 in r1c3,r4c4 connected by 8 in r7c34 => r1c4<>5
Hidden Single: r4c4=5
Naked Single: r5c6=8
XYZ-Wing: 1/3/8 in r1c4,r28c5 => r3c5<>8
Continuous Nice Loop: 4/5/7 8= r7c4 =2= r9c4 =3= r9c5 =7= r3c5 -7- r1c6 -5- r1c3 -8- r7c3 =8= r7c4 =2 => r7c4<>4, r1c7<>5, r3c6<>7
Naked Triple: 2,3,8 in r179c4 => r8c4<>8
X-Wing: 8 c34 r17 => r1c27<>8
Naked Pair: 3,6 in r16c7 => r3c7<>3, r79c7<>6
Naked Single: r7c7=4
Hidden Single: r6c6=4
Naked Single: r6c4=1
Naked Single: r8c4=4
Naked Pair: 1,5 in r8c9,r9c7 => r9c9<>1
W-Wing: 8/5 in r1c3,r3c7 connected by 5 in r9c37 => r3c2<>8
Locked Candidates Type 2 (Claiming): 8 in r3 => r2c9<>8
XYZ-Wing: 3/4/6 in r1c7,r25c8 => r3c8<>3
XY-Chain: 4 4- r3c3 -1- r3c6 -5- r3c7 -8- r4c7 -1- r5c9 -4 => r3c9<>4
AIC: 4 4- r5c8 -3- r2c8 =3= r1c7 -3- r1c4 -8- r7c4 =8= r8c5 =1= r8c9 -1- r5c9 -4 => r4c89,r5c2<>4
Hidden Single: r4c2=4
XY-Chain: 5 5- r5c2 -3- r5c8 -4- r5c9 -1- r8c9 -5 => r8c2<>5
Continuous Nice Loop: 3/6 5= r2c9 =4= r5c9 -4- r5c8 -3- r2c8 =3= r1c7 -3- r1c4 -8- r1c3 -5- r1c6 =5= r3c6 -5- r3c7 =5= r2c9 =4 => r1c12<>3, r2c9<>6
Naked Triple: 1,4,5 in r258c9 => r4c9<>1
Discontinuous Nice Loop: 7 r9c3 -7- r9c5 =7= r3c5 -7- r1c6 -5- r1c3 =5= r9c3 => r9c3<>7
Discontinuous Nice Loop: 7 r4c1 -7- r6c3 -9- r9c3 -5- r9c7 -1- r4c7 =1= r4c1 => r4c1<>7
Locked Candidates Type 1 (Pointing): 7 in b4 => r6c9<>7
XY-Wing: 2/7/6 in r48c8,r6c9 => r9c9<>6
Locked Candidates Type 1 (Pointing): 6 in b9 => r2c8<>6
Locked Candidates Type 1 (Pointing): 6 in b3 => r1c12<>6
Naked Pair: 3,4 in r25c8 => r3c8<>4
Hidden Single: r3c3=4
Naked Single: r2c3=1
Naked Pair: 3,8 in r1c4,r2c5 => r3c5<>3
Locked Candidates Type 2 (Claiming): 3 in r3 => r2c1<>3
XYZ-Wing: 2/6/9 in r16c9,r3c8 => r3c9<>2
XY-Chain: 8 8- r1c3 -5- r9c3 -9- r9c9 -7- r9c5 -3- r2c5 -8 => r1c4,r2c2<>8
Naked Single: r1c4=3
Naked Single: r1c7=6
Naked Single: r2c5=8
Naked Single: r9c4=2
Full House: r7c4=8
Naked Single: r6c7=3
Naked Single: r8c5=1
Naked Single: r5c8=4
Naked Single: r3c5=7
Naked Single: r8c9=5
Naked Single: r2c8=3
Naked Single: r5c9=1
Naked Single: r1c6=5
Full House: r3c6=1
Naked Single: r9c5=3
Naked Single: r2c9=4
Naked Single: r9c7=1
Naked Single: r4c7=8
Full House: r3c7=5
Naked Single: r1c3=8
Hidden Single: r8c2=8
Hidden Single: r6c9=6
Hidden Single: r7c1=2
Hidden Single: r9c3=5
Hidden Single: r4c1=1
Hidden Single: r3c9=8
Hidden Single: r6c5=2
Full House: r4c5=9
Locked Candidates Type 2 (Claiming): 9 in c1 => r13c2<>9
W-Wing: 9/7 in r1c1,r9c9 connected by 7 in r8c18 => r1c9<>9
Naked Single: r1c9=2
Full House: r3c8=9
Naked Single: r1c2=7
Full House: r1c1=9
Naked Single: r4c9=7
Full House: r4c8=2
Full House: r9c9=9
Naked Single: r3c1=3
Full House: r3c2=2
Naked Single: r6c2=9
Full House: r6c3=7
Full House: r7c3=9
Naked Single: r9c2=6
Full House: r8c1=7
Full House: r9c6=7
Full House: r8c8=6
Full House: r7c6=6
Full House: r7c8=7
Naked Single: r5c1=5
Full House: r2c1=6
Full House: r2c2=5
Full House: r5c2=3
|
sudoku_normal_hard_148
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
6.472......54.6...7..39..4697.65...4.5293476.4.6.7295..6.5..4...49.6713...7.4.6..
