task_name string | initial_board string | solution string | title string | rules string | visual_elements string | rows int64 | cols int64 | initial_observation string | description string | task_type string | data_source string | difficulty string | _hint_raw string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
normal_sudoku_469 | 41.6.5.37....7..56.6....48169.7.35.2...5.26.8......7.395.1.6874...9..3258.....169 | 419685237283471956765329481698713542347592618521864793952136874176948325834257169 | normal_sudoku_469 | 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 | 9 | 4 1 . 6 . 5 . 3 7
. . . . 7 . . 5 6
. 6 . . . . 4 8 1
6 9 . 7 . 3 5 . 2
. . . 5 . 2 6 . 8
. . . . . . 7 . 3
9 5 . 1 . 6 8 7 4
. . . 9 . . 3 2 5
8 . . . . . 1 6 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 419685237283471956765329481698713542347592618521864793952136874176948325834257169 #1 Easy (254)
Naked Single: r3c6=9
Hidden Single: r2c6=1
Hidden Single: r6c5=6
Hidden Single: r8c3=6
Hidden Single: r9c5=5
Hidden Single: r2c4=4
Naked Single: r6c4=8
Naked Single: r6c6=4
Naked Single: r4c5=1
Full House: r5c5=9
Naked Single: r6c2=2
Naked Single: r9c6=7
Full House: r8c6=8
Naked Single: r4c8=4
Full House: r4c3=8
Naked Single: r8c5=4
Naked Single: r5c8=1
Full House: r6c8=9
Naked Single: r8c2=7
Full House: r8c1=1
Naked Single: r6c1=5
Full House: r6c3=1
Hidden Single: r1c5=8
Hidden Single: r2c2=8
Hidden Single: r3c3=5
Hidden Single: r3c1=7
Naked Single: r5c1=3
Full House: r2c1=2
Naked Single: r5c2=4
Full House: r5c3=7
Full House: r9c2=3
Naked Single: r1c3=9
Full House: r1c7=2
Full House: r2c7=9
Full House: r2c3=3
Naked Single: r7c3=2
Full House: r7c5=3
Full House: r9c4=2
Full House: r9c3=4
Full House: r3c5=2
Full House: r3c4=3
|
normal_sudoku_1138 | .7938.51.53..91...1685.7.9..96.7......7.53.26..5..8.7.6537.9.489.183....78..65.3. | 479386512532491687168527493396172854847953126215648379653719248921834765784265931 | normal_sudoku_1138 | 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 | 9 | . 7 9 3 8 . 5 1 .
5 3 . . 9 1 . . .
1 6 8 5 . 7 . 9 .
. 9 6 . 7 . . . .
. . 7 . 5 3 . 2 6
. . 5 . . 8 . 7 .
6 5 3 7 . 9 . 4 8
9 . 1 8 3 . . . .
7 8 . . 6 5 . 3 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 479386512532491687168527493396172854847953126215648379653719248921834765784265931 #1 Hard (682)
Hidden Single: r1c6=6
Hidden Single: r6c4=6
Hidden Single: r5c4=9
Naked Pair: 2,4 in r2c34 => r2c79<>2, r2c79<>4
Naked Single: r2c9=7
Hidden Single: r8c7=7
Hidden Single: r8c8=6
Naked Single: r2c8=8
Full House: r4c8=5
Naked Single: r2c7=6
Hidden Single: r8c9=5
X-Wing: 4 r29 c34 => r4c4<>4
Remote Pair: 2/4 r1c1 -4- r2c3 -2- r9c3 -4- r8c2 -2- r8c6 -4- r4c6 => r4c1<>2, r4c1<>4
Locked Candidates Type 1 (Pointing): 2 in b4 => r6c5<>2
Remote Pair: 2/4 r2c4 -4- r2c3 -2- r9c3 -4- r8c2 -2- r8c6 -4- r4c6 => r4c4<>2
Naked Single: r4c4=1
Naked Single: r6c5=4
Full House: r4c6=2
Full House: r8c6=4
Full House: r8c2=2
Full House: r9c3=4
Full House: r2c3=2
Full House: r1c1=4
Full House: r2c4=4
Full House: r3c5=2
Full House: r9c4=2
Full House: r1c9=2
Full House: r7c5=1
Full House: r7c7=2
Naked Single: r6c2=1
Full House: r5c2=4
Naked Single: r5c1=8
Full House: r5c7=1
Naked Single: r4c1=3
Full House: r6c1=2
Naked Single: r9c7=9
Full House: r9c9=1
Naked Single: r4c9=4
Full House: r4c7=8
Naked Single: r6c7=3
Full House: r3c7=4
Full House: r3c9=3
Full House: r6c9=9
|
normal_sudoku_1041 | .4.....8.7..5.8..2832.4....37...2...68...52.3.2.3.6.7...8...75...389712.217654938 | 145269387796538412832741695379482561681975243524316879968123754453897126217654938 | normal_sudoku_1041 | 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 | 9 | . 4 . . . . . 8 .
7 . . 5 . 8 . . 2
8 3 2 . 4 . . . .
3 7 . . . 2 . . .
6 8 . . . 5 2 . 3
. 2 . 3 . 6 . 7 .
. . 8 . . . 7 5 .
. . 3 8 9 7 1 2 .
2 1 7 6 5 4 9 3 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 145269387796538412832741695379482561681975243524316879968123754453897126217654938 #1 Medium (384)
Hidden Single: r8c2=5
Naked Single: r8c1=4
Full House: r8c9=6
Full House: r7c9=4
Naked Single: r7c1=9
Full House: r7c2=6
Full House: r2c2=9
Locked Pair: 1,8 in r46c5 => r1257c5,r45c4<>1
Naked Single: r5c5=7
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c79<>5
Locked Candidates Type 1 (Pointing): 9 in b5 => r13c4<>9
Locked Candidates Type 2 (Claiming): 6 in r3 => r12c7,r2c8<>6
Naked Single: r1c7=3
Naked Single: r2c7=4
Naked Single: r2c8=1
Naked Single: r2c3=6
Full House: r2c5=3
Naked Single: r7c5=2
Naked Single: r1c5=6
Naked Single: r7c4=1
Full House: r7c6=3
Naked Single: r3c4=7
Naked Single: r1c4=2
Hidden Single: r6c3=4
Hidden Single: r5c3=1
Naked Single: r1c3=5
Full House: r1c1=1
Full House: r6c1=5
Full House: r4c3=9
Naked Single: r1c6=9
Full House: r1c9=7
Full House: r3c6=1
Naked Single: r6c7=8
Naked Single: r4c4=4
Full House: r5c4=9
Full House: r5c8=4
Naked Single: r6c5=1
Full House: r4c5=8
Full House: r6c9=9
Naked Single: r4c8=6
Full House: r3c8=9
Naked Single: r3c9=5
Full House: r3c7=6
Full House: r4c7=5
Full House: r4c9=1
|
normal_sudoku_5025 | .3.2......8...3...9.2.6...3...63.12..2.49.36.6.3..27.487...6.3.2.437...636..2..57 | 537249681186753249942168573459637128728491365613582794875916432294375816361824957 | normal_sudoku_5025 | 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 | 9 | . 3 . 2 . . . . .
. 8 . . . 3 . . .
9 . 2 . 6 . . . 3
. . . 6 3 . 1 2 .
. 2 . 4 9 . 3 6 .
6 . 3 . . 2 7 . 4
8 7 . . . 6 . 3 .
2 . 4 3 7 . . . 6
3 6 . . 2 . . 5 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 537249681186753249942168573459637128728491365613582794875916432294375816361824957 #1 Hard (740)
Locked Candidates Type 1 (Pointing): 7 in b5 => r13c6<>7
Locked Candidates Type 1 (Pointing): 5 in b6 => r12c9<>5
Locked Candidates Type 1 (Pointing): 4 in b9 => r123c7<>4
Empty Rectangle: 5 in b5 (r8c26) => r6c2<>5
Locked Candidates Type 2 (Claiming): 5 in r6 => r45c6<>5
Empty Rectangle: 8 in b6 (r16c5) => r1c9<>8
Locked Candidates Type 2 (Claiming): 8 in c9 => r6c8<>8
Naked Single: r6c8=9
Naked Single: r6c2=1
Hidden Single: r5c6=1
Hidden Single: r8c8=1
Hidden Single: r4c6=7
Hidden Single: r3c4=1
Hidden Single: r7c5=1
Hidden Single: r9c3=1
Hidden Single: r3c8=7
Naked Single: r2c8=4
Full House: r1c8=8
Naked Single: r2c5=5
Naked Single: r3c7=5
Naked Single: r1c5=4
Full House: r6c5=8
Full House: r6c4=5
Naked Single: r3c2=4
Full House: r3c6=8
Naked Single: r1c6=9
Full House: r2c4=7
Naked Single: r7c4=9
Full House: r9c4=8
Naked Single: r1c7=6
Naked Single: r1c9=1
Naked Single: r8c6=5
Full House: r9c6=4
Full House: r9c7=9
Naked Single: r2c1=1
Naked Single: r2c3=6
Naked Single: r7c3=5
Full House: r8c2=9
Full House: r8c7=8
Full House: r4c2=5
Naked Single: r7c9=2
Full House: r7c7=4
Full House: r2c7=2
Full House: r2c9=9
Naked Single: r1c3=7
Full House: r1c1=5
Naked Single: r4c1=4
Full House: r5c1=7
Naked Single: r4c9=8
Full House: r4c3=9
Full House: r5c3=8
Full House: r5c9=5
|
normal_sudoku_931 | 489.3.15.163.5....725.1...39..1....581...53.2.56...41..9.3815..5714..23....527..1 | 489632157163759824725814693942163785817945362356278419294381576571496238638527941 | normal_sudoku_931 | 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 | 9 | 4 8 9 . 3 . 1 5 .