|
694725813315486279728391546971658324852934761436172958263519487549867132187243695
|
6 . 4 7 2 . . . .
. . 5 4 . 6 . . .
7 . . 3 9 . . 4 6
9 7 . 6 5 . . . 4
. 5 2 9 3 4 7 6 .
4 . 6 . 7 2 9 5 .
. 6 . 5 . . 4 . .
. 4 9 . 6 7 1 3 .
. . 7 . 4 . 6 . .
|
6 9 4 7 2 5 8 1 3
3 1 5 4 8 6 2 7 9
7 2 8 3 9 1 5 4 6
9 7 1 6 5 8 3 2 4
8 5 2 9 3 4 7 6 1
4 3 6 1 7 2 9 5 8
2 6 3 5 1 9 4 8 7
5 4 9 8 6 7 1 3 2
1 8 7 2 4 3 6 9 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5112_hard
|
694725813315486279728391546971658324852934761436172958263519487549867132187243695 #1 Extreme (27098) bf
Hidden Single: r6c3=6
Hidden Single: r4c5=5
Hidden Single: r1c3=4
Hidden Single: r8c5=6
Hidden Single: r4c2=7
Hidden Single: r2c4=4
Hidden Single: r4c1=9
Hidden Single: r4c9=4
Hidden Single: r6c1=4
Brute Force: r5c7=7
Hidden Single: r5c8=6
Hidden Single: r9c7=6
Locked Candidates Type 1 (Pointing): 5 in b9 => r1c9<>5
Almost Locked Set XZ-Rule: A=r1c789,r23c7 {123589}, B=r4c7,r56c9 {1238}, X=2, Z=1 => r2c9<>1
Brute Force: r5c5=3
Finned Franken Swordfish: 1 c35b5 r347 fr2c5 fr6c4 => r3c4<>1
W-Wing: 8/1 in r4c6,r7c5 connected by 1 in r69c4 => r789c6<>8
Naked Single: r8c6=7
Sashimi Swordfish: 8 c356 r347 fr1c6 fr2c5 => r3c4<>8
Naked Single: r3c4=3
Naked Triple: 1,2,8 in r7c5,r89c4 => r79c6<>1
Empty Rectangle: 3 in b1 (r6c29) => r2c9<>3
Finned Jellyfish: 8 r5689 c1249 fr9c8 => r7c9<>8
Forcing Chain Contradiction in c8 => r1c8<>8
r1c8=8 r1c8<>1
r1c8=8 r123c7<>8 r4c7=8 r4c6<>8 r4c6=1 r13c6<>1 r2c5=1 r2c8<>1
r1c8=8 r123c7<>8 r4c7=8 r4c7<>2 r4c8=2 r4c8<>1
Forcing Chain Verity => r1c9<>1
r2c1=1 r5c1<>1 r5c9=1 r1c9<>1
r2c2=1 r2c2<>9 r1c2=9 r1c8<>9 r1c8=1 r1c9<>1
r2c5=1 r13c6<>1 r4c6=1 r4c8<>1 r12c8=1 r1c9<>1
r2c8=1 r1c9<>1
Locked Candidates Type 1 (Pointing): 1 in b3 => r4c8<>1
W-Wing: 8/1 in r5c1,r6c4 connected by 1 in r4c36 => r6c2<>8
Swordfish: 8 r568 c149 => r129c9,r279c1,r9c4<>8
Discontinuous Nice Loop: 3 r2c2 -3- r6c2 =3= r6c9 -3- r1c9 -9- r1c2 =9= r2c2 => r2c2<>3
Discontinuous Nice Loop: 1 r2c1 -1- r2c5 =1= r7c5 -1- r9c4 =1= r6c4 -1- r6c2 -3- r1c2 =3= r2c1 => r2c1<>1
Finned Swordfish: 1 c149 r569 fr7c1 => r9c2<>1
Discontinuous Nice Loop: 8 r7c3 -8- r7c5 -1- r9c4 =1= r6c4 -1- r6c2 -3- r4c3 =3= r7c3 => r7c3<>8
XYZ-Wing: 1/2/3 in r27c1,r7c3 => r9c1<>3
AIC: 1 1- r1c8 =1= r2c8 =7= r7c8 =8= r7c5 =1= r2c5 -1 => r1c6,r2c8<>1
Hidden Single: r1c8=1
Hidden Rectangle: 5/8 in r1c67,r3c67 => r3c7<>8
AIC: 3 3- r7c3 =3= r4c3 =8= r5c1 -8- r8c1 =8= r9c2 =3= r9c6 -3 => r7c6,r9c2<>3
Naked Single: r7c6=9
Naked Single: r9c6=3
X-Wing: 3 c29 r16 => r1c7<>3
Naked Pair: 5,8 in r1c67 => r1c2<>8
XYZ-Wing: 1/2/8 in r3c23,r9c2 => r2c2<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r3c6<>8
XYZ-Wing: 2/7/8 in r47c8,r7c9 => r9c8<>2
Hidden Rectangle: 2/7 in r2c89,r7c89 => r2c8<>2
XY-Chain: 2 2- r3c7 -5- r3c6 -1- r4c6 -8- r4c8 -2 => r4c7<>2
Hidden Single: r4c8=2
Locked Candidates Type 1 (Pointing): 2 in b9 => r2c9<>2
XY-Chain: 2 2- r7c9 -7- r7c8 -8- r7c5 -1- r9c4 -2 => r9c9<>2
Sue de Coq: r9c12 - {1258} (r9c89 - {589}, r7c13 - {123}) => r8c1<>2
Grouped AIC: 3/9 3- r1c9 -9- r9c9 =9= r9c8 =8= r9c2 =2= r79c1 -2- r2c1 -3- r1c2 -9 => r1c2<>3, r1c9<>9
Naked Single: r1c2=9
Naked Single: r1c9=3
Hidden Single: r6c2=3
Hidden Single: r2c1=3
Hidden Single: r4c7=3
Hidden Single: r7c3=3
Locked Candidates Type 1 (Pointing): 2 in b1 => r9c2<>2
Naked Single: r9c2=8
Naked Single: r8c1=5
Naked Single: r9c8=9
Naked Single: r9c9=5
Hidden Single: r3c3=8
Full House: r4c3=1
Full House: r4c6=8
Full House: r5c1=8
Full House: r6c4=1
Full House: r5c9=1
Full House: r6c9=8
Naked Single: r1c6=5
Full House: r1c7=8
Full House: r3c6=1
Full House: r2c5=8
Full House: r7c5=1
Naked Single: r9c4=2
Full House: r8c4=8
Full House: r8c9=2
Full House: r9c1=1
Full House: r7c1=2
Naked Single: r2c7=2
Full House: r3c7=5
Full House: r3c2=2
Full House: r2c2=1
Naked Single: r2c8=7
Full House: r2c9=9
Full House: r7c9=7
Full House: r7c8=8
|
sudoku_normal_extremely_hard_148
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
6..72......5..6...7...9..46...6......529.4.......7295..6.5..4...49...13...7.4....
|
694725813315486279728391546971658324852934761436172958263519487549867132187243695
|
6 . . 7 2 . . . .
. . 5 . . 6 . . .
7 . . . 9 . . 4 6
. . . 6 . . . . .
. 5 2 9 . 4 . . .
. . . . 7 2 9 5 .
. 6 . 5 . . 4 . .
. 4 9 . . . 1 3 .