1 6 3 . 5 . . . .
7 2 5 . 1 . . . 3
9 . . 1 . . . . 5
8 1 . . . 5 3 . 2
. 5 6 . . . 4 1 .
. 9 . 3 8 1 5 . .
5 7 1 4 . . 2 3 .
. . . 5 2 7 . . 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 489632157163759824725814693942163785817945362356278419294381576571496238638527941 #1 Unfair (1576)
Hidden Single: r9c3=8
Hidden Single: r2c8=2
Hidden Single: r8c9=8
Locked Candidates Type 1 (Pointing): 4 in b2 => r4c6<>4
Locked Candidates Type 1 (Pointing): 7 in b2 => r56c4<>7
Locked Candidates Type 1 (Pointing): 8 in b6 => r4c6<>8
Naked Pair: 7,9 in r6c59 => r6c46<>9
Hidden Triple: 2,3,8 in r46c6,r6c4 => r4c6<>6
XY-Chain: 7 7- r5c3 -4- r4c2 -3- r4c6 -2- r1c6 -6- r1c9 -7- r6c9 -9- r6c5 -7 => r5c5<>7
Discontinuous Nice Loop: 6/8/9 r3c6 =4= r3c8 -4- r9c8 =4= r9c2 =3= r4c2 -3- r4c6 -2- r1c6 -6- r1c9 =6= r7c9 =4= r2c9 -4- r2c6 =4= r3c6 => r3c6<>6, r3c6<>8, r3c6<>9
Naked Single: r3c6=4
Hidden Single: r2c9=4
Hidden Single: r6c9=9
Naked Single: r6c5=7
W-Wing: 6/7 in r1c9,r5c8 connected by 7 in r7c89 => r3c8<>6
XYZ-Wing: 6/8/9 in r2c6,r35c4 => r2c4<>9
XYZ-Wing: 6/8/9 in r3c78,r9c7 => r2c7<>9
Hidden Single: r2c6=9
Naked Single: r8c6=6
Full House: r8c5=9
Naked Single: r1c6=2
Naked Single: r4c6=3
Full House: r6c6=8
Naked Single: r4c2=4
Full House: r9c2=3
Naked Single: r6c4=2
Full House: r6c1=3
Naked Single: r4c5=6
Full House: r5c5=4
Full House: r5c4=9
Naked Single: r5c3=7
Full House: r4c3=2
Full House: r5c8=6
Full House: r7c3=4
Naked Single: r9c1=6
Full House: r7c1=2
Naked Single: r7c8=7
Full House: r7c9=6
Full House: r1c9=7
Full House: r1c4=6
Naked Single: r9c7=9
Full House: r9c8=4
Naked Single: r4c8=8
Full House: r3c8=9
Full House: r4c7=7
Naked Single: r2c7=8
Full House: r2c4=7
Full House: r3c4=8
Full House: r3c7=6
|
normal_sudoku_283 | .89...67.147.8...9..597.148..4.9..2.95...8.17..37...9.59.8.7..1..1..598...8.197.. | 289154673147386259635972148714593826956428317823761594592837461371645982468219735 | normal_sudoku_283 | 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 | 9 | . 8 9 . . . 6 7 .
1 4 7 . 8 . . . 9
. . 5 9 7 . 1 4 8
. . 4 . 9 . . 2 .
9 5 . . . 8 . 1 7
. . 3 7 . . . 9 .
5 9 . 8 . 7 . . 1
. . 1 . . 5 9 8 .
. . 8 . 1 9 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 289154673147386259635972148714593826956428317823761594592837461371645982468219735 #1 Extreme (1878)
Locked Candidates Type 1 (Pointing): 6 in b1 => r3c6<>6
Locked Candidates Type 1 (Pointing): 6 in b6 => r89c9<>6
Empty Rectangle: 4 in b6 (r7c57) => r6c5<>4
Discontinuous Nice Loop: 5 r2c7 -5- r2c8 -3- r7c8 -6- r7c3 -2- r7c7 =2= r2c7 => r2c7<>5
Locked Candidates Type 2 (Claiming): 5 in c7 => r46c9<>5
Naked Triple: 3,4,6 in r46c9,r5c7 => r4c7<>3, r6c7<>4
Simple Colors Trap: 4 (r1c6,r6c9,r7c7) / (r5c7,r6c6,r7c5) => r1c5<>4
Naked Triple: 2,3,5 in r1c159 => r1c46<>2, r1c46<>3, r1c4<>5
Finned Swordfish: 2 c347 r257 fr8c4 fr9c4 => r7c5<>2
AIC: 6 6- r4c9 =6= r6c9 =4= r6c6 -4- r1c6 -1- r1c4 =1= r4c4 =5= r2c4 -5- r2c8 -3- r7c8 -6- r7c3 =6= r5c3 -6 => r4c12<>6
AIC: 6 6- r5c3 -2- r7c3 =2= r7c7 =4= r5c7 -4- r6c9 -6 => r6c12<>6
Hidden Single: r5c3=6
Full House: r7c3=2
Hidden Single: r2c7=2
Locked Candidates Type 1 (Pointing): 2 in b4 => r6c56<>2
Hidden Single: r3c6=2
Hidden Single: r1c1=2
Naked Single: r6c1=8
Naked Single: r4c1=7
Naked Single: r6c7=5
Naked Single: r4c2=1
Full House: r6c2=2
Naked Single: r4c7=8
Naked Single: r6c5=6
Naked Single: r4c6=3
Naked Single: r6c9=4
Full House: r6c6=1
Naked Single: r2c6=6
Full House: r1c6=4
Naked Single: r4c4=5
Full House: r4c9=6
Full House: r5c7=3
Full House: r7c7=4
Naked Single: r1c4=1
Naked Single: r2c4=3
Full House: r1c5=5
Full House: r2c8=5
Full House: r1c9=3
Naked Single: r7c5=3
Full House: r7c8=6
Full House: r9c8=3
Naked Single: r8c9=2
Full House: r9c9=5
Naked Single: r9c2=6
Naked Single: r8c5=4
Full House: r5c5=2
Full House: r5c4=4
Naked Single: r3c2=3
Full House: r3c1=6
Full House: r8c2=7
Naked Single: r9c1=4
Full House: r8c1=3
Full House: r8c4=6
Full House: r9c4=2
|
normal_sudoku_1224 | 37..1.....1.4...3.684793251...3.1592.5.2.93..932.....6....3..8.1.3.....5....5.7.3 | 375612849219485637684793251768341592451269378932578416527936184143827965896154723 | normal_sudoku_1224 | 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 | 9 | 3 7 . . 1 . . . .
. 1 . 4 . . . 3 .
6 8 4 7 9 3 2 5 1
. . . 3 . 1 5 9 2
. 5 . 2 . 9 3 . .
9 3 2 . . . . . 6
. . . . 3 . . 8 .
1 . 3 . . . . . 5
. . . . 5 . 7 . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 375612849219485637684793251768341592451269378932578416527936184143827965896154723 #1 Easy (330)
Hidden Single: r1c6=2
Hidden Single: r2c1=2
Hidden Single: r5c3=1
Hidden Single: r2c9=7
Hidden Single: r8c5=2
Hidden Single: r7c2=2
Hidden Single: r7c1=5
Hidden Single: r5c5=6
Naked Single: r2c5=8
Hidden Single: r9c8=2
Hidden Single: r8c6=7
Hidden Single: r7c3=7
Hidden Single: r9c4=1
Hidden Single: r6c8=1
Hidden Single: r7c7=1
Hidden Single: r8c4=8
Naked Single: r6c4=5
Naked Single: r1c4=6
Full House: r2c6=5
Full House: r7c4=9
Naked Single: r1c8=4
Naked Single: r2c3=9
Full House: r1c3=5
Full House: r2c7=6
Naked Single: r7c9=4
Full House: r7c6=6
Full House: r9c6=4
Full House: r6c6=8
Naked Single: r5c8=7
Full House: r8c8=6
Full House: r8c7=9
Full House: r8c2=4
Naked Single: r5c9=8
Full House: r6c7=4
Full House: r1c7=8
Full House: r1c9=9
Full House: r5c1=4
Full House: r6c5=7
Full House: r4c5=4
Naked Single: r9c1=8
Full House: r4c1=7
Naked Single: r4c2=6
Full House: r4c3=8
Full House: r9c3=6
Full House: r9c2=9
|
normal_sudoku_4474 | ..2..7.1...714.....9.6....5...2.....356.91..2.2....59..6.5....38...1.4.......8... | 682957314537142968491683275749265831356891742128734596264579183875316429913428657 | normal_sudoku_4474 | 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 | 9 | . . 2 . . 7 . 1 .