. . 7 . 4 . . . .
|
6 9 4 7 2 5 8 1 3
3 1 5 4 8 6 2 7 9
7 2 8 3 9 1 5 4 6
9 7 1 6 5 8 3 2 4
8 5 2 9 3 4 7 6 1
4 3 6 1 7 2 9 5 8
2 6 3 5 1 9 4 8 7
5 4 9 8 6 7 1 3 2
1 8 7 2 4 3 6 9 5
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_5112_hard
|
694725813315486279728391546971658324852934761436172958263519487549867132187243695 #1 Extreme (27098) bf
Hidden Single: r6c3=6
Hidden Single: r4c5=5
Hidden Single: r1c3=4
Hidden Single: r8c5=6
Hidden Single: r4c2=7
Hidden Single: r2c4=4
Hidden Single: r4c1=9
Hidden Single: r4c9=4
Hidden Single: r6c1=4
Brute Force: r5c7=7
Hidden Single: r5c8=6
Hidden Single: r9c7=6
Locked Candidates Type 1 (Pointing): 5 in b9 => r1c9<>5
Almost Locked Set XZ-Rule: A=r1c789,r23c7 {123589}, B=r4c7,r56c9 {1238}, X=2, Z=1 => r2c9<>1
Brute Force: r5c5=3
Finned Franken Swordfish: 1 c35b5 r347 fr2c5 fr6c4 => r3c4<>1
W-Wing: 8/1 in r4c6,r7c5 connected by 1 in r69c4 => r789c6<>8
Naked Single: r8c6=7
Sashimi Swordfish: 8 c356 r347 fr1c6 fr2c5 => r3c4<>8
Naked Single: r3c4=3
Naked Triple: 1,2,8 in r7c5,r89c4 => r79c6<>1
Empty Rectangle: 3 in b1 (r6c29) => r2c9<>3
Finned Jellyfish: 8 r5689 c1249 fr9c8 => r7c9<>8
Forcing Chain Contradiction in c8 => r1c8<>8
r1c8=8 r1c8<>1
r1c8=8 r123c7<>8 r4c7=8 r4c6<>8 r4c6=1 r13c6<>1 r2c5=1 r2c8<>1
r1c8=8 r123c7<>8 r4c7=8 r4c7<>2 r4c8=2 r4c8<>1
Forcing Chain Verity => r1c9<>1
r2c1=1 r5c1<>1 r5c9=1 r1c9<>1
r2c2=1 r2c2<>9 r1c2=9 r1c8<>9 r1c8=1 r1c9<>1
r2c5=1 r13c6<>1 r4c6=1 r4c8<>1 r12c8=1 r1c9<>1
r2c8=1 r1c9<>1
Locked Candidates Type 1 (Pointing): 1 in b3 => r4c8<>1
W-Wing: 8/1 in r5c1,r6c4 connected by 1 in r4c36 => r6c2<>8
Swordfish: 8 r568 c149 => r129c9,r279c1,r9c4<>8
Discontinuous Nice Loop: 3 r2c2 -3- r6c2 =3= r6c9 -3- r1c9 -9- r1c2 =9= r2c2 => r2c2<>3
Discontinuous Nice Loop: 1 r2c1 -1- r2c5 =1= r7c5 -1- r9c4 =1= r6c4 -1- r6c2 -3- r1c2 =3= r2c1 => r2c1<>1
Finned Swordfish: 1 c149 r569 fr7c1 => r9c2<>1
Discontinuous Nice Loop: 8 r7c3 -8- r7c5 -1- r9c4 =1= r6c4 -1- r6c2 -3- r4c3 =3= r7c3 => r7c3<>8
XYZ-Wing: 1/2/3 in r27c1,r7c3 => r9c1<>3
AIC: 1 1- r1c8 =1= r2c8 =7= r7c8 =8= r7c5 =1= r2c5 -1 => r1c6,r2c8<>1
Hidden Single: r1c8=1
Hidden Rectangle: 5/8 in r1c67,r3c67 => r3c7<>8
AIC: 3 3- r7c3 =3= r4c3 =8= r5c1 -8- r8c1 =8= r9c2 =3= r9c6 -3 => r7c6,r9c2<>3
Naked Single: r7c6=9
Naked Single: r9c6=3
X-Wing: 3 c29 r16 => r1c7<>3
Naked Pair: 5,8 in r1c67 => r1c2<>8
XYZ-Wing: 1/2/8 in r3c23,r9c2 => r2c2<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r3c6<>8