. . 7 1 4 . . . .
. 9 . 6 . . . . 5
. . . 2 . . . . .
3 5 6 . 9 1 . . 2
. 2 . . . . 5 9 .
. 6 . 5 . . . . 3
8 . . . 1 . 4 . .
. . . . . 8 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 682957314537142968491683275749265831356891742128734596264579183875316429913428657 #1 Extreme (9292)
Locked Candidates Type 1 (Pointing): 5 in b1 => r9c1<>5
Locked Candidates Type 1 (Pointing): 3 in b6 => r4c56<>3
Hidden Pair: 5,6 in r12c1 => r1c1<>4
Empty Rectangle: 1 in b6 (r49c2) => r9c9<>1
Locked Candidates Type 1 (Pointing): 1 in b9 => r4c7<>1
Empty Rectangle: 2 in b2 (r8c68) => r3c8<>2
AIC: 7/8 7- r3c8 =7= r3c7 -7- r5c7 -8- r7c7 =8= r7c8 -8 => r7c8<>7, r3c8<>8
Discontinuous Nice Loop: 6 r9c8 -6- r9c5 =6= r8c6 =2= r8c8 =5= r9c8 => r9c8<>6
Grouped Discontinuous Nice Loop: 7 r8c8 -7- r8c2 -3- r12c2 =3= r3c3 -3- r3c6 -2- r8c6 =2= r8c8 => r8c8<>7
Almost Locked Set XY-Wing: A=r8c2469 {23679}, B=r3467c3 {13489}, C=r3c6 {23}, X,Y=2,3, Z=9 => r8c3<>9
Forcing Chain Contradiction in r3c7 => r7c8=8
r7c8<>8 r7c8=2 r8c8<>2 r8c6=2 r2c6<>2 r2c78=2 r3c7<>2
r7c8<>8 r7c8=2 r8c8<>2 r8c6=2 r3c6<>2 r3c6=3 r3c7<>3
r7c8<>8 r7c7=8 r5c7<>8 r5c7=7 r3c7<>7
r7c8<>8 r7c7=8 r3c7<>8
Finned Franken Swordfish: 8 r35b4 c357 fr4c2 fr5c4 => r4c5<>8
Forcing Chain Contradiction in r4c6 => r1c9<>6
r1c9=6 r1c9<>4 r3c8=4 r5c8<>4 r5c4=4 r4c6<>4
r1c9=6 r1c1<>6 r1c1=5 r1c5<>5 r4c5=5 r4c6<>5
r1c9=6 r6c9<>6 r4c789=6 r4c6<>6
Forcing Chain Contradiction in r7 => r4c5<>7
r4c5=7 r4c2<>7 r46c1=7 r7c1<>7
r4c5=7 r7c5<>7
r4c5=7 r5c4<>7 r5c78=7 r46c9<>7 r89c9=7 r7c7<>7
Discontinuous Nice Loop: 6 r4c7 -6- r4c5 -5- r1c5 =5= r1c1 =6= r1c7 -6- r4c7 => r4c7<>6
Grouped Discontinuous Nice Loop: 6 r2c9 -6- r2c1 -5- r2c6 =5= r4c6 -5- r4c5 -6- r4c8 =6= r46c9 -6- r2c9 => r2c9<>6
Almost Locked Set XZ-Rule: A=r4c56 {456}, B=r4c78,r5c78 {34678}, X=6, Z=4 => r4c9<>4
Grouped Discontinuous Nice Loop: 9 r1c9 -9- r1c4 =9= r2c6 =5= r4c6 -5- r4c5 -6- r4c89 =6= r6c9 =4= r1c9 => r1c9<>9
Almost Locked Set XY-Wing: A=r1c2459 {34589}, B=r4c78,r5c78 {34678}, C=r4c5 {56}, X,Y=5,6, Z=8 => r1c7<>8
Almost Locked Set XY-Wing: A=r1c29 {348}, B=r13c5,r23c6 {23589}, C=r2c29 {389}, X,Y=3,9, Z=8 => r1c4<>8
Locked Candidates Type 1 (Pointing): 8 in b2 => r6c5<>8
Almost Locked Set XY-Wing: A=r2c2 {38}, B=r4c79,r5c78,r6c9 {134678}, C=r289c9 {6789}, X,Y=6,8, Z=3 => r2c7<>3
Almost Locked Set XY-Wing: A=r123467c1 {1245679}, B=r189c4 {3479}, C=r7c5 {27}, X,Y=2,7, Z=4 => r9c1<>4
Forcing Chain Contradiction in r8 => r1c4=9
r1c4<>9 r1c7=9 r2c9<>9 r2c9=8 r2c2<>8 r2c2=3 r8c2<>3
r1c4<>9 r1c4=3 r3c6<>3 r3c6=2 r8c6<>2 r8c8=2 r8c8<>5 r8c3=5 r8c3<>3
r1c4<>9 r1c4=3 r8c4<>3
r1c4<>9 r2c6=9 r2c6<>5 r4c6=5 r4c5<>5 r4c5=6 r9c5<>6 r8c6=6 r8c6<>3
Naked Pair: 3,7 in r8c24 => r8c36<>3, r8c9<>7
Naked Single: r8c3=5
Hidden Single: r9c8=5
Discontinuous Nice Loop: 3 r2c6 -3- r2c2 -8- r2c9 -9- r8c9 -6- r8c6 =6= r9c5 -6- r4c5 -5- r4c6 =5= r2c6 => r2c6<>3
Empty Rectangle: 3 in b2 (r39c3) => r9c5<>3
Locked Candidates Type 1 (Pointing): 3 in b8 => r6c4<>3
Discontinuous Nice Loop: 6 r2c7 -6- r2c1 -5- r2c6 =5= r4c6 -5- r4c5 -6- r9c5 =6= r8c6 =9= r8c9 -9- r2c9 =9= r2c7 => r2c7<>6
Discontinuous Nice Loop: 7 r9c1 -7- r8c2 =7= r8c4 -7- r7c5 -2- r7c1 =2= r9c1 => r9c1<>7
Grouped Discontinuous Nice Loop: 4 r4c8 -4- r5c8 =4= r5c4 -4- r9c4 =4= r7c6 =9= r8c6 -9- r8c9 -6- r46c9 =6= r4c8 => r4c8<>4
Grouped Discontinuous Nice Loop: 7 r9c2 -7- r9c9 =7= r46c9 -7- r5c78 =7= r5c4 -7- r8c4 =7= r8c2 -7- r9c2 => r9c2<>7
Grouped Discontinuous Nice Loop: 7 r9c4 -7- r9c9 =7= r46c9 -7- r5c78 =7= r5c4 -7- r9c4 => r9c4<>7
Discontinuous Nice Loop: 4 r9c2 -4- r9c4 -3- r8c4 -7- r8c2 =7= r4c2 =1= r9c2 => r9c2<>4
Skyscraper: 4 in r4c2,r6c9 (connected by r1c29) => r6c13<>4
Locked Candidates Type 1 (Pointing): 4 in b4 => r4c6<>4
Locked Pair: 5,6 in r4c56 => r4c89,r6c56<>6
Hidden Single: r6c9=6
Naked Single: r8c9=9
Naked Single: r2c9=8
Naked Single: r9c9=7
Naked Single: r1c9=4
Full House: r4c9=1
Naked Single: r2c2=3
Naked Single: r1c2=8
Naked Single: r8c2=7
Naked Single: r9c2=1
Full House: r4c2=4
Naked Single: r8c4=3
Naked Single: r9c4=4
Hidden Single: r5c8=4
Hidden Single: r2c7=9
Hidden Single: r7c6=9
Naked Single: r7c3=4
Naked Single: r3c3=1
Naked Single: r7c1=2
Naked Single: r3c1=4
Naked Single: r6c3=8
Naked Single: r7c5=7
Full House: r7c7=1
Naked Single: r9c1=9
Full House: r9c3=3
Full House: r4c3=9
Naked Single: r6c4=7
Full House: r5c4=8
Full House: r5c7=7
Naked Single: r6c5=3
Naked Single: r4c1=7
Full House: r6c1=1
Full House: r6c6=4
Naked Single: r4c8=3
Full House: r4c7=8
Naked Single: r1c5=5
Naked Single: r3c8=7
Naked Single: r1c1=6
Full House: r1c7=3
Full House: r2c1=5
Naked Single: r2c6=2
Full House: r2c8=6
Full House: r3c7=2
Full House: r8c8=2
Full House: r8c6=6
Full House: r9c7=6
Full House: r9c5=2
Naked Single: r4c5=6
Full House: r3c5=8
Full House: r3c6=3
Full House: r4c6=5
|
normal_sudoku_629 | .4..3....835......621...3.5182973456.7.62.18356.1..972.18....3..9.......25..6...8 | 947532861835416297621897345182973456479625183563148972718254639396781524254369718 | normal_sudoku_629 | 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 | 9 | . 4 . . 3 . . . .
8 3 5 . . . . . .
6 2 1 . . . 3 . 5
1 8 2 9 7 3 4 5 6
. 7 . 6 2 . 1 8 3
5 6 . 1 . . 9 7 2
. 1 8 . . . . 3 .
. 9 . . . . . . .
2 5 . . 6 . . . 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 947532861835416297621897345182973456479625183563148972718254639396781524254369718 #1 Easy (188)
Naked Single: r9c7=7
Hidden Single: r5c6=5
Hidden Single: r6c3=3
Naked Single: r9c3=4
Naked Single: r5c3=9
Full House: r5c1=4
Naked Single: r7c1=7
Naked Single: r9c4=3
Naked Single: r1c3=7
Full House: r1c1=9
Full House: r8c1=3
Full House: r8c3=6
Naked Single: r1c9=1
Naked Single: r8c9=4
Naked Single: r7c9=9
Full House: r2c9=7
Naked Single: r9c8=1
Full House: r9c6=9
Naked Single: r8c8=2
Naked Single: r1c8=6
Naked Single: r8c7=5
Full House: r7c7=6
Naked Single: r2c7=2
Full House: r1c7=8
Naked Single: r2c4=4
Naked Single: r1c6=2
Full House: r1c4=5
Naked Single: r2c8=9
Full House: r3c8=4
Naked Single: r7c6=4
Naked Single: r7c4=2
Full House: r7c5=5
Naked Single: r2c5=1
Full House: r2c6=6
Naked Single: r6c6=8
Full House: r6c5=4
Naked Single: r8c5=8
Full House: r3c5=9
Naked Single: r3c6=7
Full House: r3c4=8
Full House: r8c4=7
Full House: r8c6=1
|
normal_sudoku_6883 | 2...1...8..98...7.831..75.....9....51...2.....9...37..31...4..796.....54..46..3.. | 247519638659832471831467592473986125186725943592143786315294867968371254724658319 | normal_sudoku_6883 | 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 | 9 | 2 . . . 1 . . . 8
. . 9 8 . . . 7 .
8 3 1 . . 7 5 . .
. . . 9 . . . . 5
1 . . . 2 . . . .
. 9 . . . 3 7 . .
3 1 . . . 4 . . 7
9 6 . . . . . 5 4
. . 4 6 . . 3 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 247519638659832471831467592473986125186725943592143786315294867968371254724658319 #1 Extreme (12666)
Almost Locked Set XZ-Rule: A=r2c126 {2456}, B=r3c4 {24}, X=2, Z=4 => r2c5<>4
Forcing Chain Contradiction in r8 => r4c3<>7
r4c3=7 r8c3<>7
r4c3=7 r4c5<>7 r5c4=7 r8c4<>7
r4c3=7 r4c3<>3 r4c8=3 r1c8<>3 r1c4=3 r8c4<>3 r8c5=3 r8c5<>7
Forcing Chain Contradiction in r2 => r5c4<>4
r5c4=4 r3c4<>4 r3c4=2 r2c6<>2
r5c4=4 r5c4<>7 r8c4=7 r8c4<>3 r8c5=3 r2c5<>3 r2c9=3 r2c9<>1 r2c7=1 r2c7<>2
r5c4=4 r5c4<>7 r8c4=7 r8c4<>3 r8c5=3 r2c5<>3 r2c9=3 r2c9<>2
Forcing Chain Contradiction in r2 => r3c5<>4
r3c5=4 r3c4<>4 r3c4=2 r2c6<>2
r3c5=4 r13c4<>4 r6c4=4 r6c4<>1 r8c4=1 r8c4<>3 r8c5=3 r2c5<>3 r2c9=3 r2c9<>1 r2c7=1 r2c7<>2
r3c5=4 r13c4<>4 r6c4=4 r6c4<>1 r8c4=1 r8c4<>3 r8c5=3 r2c5<>3 r2c9=3 r2c9<>2
Locked Candidates Type 1 (Pointing): 4 in b2 => r6c4<>4
Forcing Chain Contradiction in c9 => r2c6<>6
r2c6=6 r3c5<>6 r3c5=9 r3c9<>9
r2c6=6 r2c6<>2 r3c4=2 r3c4<>4 r1c4=4 r1c4<>3 r1c8=3 r2c9<>3 r5c9=3 r5c9<>9
r2c6=6 r3c5<>6 r3c5=9 r7c5<>9 r7c78=9 r9c9<>9
Forcing Net Contradiction in c3 => r4c3=3
r4c3<>3 r4c8=3 (r4c8<>1) r1c8<>3 r1c4=3 r2c5<>3 r2c9=3 r2c9<>1 r2c7=1 (r2c7<>2) (r8c7<>1) r4c7<>1 r4c6=1 (r6c4<>1 r6c4=5 r5c6<>5) r8c6<>1 r8c4=1 r8c4<>3 r8c5=3 (r8c5<>7 r8c3=7 r9c1<>7 r9c1=5 r9c6<>5) r2c5<>3 r2c9=3 r2c9<>2 r2c6=2 r2c6<>5 r1c6=5 r1c3<>5
r4c3<>3 r4c8=3 (r5c8<>3) r5c9<>3 r5c3=3 r5c3<>5
r4c3<>3 r4c8=3 (r4c8<>1) r1c8<>3 r1c4=3 r2c5<>3 r2c9=3 r2c9<>1 r2c7=1 r4c7<>1 r4c6=1 r6c4<>1 r6c4=5 r6c3<>5
r4c3<>3 r4c8=3 (r4c8<>1) r1c8<>3 r1c4=3 r2c5<>3 r2c9=3 r2c9<>1 r2c7=1 r4c7<>1 r4c6=1 r6c4<>1 r8c4=1 (r8c4<>7) r8c4<>3 r8c5=3 r8c5<>7 r8c3=7 r9c1<>7 r9c1=5 r7c3<>5
Forcing Chain Contradiction in c8 => r1c8<>6
r1c8=6 r1c8<>4
r1c8=6 r1c8<>3 r1c4=3 r1c4<>4 r3c4=4 r3c8<>4
r1c8=6 r1c3<>6 r2c1=6 r2c1<>4 r46c1=4 r5c2<>4 r5c78=4 r4c8<>4
r1c8=6 r1c8<>3 r5c8=3 r5c8<>4
r1c8=6 r1c3<>6 r2c1=6 r2c1<>4 r46c1=4 r5c2<>4 r5c78=4 r6c8<>4
Forcing Net Contradiction in c4 => r2c7<>6
r2c7=6 (r3c9<>6 r3c5=6 r4c5<>6) (r4c7<>6) (r7c7<>6 r7c8=6 r4c8<>6) (r5c7<>6) (r7c7<>6 r7c8=6 r5c8<>6) r2c7<>1 r2c9=1 r2c9<>3 r5c9=3 r5c9<>6 r5c6=6 r4c6<>6 r4c1=6 (r4c1<>7) r6c3<>6 r1c3=6 (r5c3<>6) (r5c3<>6) r1c3<>7 r1c2=7 r4c2<>7 r4c5=7 r5c4<>7
r2c7=6 r2c7<>1 r2c9=1 r2c9<>3 r2c5=3 r8c5<>3 r8c4=3 r8c4<>7
Forcing Net Contradiction in c3 => r2c9<>6
r2c9=6 (r6c9<>6) r2c9<>3 r2c5=3 r8c5<>3 r8c4=3 r8c4<>1 r6c4=1 r6c9<>1 r6c9=2 r6c3<>2
r2c9=6 (r2c9<>1 r2c7=1 r2c7<>2 r2c6=2 r3c4<>2) r2c9<>3 r2c5=3 r8c5<>3 r8c4=3 r8c4<>2 r7c4=2 r7c3<>2
r2c9=6 (r2c1<>6 r1c3=6 r1c3<>7) r2c9<>3 r2c5=3 r8c5<>3 r8c4=3 r8c4<>7 r5c4=7 r5c3<>7 r8c3=7 r8c3<>2
Forcing Chain Contradiction in c9 => r5c8<>6
r5c8=6 r56c9<>6 r3c9=6 r3c9<>9
r5c8=6 r5c8<>3 r5c9=3 r5c9<>9
r5c8=6 r56c9<>6 r3c9=6 r3c5<>6 r3c5=9 r7c5<>9 r7c78=9 r9c9<>9
Forcing Chain Contradiction in r7 => r7c8<>2
r7c8=2 r7c8<>6 r7c7=6 r1c7<>6 r3c89=6 r3c5<>6 r3c5=9 r7c5<>9
r7c8=2 r7c8<>6 r7c7=6 r7c7<>9
r7c8=2 r7c8<>9
Empty Rectangle: 2 in b9 (r49c2) => r4c7<>2
Forcing Chain Contradiction in r9 => r3c8<>2
r3c8=2 r4c8<>2 r4c2=2 r9c2<>2
r3c8=2 r3c4<>2 r2c6=2 r9c6<>2
r3c8=2 r9c8<>2
r3c8=2 r2c7<>2 r78c7=2 r9c9<>2
Forcing Chain Contradiction in c9 => r3c9<>6
r3c9=6 r3c9<>9