XYZ-Wing: 2/7/8 in r47c8,r7c9 => r9c8<>2
Hidden Rectangle: 2/7 in r2c89,r7c89 => r2c8<>2
XY-Chain: 2 2- r3c7 -5- r3c6 -1- r4c6 -8- r4c8 -2 => r4c7<>2
Hidden Single: r4c8=2
Locked Candidates Type 1 (Pointing): 2 in b9 => r2c9<>2
XY-Chain: 2 2- r7c9 -7- r7c8 -8- r7c5 -1- r9c4 -2 => r9c9<>2
Sue de Coq: r9c12 - {1258} (r9c89 - {589}, r7c13 - {123}) => r8c1<>2
Grouped AIC: 3/9 3- r1c9 -9- r9c9 =9= r9c8 =8= r9c2 =2= r79c1 -2- r2c1 -3- r1c2 -9 => r1c2<>3, r1c9<>9
Naked Single: r1c2=9
Naked Single: r1c9=3
Hidden Single: r6c2=3
Hidden Single: r2c1=3
Hidden Single: r4c7=3
Hidden Single: r7c3=3
Locked Candidates Type 1 (Pointing): 2 in b1 => r9c2<>2
Naked Single: r9c2=8
Naked Single: r8c1=5
Naked Single: r9c8=9
Naked Single: r9c9=5
Hidden Single: r3c3=8
Full House: r4c3=1
Full House: r4c6=8
Full House: r5c1=8
Full House: r6c4=1
Full House: r5c9=1
Full House: r6c9=8
Naked Single: r1c6=5
Full House: r1c7=8
Full House: r3c6=1
Full House: r2c5=8
Full House: r7c5=1
Naked Single: r9c4=2
Full House: r8c4=8
Full House: r8c9=2
Full House: r9c1=1
Full House: r7c1=2
Naked Single: r2c7=2
Full House: r3c7=5
Full House: r3c2=2
Full House: r2c2=1
Naked Single: r2c8=7
Full House: r2c9=9
Full House: r7c9=7
Full House: r7c8=8
|
sudoku_normal_hard_149
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
...74.19.4...182.7.7.2.9.485........3.71.28...2...4..99.4.27.81...48.97.78.9.1...
|
832745196495618237671239548549863712367192854128574369954327681213486975786951423
|
. . . 7 4 . 1 9 .
4 . . . 1 8 2 . 7
. 7 . 2 . 9 . 4 8
5 . . . . . . . .
3 . 7 1 . 2 8 . .
. 2 . . . 4 . . 9
9 . 4 . 2 7 . 8 1
. . . 4 8 . 9 7 .
7 8 . 9 . 1 . . .
|
8 3 2 7 4 5 1 9 6
4 9 5 6 1 8 2 3 7
6 7 1 2 3 9 5 4 8
5 4 9 8 6 3 7 1 2
3 6 7 1 9 2 8 5 4
1 2 8 5 7 4 3 6 9
9 5 4 3 2 7 6 8 1
2 1 3 4 8 6 9 7 5
7 8 6 9 5 1 4 2 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4078_hard
|
832745196495618237671239548549863712367192854128574369954327681213486975786951423 #1 Extreme (42008) bf
Hidden Single: r2c9=7
Hidden Single: r9c1=7
Hidden Single: r7c8=8
Hidden Single: r8c7=9
Locked Candidates Type 1 (Pointing): 4 in b4 => r12c2<>4
Locked Candidates Type 2 (Claiming): 2 in r7 => r8c56,r9c5<>2
Naked Triple: 3,5,6 in r1c269 => r1c135<>6, r1c35<>3, r1c35<>5
Naked Single: r1c5=4
Hidden Single: r2c1=4
Hidden Single: r8c4=4
Hidden Single: r8c5=8
Naked Triple: 3,5,6 in r7c4,r8c6,r9c5 => r7c56<>3, r7c56<>5, r7c56<>6
Brute Force: r5c6=2
Naked Single: r7c6=7
Naked Single: r7c5=2