r3c9=6 r3c9<>2 r3c4=2 r3c4<>4 r1c4=4 r1c4<>3 r1c8=3 r5c8<>3 r5c9=3 r5c9<>9
r3c9=6 r3c5<>6 r3c5=9 r7c5<>9 r7c78=9 r9c9<>9
Locked Candidates Type 2 (Claiming): 6 in c9 => r4c78,r5c7,r6c8<>6
Finned X-Wing: 6 r24 c15 fr4c6 => r6c5<>6
Discontinuous Nice Loop: 2 r6c9 -2- r3c9 =2= r3c4 =4= r1c4 =3= r1c8 -3- r5c8 =3= r5c9 =6= r6c9 => r6c9<>2
Locked Candidates Type 1 (Pointing): 2 in b6 => r9c8<>2
Almost Locked Set XY-Wing: A=r7c345 {2589}, B=r134569c8 {1234689}, C=r3c5 {69}, X,Y=6,9, Z=8 => r7c8<>8
Discontinuous Nice Loop: 9 r1c8 -9- r1c6 =9= r3c5 =6= r3c8 -6- r7c8 -9- r1c8 => r1c8<>9
Sue de Coq: r3c89 - {2469} (r3c5 - {69}, r1c8,r2c79 - {1234}) => r1c7<>4
Finned Swordfish: 4 r135 c248 fr5c7 => r46c8<>4
Forcing Chain Verity => r6c1<>6
r4c1=6 r6c1<>6
r4c5=6 r2c5<>6 r2c1=6 r6c1<>6
r4c6=6 r4c6<>1 r6c4=1 r6c9<>1 r6c9=6 r6c1<>6
Almost Locked Set XZ-Rule: A=r5c2346 {45678}, B=r6c149 {1456}, X=4, Z=6 => r5c9<>6
Hidden Single: r6c9=6
Forcing Chain Contradiction in r4 => r2c1<>5
r2c1=5 r2c1<>6 r4c1=6 r4c1<>7
r2c1=5 r2c1<>6 r1c3=6 r1c3<>7 r1c2=7 r4c2<>7
r2c1=5 r6c1<>5 r6c1=4 r6c5<>4 r4c5=4 r4c5<>7
Discontinuous Nice Loop: 5 r5c3 -5- r6c1 -4- r2c1 -6- r4c1 =6= r5c3 => r5c3<>5
Forcing Chain Contradiction in r4 => r6c4=1
r6c4<>1 r6c4=5 r6c1<>5 r6c1=4 r2c1<>4 r2c1=6 r4c1<>6
r6c4<>1 r6c4=5 r6c1<>5 r6c1=4 r6c5<>4 r4c5=4 r4c5<>6
r6c4<>1 r4c6=1 r4c6<>6
Grouped Discontinuous Nice Loop: 4 r4c2 -4- r46c1 =4= r2c1 =6= r2c5 =3= r2c9 =1= r2c7 -1- r4c7 =1= r4c8 =2= r4c2 => r4c2<>4
Forcing Chain Verity => r1c8=3
r9c2=2 r4c2<>2 r4c8=2 r4c8<>1 r4c7=1 r2c7<>1 r2c9=1 r2c9<>3 r1c8=3
r9c6=2 r2c6<>2 r3c4=2 r3c4<>4 r3c8=4 r1c8<>4 r1c8=3
r9c9=2 r9c9<>1 r2c9=1 r2c9<>3 r1c8=3
Hidden Single: r8c4=3
Hidden Single: r2c5=3
Hidden Single: r5c9=3
Hidden Single: r5c4=7
Hidden Single: r2c1=6
Hidden Single: r5c3=6
Locked Candidates Type 1 (Pointing): 4 in b1 => r5c2<>4
Locked Candidates Type 2 (Claiming): 4 in r5 => r4c7<>4
Naked Pair: 5,8 in r5c26 => r5c78<>8
Naked Triple: 2,4,5 in r13c4,r2c6 => r1c6<>5
Naked Triple: 4,6,9 in r357c8 => r9c8<>9
X-Wing: 5 r25 c26 => r19c2,r9c6<>5
Skyscraper: 9 in r1c6,r3c9 (connected by r9c69) => r1c7,r3c5<>9
Naked Single: r1c7=6
Naked Single: r3c5=6
Naked Single: r1c6=9
Hidden Single: r4c6=6
Hidden Single: r7c8=6
AIC: 2 2- r2c6 -5- r2c2 =5= r1c3 =7= r8c3 -7- r8c5 =7= r9c5 =9= r9c9 -9- r3c9 -2 => r2c79,r3c4<>2
Naked Single: r2c9=1
Naked Single: r3c4=4
Naked Single: r2c7=4
Naked Single: r1c4=5
Full House: r2c6=2
Full House: r2c2=5
Full House: r7c4=2
Naked Single: r3c8=9
Full House: r3c9=2
Full House: r9c9=9
Naked Single: r5c7=9
Naked Single: r1c3=7
Full House: r1c2=4
Naked Single: r5c2=8
Naked Single: r5c8=4
Full House: r5c6=5
Naked Single: r7c7=8
Naked Single: r4c7=1
Full House: r8c7=2
Full House: r9c8=1
Naked Single: r7c3=5
Full House: r7c5=9
Naked Single: r8c3=8
Full House: r6c3=2
Naked Single: r9c6=8
Full House: r8c6=1
Full House: r8c5=7
Full House: r9c5=5
Naked Single: r9c1=7
Full House: r9c2=2
Full House: r4c2=7
Naked Single: r6c8=8
Full House: r4c8=2
Naked Single: r4c1=4
Full House: r4c5=8
Full House: r6c5=4
Full House: r6c1=5
|
normal_sudoku_1798 | 67.93....92156.34783....9..1....3.2.34....7..5.27...347....6..325637941841.2...7. | 675934182921568347834127965197843526348652791562791834789416253256379418413285679 | normal_sudoku_1798 | 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 | 9 | 6 7 . 9 3 . . . .
9 2 1 5 6 . 3 4 7
8 3 . . . . 9 . .
1 . . . . 3 . 2 .
3 4 . . . . 7 . .
5 . 2 7 . . . 3 4
7 . . . . 6 . . 3
2 5 6 3 7 9 4 1 8
4 1 . 2 . . . 7 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 675934182921568347834127965197843526348652791562791834789416253256379418413285679 #1 Easy (156)
Full House: r2c6=8
Naked Single: r6c6=1
Naked Single: r9c6=5
Naked Single: r5c6=2
Naked Single: r9c5=8
Naked Single: r9c7=6
Naked Single: r1c6=4
Full House: r3c6=7
Naked Single: r6c5=9
Naked Single: r6c7=8
Full House: r6c2=6
Naked Single: r9c9=9
Full House: r9c3=3
Naked Single: r1c3=5
Full House: r3c3=4
Naked Single: r3c4=1
Full House: r3c5=2
Naked Single: r5c5=5
Naked Single: r4c7=5
Naked Single: r7c8=5
Full House: r7c7=2
Full House: r1c7=1
Naked Single: r1c8=8
Full House: r1c9=2
Naked Single: r7c4=4
Full House: r7c5=1
Full House: r4c5=4
Naked Single: r4c9=6
Naked Single: r3c8=6
Full House: r3c9=5
Full House: r5c8=9
Full House: r5c9=1
Naked Single: r4c4=8
Full House: r5c4=6
Full House: r5c3=8
Naked Single: r4c2=9
Full House: r4c3=7
Full House: r7c3=9
Full House: r7c2=8
|
normal_sudoku_1171 | ..5...1.2.7.2...59.12...74.2.763......4.2....1..9..2..7.9..24.1.21498.7554....92. | 635749182478216359912853746297635814864127593153984267789562431321498675546371928 | normal_sudoku_1171 | 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 | 9 | . . 5 . . . 1 . 2
. 7 . 2 . . . 5 9
. 1 2 . . . 7 4 .
2 . 7 6 3 . . . .
. . 4 . 2 . . . .
1 . . 9 . . 2 . .
7 . 9 . . 2 4 . 1
. 2 1 4 9 8 . 7 5
5 4 . . . . 9 2 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 635749182478216359912853746297635814864127593153984267789562431321498675546371928 #1 Extreme (7902)
Naked Triple: 3,6,8 in r167c8 => r45c8<>8, r5c8<>3, r5c8<>6
Sashimi X-Wing: 8 r47 c28 fr4c7 fr4c9 => r6c8<>8
Discontinuous Nice Loop: 8 r2c5 -8- r6c5 =8= r5c4 =1= r9c4 -1- r9c5 =1= r2c5 => r2c5<>8
Almost Locked Set XY-Wing: A=r2c1367 {13468}, B=r37c5 {568}, C=r456c6,r6c5 {14578}, X,Y=1,8, Z=6 => r2c5<>6
Forcing Net Verity => r4c9=4
r5c7=3 (r5c2<>3) (r2c7<>3) r8c7<>3 (r8c1=3 r7c2<>3) r8c7=6 r2c7<>6 r2c7=8 r1c8<>8 r1c8=3 r1c2<>3 r6c2=3 (r6c3<>3) r6c8<>3 r6c8=6 (r1c8<>6) r6c3<>6 r6c3=8 r9c3<>8 r9c9=8 r4c9<>8 r4c9=4
r5c7=5 r4c7<>5 r4c7=8 r4c9<>8 r4c9=4
r5c7=6 (r5c2<>6) (r2c7<>6) r8c7<>6 (r8c1=6 r7c2<>6) r8c7=3 r2c7<>3 r2c7=8 r1c8<>8 r1c8=6 r1c2<>6 r6c2=6 (r6c3<>6) r6c8<>6 r6c8=3 (r1c8<>3) r6c3<>3 r6c3=8 r9c3<>8 r9c9=8 r4c9<>8 r4c9=4
r5c7=8 r4c9<>8 r4c9=4
Sashimi X-Wing: 8 r24 c27 fr2c1 fr2c3 => r1c2<>8
Forcing Net Contradiction in c3 => r1c1<>3
r1c1=3 r2c3<>3
r1c1=3 (r1c8<>3) r8c1<>3 r8c7=3 r7c8<>3 r6c8=3 r6c3<>3
r1c1=3 (r2c3<>3) (r2c3<>3) (r1c8<>3) r8c1<>3 r8c7=3 (r2c7<>3 r2c6=3 r3c6<>3 r3c9=3 r5c9<>3 r5c2=3 r7c2<>3 r7c2=8 r4c2<>8 r4c7=8 r4c7<>5 r5c7=5 r5c4<>5) (r2c7<>3 r2c6=3 r3c6<>3 r3c9=3 r3c9<>8) (r2c7<>3 r2c6=3 r3c6<>3 r3c9=3 r5c9<>3 r5c2=3 r7c2<>3 r7c2=8 r6c2<>8) (r2c7<>3) r7c8<>3 r6c8=3 r6c3<>3 r9c3=3 r9c3<>8 r9c9=8 r7c8<>8 r1c8=8 r2c7<>8 r2c7=6 r2c3<>6 r2c3=8 (r3c1<>8) (r6c3<>8) r9c3<>8 r9c9=8 r6c9<>8 r6c5=8 r3c5<>8 r3c4=8 r3c4<>5 r7c4=5 r7c4<>3 r9c46=3 r9c3<>3
Forcing Net Contradiction in r8 => r1c8<>3
r1c8=3 (r1c2<>3) (r6c8<>3 r6c8=6 r6c3<>6) r1c8<>8 r7c8=8 r9c9<>8 r9c3=8 r6c3<>8 r6c3=3 (r5c2<>3) r6c2<>3 r7c2=3 r8c1<>3 r8c1=6
r1c8=3 (r6c8<>3 r6c8=6 r5c7<>6) (r6c8<>3 r6c8=6 r6c3<>6) r1c8<>8 r7c8=8 r9c9<>8 r9c3=8 r9c3<>6 r2c3=6 r2c7<>6 r8c7=6
Turbot Fish: 3 r3c9 =3= r2c7 -3- r8c7 =3= r8c1 => r3c1<>3
Discontinuous Nice Loop: 3 r5c7 -3- r6c8 =3= r7c8 =8= r7c2 -8- r4c2 =8= r4c7 =5= r5c7 => r5c7<>3
Sashimi Swordfish: 3 c378 r269 fr7c8 fr8c7 => r9c9<>3
Discontinuous Nice Loop: 8 r3c9 -8- r9c9 -6- r8c7 -3- r2c7 =3= r3c9 => r3c9<>8
W-Wing: 6/3 in r3c9,r8c1 connected by 3 in r28c7 => r3c1<>6
Multi Colors 1: 8 (r1c8,r7c2,r9c9) / (r2c7,r7c8,r9c3), (r4c2) / (r4c7) => r5c27,r6c2<>8
Discontinuous Nice Loop: 6 r7c2 -6- r8c1 -3- r8c7 =3= r7c8 =8= r7c2 => r7c2<>6
Discontinuous Nice Loop: 5 r5c4 -5- r5c7 =5= r4c7 =8= r4c2 -8- r7c2 -3- r7c4 -5- r5c4 => r5c4<>5
Grouped Discontinuous Nice Loop: 6 r1c5 -6- r7c5 =6= r7c8 =3= r6c8 -3- r56c9 =3= r3c9 =6= r3c56 -6- r1c5 => r1c5<>6
Grouped Discontinuous Nice Loop: 6 r1c6 -6- r1c8 -8- r2c7 =8= r2c13 -8- r3c1 -9- r3c6 =9= r1c6 => r1c6<>6
Grouped Discontinuous Nice Loop: 6 r2c1 -6- r2c6 =6= r3c56 -6- r3c9 -3- r2c7 =3= r8c7 =6= r8c1 -6- r2c1 => r2c1<>6
Grouped Discontinuous Nice Loop: 6 r5c1 -6- r8c1 -3- r8c7 =3= r2c7 -3- r2c13 =3= r1c2 =6= r56c2 -6- r5c1 => r5c1<>6
Grouped Discontinuous Nice Loop: 3 r6c2 -3- r6c8 =3= r7c8 -3- r8c7 =3= r2c7 -3- r2c13 =3= r1c2 -3- r6c2 => r6c2<>3
Almost Locked Set Chain: 5- r6c2 {56} -6- r6c38 {368} -8- r9c3456 {13678} -6- r9c9 {68} -8- r5c79,r6c89 {35678} -5 => r5c2<>5
Forcing Chain Contradiction in r3c4 => r1c6=9
r1c6<>9 r3c6=9 r3c1<>9 r3c1=8 r2c13<>8 r2c7=8 r2c7<>3 r3c9=3 r3c4<>3
r1c6<>9 r3c6=9 r3c1<>9 r3c1=8 r2c13<>8 r2c7=8 r4c7<>8 r4c2=8 r7c2<>8 r7c2=3 r7c4<>3 r7c4=5 r3c4<>5
r1c6<>9 r3c6=9 r3c1<>9 r3c1=8 r3c4<>8
Hidden Single: r3c1=9
Locked Candidates Type 2 (Claiming): 8 in r3 => r1c45<>8
XY-Wing: 3/6/8 in r1c28,r7c2 => r7c8<>8
Hidden Single: r7c2=8
Hidden Single: r1c8=8
Hidden Single: r9c9=8
Hidden Single: r4c7=8
Hidden Single: r5c7=5
Locked Candidates Type 2 (Claiming): 6 in r1 => r2c3<>6
Remote Pair: 3/6 r2c7 -6- r8c7 -3- r8c1 -6- r9c3 => r2c3<>3
Naked Single: r2c3=8
Hidden Single: r5c1=8
Hidden Single: r6c5=8
Hidden Single: r3c4=8
Hidden Single: r6c6=4
Hidden Single: r7c4=5
Naked Single: r7c5=6
Full House: r7c8=3
Full House: r8c7=6
Full House: r2c7=3
Full House: r8c1=3
Full House: r3c9=6
Full House: r9c3=6
Full House: r6c3=3
Naked Single: r3c5=5
Full House: r3c6=3
Naked Single: r6c8=6
Naked Single: r2c1=4
Full House: r1c1=6
Full House: r1c2=3
Naked Single: r6c9=7
Full House: r6c2=5
Full House: r5c9=3
Naked Single: r1c4=7
Full House: r1c5=4
Naked Single: r2c5=1
Full House: r2c6=6
Full House: r9c5=7
Naked Single: r4c2=9
Full House: r5c2=6
Naked Single: r5c4=1
Full House: r9c4=3
Full House: r9c6=1
Naked Single: r4c8=1
Full House: r4c6=5
Full House: r5c6=7
Full House: r5c8=9
|
normal_sudoku_1805 | 3.9481..6...372.9...25961.3...7.83.9.93.64...4..935.6.2..849..1.1..538....8..793. | 359481726186372495742596183625718349893264517471935268237849651914653872568127934 | normal_sudoku_1805 | 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 | 9 | 3 . 9 4 8 1 . . 6
. . . 3 7 2 . 9 .
. . 2 5 9 6 1 . 3
. . . 7 . 8 3 . 9
. 9 3 . 6 4 . . .
4 . . 9 3 5 . 6 .
2 . . 8 4 9 . . 1
. 1 . . 5 3 8 . .