Brute Force: r5c4=1
Brute Force: r5c5=9
Locked Candidates Type 1 (Pointing): 5 in b5 => r6c78<>5
Almost Locked Set XZ-Rule: A=r4c4567 {34678}, B=r5c89 {456}, X=4, Z=6 => r4c89<>6
Forcing Net Contradiction in r9 => r4c7<>6
r4c7=6 (r4c7<>7 r4c5=7 r6c5<>7 r6c7=7 r6c7<>3 r6c8=3 r2c8<>3 r2c8=6 r2c3<>6) (r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 r7c4<>3 r2c4=3 r2c3<>3) (r4c7<>4) (r5c9<>6) r5c8<>6 r5c8=5 r5c9<>5 r5c9=4 r4c9<>4 r4c2=4 r4c2<>9 r4c3=9 r2c3<>9 r2c3=5 r9c3<>5
r4c7=6 (r4c6<>6 r4c6=3 r8c6<>3) (r7c7<>6) (r5c8<>6) r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 r8c6<>6 r8c6=5 r9c5<>5
r4c7=6 r4c7<>4 r9c7=4 r9c7<>5
r4c7=6 r5c8<>6 r5c8=5 r9c8<>5
r4c7=6 (r4c6<>6 r4c6=3 r4c4<>3) (r4c6<>6 r4c6=3 r6c4<>3) (r7c7<>6) (r5c8<>6) r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 (r6c4<>6 r6c5=6 r3c5<>6) r7c4<>3 r2c4=3 r3c5<>3 r3c5=5 r3c7<>5 r79c7=5 r9c9<>5
Brute Force: r5c2=6
Naked Single: r5c8=5
Full House: r5c9=4
Hidden Single: r4c2=4
Hidden Single: r9c7=4
Hidden Single: r8c2=1
Hidden Single: r4c3=9
Hidden Single: r2c2=9
Hidden Single: r4c8=1
Hidden Single: r4c4=8
Hidden Single: r4c9=2
Hidden Single: r9c8=2
Locked Candidates Type 1 (Pointing): 6 in b6 => r6c45<>6
Skyscraper: 5 in r7c2,r8c6 (connected by r1c26) => r7c4,r8c3<>5
Skyscraper: 5 in r1c2,r3c7 (connected by r7c27) => r1c9,r3c3<>5
Hidden Single: r3c7=5
Hidden Single: r7c2=5
Full House: r1c2=3
Naked Single: r1c9=6
Full House: r2c8=3
Full House: r6c8=6
Naked Single: r1c6=5
Naked Single: r2c4=6
Full House: r2c3=5
Full House: r3c5=3
Naked Single: r7c4=3
Full House: r6c4=5
Full House: r7c7=6
Naked Single: r8c6=6
Full House: r4c6=3
Full House: r9c5=5
Naked Single: r6c5=7
Full House: r4c5=6
Full House: r4c7=7
Full House: r6c7=3
Naked Single: r8c1=2
Naked Single: r9c9=3
Full House: r8c9=5
Full House: r8c3=3
Full House: r9c3=6
Naked Single: r1c1=8
Full House: r1c3=2
Naked Single: r3c3=1
Full House: r3c1=6
Full House: r6c1=1
Full House: r6c3=8
|
sudoku_normal_extremely_hard_149
| 9
| 9
|
Each row, column, and 3×3 subgrid must contain all digits from 1 to 9 exactly once. Digits cannot be repeated within any row, column, or 3×3 subgrid.
|
None
|
...7..19.....182...7.2.9.485........3.7...8...2...4..99.4.....1.......7..8.9.1...
|
832745196495618237671239548549863712367192854128574369954327681213486975786951423
|
. . . 7 . . 1 9 .
. . . . 1 8 2 . .
. 7 . 2 . 9 . 4 8
5 . . . . . . . .
3 . 7 . . . 8 . .
. 2 . . . 4 . . 9
9 . 4 . . . . . 1
. . . . . . . 7 .