. . 8 . . 7 9 3 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 359481726186372495742596183625718349893264517471935268237849651914653872568127934 #1 Easy (276)
Hidden Single: r4c8=4
Hidden Single: r6c3=1
Hidden Single: r8c1=9
Hidden Single: r2c7=4
Hidden Single: r7c7=6
Hidden Single: r7c2=3
Hidden Single: r3c2=4
Hidden Single: r5c8=1
Naked Single: r5c4=2
Full House: r4c5=1
Full House: r9c5=2
Naked Single: r8c4=6
Full House: r9c4=1
Hidden Single: r2c1=1
Hidden Single: r8c3=4
Hidden Single: r9c9=4
Hidden Single: r3c8=8
Full House: r3c1=7
Naked Single: r2c9=5
Naked Single: r1c2=5
Naked Single: r2c3=6
Full House: r2c2=8
Naked Single: r9c2=6
Full House: r9c1=5
Full House: r7c3=7
Full House: r4c3=5
Full House: r7c8=5
Naked Single: r4c2=2
Full House: r4c1=6
Full House: r5c1=8
Full House: r6c2=7
Naked Single: r5c9=7
Full House: r5c7=5
Naked Single: r6c7=2
Full House: r1c7=7
Full House: r6c9=8
Full House: r8c9=2
Full House: r1c8=2
Full House: r8c8=7
|
normal_sudoku_5088 | ....8..574....59.8...3.9..2...964275574218369..65..184.4....721..8..1.9391....8.6 | 639182457421675938857349612183964275574218369296537184345896721768421593912753846 | normal_sudoku_5088 | 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 | 9 | . . . . 8 . . 5 7
4 . . . . 5 9 . 8
. . . 3 . 9 . . 2
. . . 9 6 4 2 7 5
5 7 4 2 1 8 3 6 9
. . 6 5 . . 1 8 4
. 4 . . . . 7 2 1
. . 8 . . 1 . 9 3
9 1 . . . . 8 . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 639182457421675938857349612183964275574218369296537184345896721768421593912753846 #1 Easy (206)
Naked Single: r9c8=4
Full House: r8c7=5
Naked Single: r3c8=1
Full House: r2c8=3
Naked Single: r9c4=7
Hidden Single: r7c4=8
Hidden Single: r6c2=9
Hidden Single: r7c5=9
Hidden Single: r1c3=9
Hidden Single: r3c2=5
Naked Single: r3c3=7
Naked Single: r3c5=4
Naked Single: r3c7=6
Full House: r1c7=4
Full House: r3c1=8
Naked Single: r8c5=2
Naked Single: r2c5=7
Naked Single: r8c2=6
Naked Single: r9c6=3
Naked Single: r6c5=3
Full House: r6c6=7
Full House: r9c5=5
Full House: r6c1=2
Full House: r9c3=2
Naked Single: r2c2=2
Naked Single: r7c1=3
Naked Single: r8c1=7
Full House: r8c4=4
Full House: r7c6=6
Full House: r7c3=5
Full House: r1c6=2
Naked Single: r2c3=1
Full House: r2c4=6
Full House: r4c3=3
Full House: r1c4=1
Naked Single: r1c2=3
Full House: r1c1=6
Full House: r4c1=1
Full House: r4c2=8
|
normal_sudoku_314 | .9.2..7.1..6....3.71.3.86..67..3....85.9....7..148756..6...18.3...84.1761..6....2 | 593264781486719235712358694679135428854926317321487569267591843935842176148673952 | normal_sudoku_314 | 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 | 9 | . 9 . 2 . . 7 . 1
. . 6 . . . . 3 .
7 1 . 3 . 8 6 . .
6 7 . . 3 . . . .
8 5 . 9 . . . . 7
. . 1 4 8 7 5 6 .
. 6 . . . 1 8 . 3
. . . 8 4 . 1 7 6
1 . . 6 . . . . 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 593264781486719235712358694679135428854926317321487569267591843935842176148673952 #1 Medium (360)
Naked Single: r6c9=9
Hidden Single: r5c7=3
Hidden Single: r4c3=9
Hidden Single: r5c3=4
Locked Candidates Type 1 (Pointing): 5 in b9 => r13c8<>5
Locked Candidates Type 2 (Claiming): 4 in r3 => r1c8,r2c79<>4
Naked Single: r1c8=8
Naked Single: r2c9=5
Naked Single: r3c9=4
Full House: r4c9=8
Hidden Single: r9c3=8
Hidden Single: r2c2=8
Hidden Single: r9c5=7
Naked Single: r7c4=5
Naked Single: r4c4=1
Full House: r2c4=7
Hidden Single: r7c3=7
Hidden Single: r9c2=4
Naked Single: r9c7=9
Naked Single: r2c7=2
Full House: r3c8=9
Full House: r4c7=4
Naked Single: r7c8=4
Full House: r9c8=5
Full House: r9c6=3
Naked Single: r2c1=4
Naked Single: r3c5=5
Full House: r3c3=2
Naked Single: r4c8=2
Full House: r4c6=5
Full House: r5c8=1
Naked Single: r2c6=9
Full House: r2c5=1
Naked Single: r1c5=6
Full House: r1c6=4
Naked Single: r8c6=2
Full House: r5c6=6
Full House: r5c5=2
Full House: r7c5=9
Full House: r7c1=2
Naked Single: r8c2=3
Full House: r6c2=2
Full House: r6c1=3
Naked Single: r8c3=5
Full House: r1c3=3
Full House: r1c1=5
Full House: r8c1=9
|
normal_sudoku_2780 | 5.218...46...291......7...2.2965.4.3....9..56....34..9..38.2....41965..8...3.79.. | 592186734637429185418573692129658473374291856856734219963812547741965328285347961 | normal_sudoku_2780 | 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 | 9 | 5 . 2 1 8 . . . 4
6 . . . 2 9 1 . .
. . . . 7 . . . 2
. 2 9 6 5 . 4 . 3
. . . . 9 . . 5 6
. . . . 3 4 . . 9
. . 3 8 . 2 . . .
. 4 1 9 6 5 . . 8
. . . 3 . 7 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 592186734637429185418573692129658473374291856856734219963812547741965328285347961 #1 Medium (564)
Locked Candidates Type 1 (Pointing): 1 in b6 => r79c8<>1
Naked Triple: 4,7,8 in r235c3 => r6c3<>7, r69c3<>8
Hidden Pair: 5,6 in r6c23 => r6c2<>1, r6c2<>7, r6c2<>8
Hidden Pair: 3,4 in r35c1 => r35c1<>1, r35c1<>8, r3c1<>9, r5c1<>7
Hidden Single: r3c2=1
Hidden Single: r7c1=9
Hidden Single: r5c6=1
Naked Single: r4c6=8
Hidden Single: r3c8=9
Hidden Single: r1c2=9
Locked Candidates Type 1 (Pointing): 7 in b1 => r2c89<>7
Naked Single: r2c9=5
Naked Single: r2c4=4
Naked Single: r9c9=1
Full House: r7c9=7
Naked Single: r3c4=5
Naked Single: r9c5=4
Full House: r7c5=1
Hidden Single: r7c7=5
Naked Single: r7c2=6
Full House: r7c8=4
Naked Single: r6c2=5
Naked Single: r9c3=5
Naked Single: r6c3=6
Naked Single: r9c2=8
Naked Single: r9c1=2
Full House: r8c1=7
Full House: r9c8=6
Naked Single: r4c1=1
Full House: r4c8=7
Naked Single: r6c1=8
Naked Single: r1c8=3
Naked Single: r6c7=2
Naked Single: r1c6=6
Full House: r1c7=7
Full House: r3c6=3
Naked Single: r2c8=8
Full House: r3c7=6
Naked Single: r8c8=2
Full House: r6c8=1
Full House: r5c7=8
Full House: r6c4=7
Full House: r8c7=3
Full House: r5c4=2
Naked Single: r3c1=4
Full House: r3c3=8
Full House: r5c1=3
Naked Single: r2c3=7
Full House: r2c2=3
Full House: r5c2=7
Full House: r5c3=4
|
normal_sudoku_2009 | ....8...3.2.7..6.....635.....24...974...9728..7.....6...8.7..1..4.9..7..5.7..1... | 695284173823719645714635829182456397456397281379128564938572416241963758567841932 | normal_sudoku_2009 | 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 | 9 | . . . . 8 . . . 3
. 2 . 7 . . 6 . .
. . . 6 3 5 . . .
. . 2 4 . . . 9 7
4 . . . 9 7 2 8 .
. 7 . . . . . 6 .
. . 8 . 7 . . 1 .
. 4 . 9 . . 7 . .