. 8 . 9 . 1 . . .
|
8 3 2 7 4 5 1 9 6
4 9 5 6 1 8 2 3 7
6 7 1 2 3 9 5 4 8
5 4 9 8 6 3 7 1 2
3 6 7 1 9 2 8 5 4
1 2 8 5 7 4 3 6 9
9 5 4 3 2 7 6 8 1
2 1 3 4 8 6 9 7 5
7 8 6 9 5 1 4 2 3
|
Complete the sudoku board based on the rules and visual elements.
|
9x9_sudoku_4078_hard
|
832745196495618237671239548549863712367192854128574369954327681213486975786951423 #1 Extreme (42008) bf
Hidden Single: r2c9=7
Hidden Single: r9c1=7
Hidden Single: r7c8=8
Hidden Single: r8c7=9
Locked Candidates Type 1 (Pointing): 4 in b4 => r12c2<>4
Locked Candidates Type 2 (Claiming): 2 in r7 => r8c56,r9c5<>2
Naked Triple: 3,5,6 in r1c269 => r1c135<>6, r1c35<>3, r1c35<>5
Naked Single: r1c5=4
Hidden Single: r2c1=4
Hidden Single: r8c4=4
Hidden Single: r8c5=8
Naked Triple: 3,5,6 in r7c4,r8c6,r9c5 => r7c56<>3, r7c56<>5, r7c56<>6
Brute Force: r5c6=2
Naked Single: r7c6=7
Naked Single: r7c5=2
Brute Force: r5c4=1
Brute Force: r5c5=9
Locked Candidates Type 1 (Pointing): 5 in b5 => r6c78<>5
Almost Locked Set XZ-Rule: A=r4c4567 {34678}, B=r5c89 {456}, X=4, Z=6 => r4c89<>6
Forcing Net Contradiction in r9 => r4c7<>6
r4c7=6 (r4c7<>7 r4c5=7 r6c5<>7 r6c7=7 r6c7<>3 r6c8=3 r2c8<>3 r2c8=6 r2c3<>6) (r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 r7c4<>3 r2c4=3 r2c3<>3) (r4c7<>4) (r5c9<>6) r5c8<>6 r5c8=5 r5c9<>5 r5c9=4 r4c9<>4 r4c2=4 r4c2<>9 r4c3=9 r2c3<>9 r2c3=5 r9c3<>5
r4c7=6 (r4c6<>6 r4c6=3 r8c6<>3) (r7c7<>6) (r5c8<>6) r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 r8c6<>6 r8c6=5 r9c5<>5
r4c7=6 r4c7<>4 r9c7=4 r9c7<>5
r4c7=6 r5c8<>6 r5c8=5 r9c8<>5
r4c7=6 (r4c6<>6 r4c6=3 r4c4<>3) (r4c6<>6 r4c6=3 r6c4<>3) (r7c7<>6) (r5c8<>6) r5c9<>6 r5c2=6 r7c2<>6 r7c4=6 (r6c4<>6 r6c5=6 r3c5<>6) r7c4<>3 r2c4=3 r3c5<>3 r3c5=5 r3c7<>5 r79c7=5 r9c9<>5
Brute Force: r5c2=6
Naked Single: r5c8=5
Full House: r5c9=4
Hidden Single: r4c2=4
Hidden Single: r9c7=4
Hidden Single: r8c2=1
Hidden Single: r4c3=9
Hidden Single: r2c2=9
Hidden Single: r4c8=1
Hidden Single: r4c4=8
Hidden Single: r4c9=2
Hidden Single: r9c8=2
Locked Candidates Type 1 (Pointing): 6 in b6 => r6c45<>6
Skyscraper: 5 in r7c2,r8c6 (connected by r1c26) => r7c4,r8c3<>5
Skyscraper: 5 in r1c2,r3c7 (connected by r7c27) => r1c9,r3c3<>5
Hidden Single: r3c7=5
Hidden Single: r7c2=5
Full House: r1c2=3
Naked Single: r1c9=6
Full House: r2c8=3
Full House: r6c8=6
Naked Single: r1c6=5
Naked Single: r2c4=6
Full House: r2c3=5
Full House: r3c5=3
Naked Single: r7c4=3
Full House: r6c4=5
Full House: r7c7=6
Naked Single: r8c6=6
Full House: r4c6=3
Full House: r9c5=5
Naked Single: r6c5=7
Full House: r4c5=6
Full House: r4c7=7
Full House: r6c7=3
Naked Single: r8c1=2
Naked Single: r9c9=3
Full House: r8c9=5
Full House: r8c3=3
Full House: r9c3=6
Naked Single: r1c1=8
Full House: r1c3=2
Naked Single: r3c3=1
Full House: r3c1=6
Full House: r6c1=1
Full House: r6c3=8
|
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