5 . 7 . . 1 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 695284173823719645714635829182456397456397281379128564938572416241963758567841932 #1 Extreme (6598)
Locked Candidates Type 1 (Pointing): 2 in b2 => r1c8<>2
Locked Candidates Type 1 (Pointing): 6 in b5 => r4c12<>6
Locked Candidates Type 1 (Pointing): 3 in b6 => r79c7<>3
Finned X-Wing: 4 c58 r29 fr1c8 fr3c8 => r2c9<>4
Finned Swordfish: 8 r248 c169 fr4c2 => r6c1<>8
Locked Candidates Type 1 (Pointing): 8 in b4 => r4c6<>8
Forcing Chain Contradiction in r9c4 => r1c7<>5
r1c7=5 r2c8<>5 r2c8=4 r2c5<>4 r2c5=1 r1c4<>1 r1c4=2 r9c4<>2
r1c7=5 r12c8<>5 r8c8=5 r8c8<>3 r9c8=3 r9c4<>3
r1c7=5 r1c23<>5 r2c3=5 r2c3<>3 r2c1=3 r2c1<>8 r2c9=8 r8c9<>8 r8c6=8 r9c4<>8
Forcing Chain Contradiction in r4 => r2c9<>1
r2c9=1 r2c9<>8 r2c1=8 r4c1<>8 r4c2=8 r4c2<>5
r2c9=1 r5c9<>1 r5c9=5 r46c7<>5 r7c7=5 r7c4<>5 r8c5=5 r4c5<>5
r2c9=1 r5c9<>1 r5c9=5 r4c7<>5
Almost Locked Set XY-Wing: A=r4689c5 {12456}, B=r13467c7 {134589}, C=r2c5689 {14589}, X,Y=1,8, Z=4 => r9c7<>4
Forcing Chain Contradiction in r2c9 => r6c4<>2
r6c4=2 r1c4<>2 r1c4=1 r2c5<>1 r2c5=4 r2c8<>4 r2c8=5 r2c9<>5
r6c4=2 r6c4<>8 r6c6=8 r8c6<>8 r8c9=8 r2c9<>8
r6c4=2 r1c4<>2 r1c6=2 r1c6<>9 r2c6=9 r2c9<>9
Discontinuous Nice Loop: 1 r6c5 -1- r2c5 =1= r1c4 =2= r1c6 -2- r6c6 =2= r6c5 => r6c5<>1
Discontinuous Nice Loop: 2 r9c5 -2- r6c5 =2= r6c6 -2- r1c6 =2= r1c4 =1= r2c5 =4= r9c5 => r9c5<>2
Forcing Chain Contradiction in c4 => r6c5=2
r6c5<>2 r6c6=2 r1c6<>2 r1c4=2 r1c4<>1
r6c5<>2 r6c5=5 r8c5<>5 r7c4=5 r7c7<>5 r46c7=5 r5c9<>5 r5c9=1 r5c4<>1
r6c5<>2 r6c6=2 r6c6<>8 r6c4=8 r6c4<>1
Discontinuous Nice Loop: 3 r4c2 -3- r4c7 =3= r6c7 -3- r6c6 -8- r6c4 =8= r9c4 -8- r9c7 =8= r3c7 -8- r3c2 =8= r4c2 => r4c2<>3
Discontinuous Nice Loop: 3 r6c3 -3- r6c6 -8- r8c6 =8= r8c9 -8- r2c9 =8= r2c1 =3= r2c3 -3- r6c3 => r6c3<>3
Forcing Chain Contradiction in r7 => r4c7<>1
r4c7=1 r4c5<>1 r2c5=1 r2c5<>4 r9c5=4 r7c6<>4
r4c7=1 r5c9<>1 r5c9=5 r46c7<>5 r7c7=5 r7c7<>4
r4c7=1 r4c7<>3 r6c7=3 r6c7<>4 r6c9=4 r7c9<>4
Finned Swordfish: 1 r248 c135 fr4c2 => r56c3,r6c1<>1
Discontinuous Nice Loop: 5 r2c3 -5- r6c3 -9- r6c1 -3- r2c1 =3= r2c3 => r2c3<>5
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c8<>5
Discontinuous Nice Loop: 9 r2c1 -9- r6c1 -3- r6c6 -8- r8c6 =8= r8c9 -8- r2c9 =8= r2c1 => r2c1<>9
Discontinuous Nice Loop: 5 r4c2 -5- r6c3 -9- r6c1 -3- r6c6 -8- r6c4 =8= r9c4 -8- r9c7 =8= r3c7 -8- r3c2 =8= r4c2 => r4c2<>5
Turbot Fish: 5 r4c7 =5= r4c5 -5- r8c5 =5= r7c4 => r7c7<>5
Locked Candidates Type 2 (Claiming): 5 in c7 => r56c9<>5
Naked Single: r5c9=1
Naked Single: r6c9=4
Hidden Single: r6c4=1
Naked Single: r1c4=2
Hidden Single: r2c5=1
Hidden Single: r6c6=8
Hidden Single: r9c4=8
Naked Single: r9c7=9
Naked Single: r7c7=4
Naked Single: r1c7=1
Naked Single: r3c7=8
Hidden Single: r9c5=4
Hidden Single: r8c9=8
Hidden Single: r2c1=8
Hidden Single: r4c2=8
Hidden Single: r2c3=3
Hidden Single: r4c1=1
Hidden Single: r3c2=1
Hidden Single: r8c3=1
Locked Candidates Type 2 (Claiming): 2 in r9 => r7c9,r8c8<>2
Turbot Fish: 3 r6c1 =3= r5c2 -3- r5c4 =3= r7c4 => r7c1<>3
Hidden Rectangle: 5/6 in r1c23,r5c23 => r1c2<>6
XY-Chain: 3 3- r6c1 -9- r6c3 -5- r6c7 -3- r4c7 -5- r4c5 -6- r8c5 -5- r8c8 -3- r9c8 -2- r9c9 -6- r9c2 -3 => r5c2,r8c1<>3
Hidden Single: r5c4=3
Full House: r7c4=5
Naked Single: r4c6=6
Full House: r4c5=5
Full House: r8c5=6
Full House: r4c7=3
Full House: r6c7=5
Naked Single: r7c9=6
Naked Single: r8c1=2
Naked Single: r6c3=9
Full House: r6c1=3
Naked Single: r9c9=2
Naked Single: r7c1=9
Naked Single: r8c6=3
Full House: r7c6=2
Full House: r7c2=3
Full House: r8c8=5
Full House: r9c8=3
Full House: r9c2=6
Naked Single: r3c3=4
Naked Single: r3c9=9
Full House: r2c9=5
Naked Single: r3c1=7
Full House: r1c1=6
Full House: r3c8=2
Naked Single: r2c8=4
Full House: r1c8=7
Full House: r2c6=9
Full House: r1c6=4
Naked Single: r5c2=5
Full House: r1c2=9
Full House: r1c3=5
Full House: r5c3=6
|
normal_sudoku_5109 | 76.8......5..9.6....4..6.5.2.7...3..548372196....1.....7....5.94..5.7.6.6.5..947. | 769851234352794618184236957217968345548372196936415782871643529493527861625189473 | normal_sudoku_5109 | 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 | 9 | 7 6 . 8 . . . . .
. 5 . . 9 . 6 . .
. . 4 . . 6 . 5 .
2 . 7 . . . 3 . .
5 4 8 3 7 2 1 9 6
. . . . 1 . . . .
. 7 . . . . 5 . 9
4 . . 5 . 7 . 6 .
6 . 5 . . 9 4 7 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 769851234352794618184236957217968345548372196936415782871643529493527861625189473 #1 Unfair (1158)
Hidden Single: r4c2=1
Hidden Single: r6c3=6
Hidden Single: r4c4=9
Naked Single: r6c4=4
Hidden Single: r4c5=6
Hidden Single: r7c4=6
Hidden Single: r1c5=5
Hidden Single: r7c5=4
Locked Candidates Type 1 (Pointing): 8 in b5 => r7c6<>8
Uniqueness Test 4: 5/8 in r4c69,r6c69 => r46c9<>8
Finned X-Wing: 2 r17 c38 fr1c7 fr1c9 => r2c8<>2
Finned Swordfish: 1 r389 c349 fr3c1 => r12c3<>1
Locked Candidates Type 1 (Pointing): 1 in b1 => r7c1<>1
Finned Swordfish: 3 c368 r127 fr8c3 => r7c1<>3
Naked Single: r7c1=8
Hidden Single: r3c2=8
Locked Candidates Type 1 (Pointing): 2 in b1 => r78c3<>2
Hidden Single: r7c8=2
Naked Single: r6c8=8
Naked Single: r8c7=8
Naked Single: r4c8=4
Naked Single: r6c6=5
Full House: r4c6=8
Full House: r4c9=5
Hidden Single: r2c9=8
Hidden Single: r9c5=8
Hidden Single: r2c6=4
Hidden Single: r1c9=4
Hidden Single: r2c4=7
Hidden Single: r2c3=2
Hidden Single: r1c7=2
Naked Single: r6c7=7
Full House: r3c7=9
Full House: r6c9=2
Hidden Single: r1c3=9
Hidden Single: r3c9=7
Hidden Single: r6c1=9
Full House: r6c2=3
Naked Single: r9c2=2
Full House: r8c2=9
Naked Single: r9c4=1
Full House: r3c4=2
Full House: r9c9=3
Full House: r8c9=1
Naked Single: r7c6=3
Full House: r1c6=1
Full House: r3c5=3
Full House: r7c3=1
Full House: r8c3=3
Full House: r8c5=2
Full House: r1c8=3
Full House: r3c1=1
Full House: r2c8=1
Full House: r2c1=3
|
normal_sudoku_835 | ..8...2.6.9..5....5.......8157...649289546713364..9825.76...9..913..7....254..... | 748931256692854371531672498157328649289546713364719825476185932913267584825493167 | normal_sudoku_835 | 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 | 9 | . . 8 . . . 2 . 6
. 9 . . 5 . . . .
5 . . . . . . . 8
1 5 7 . . . 6 4 9
2 8 9 5 4 6 7 1 3
3 6 4 . . 9 8 2 5
. 7 6 . . . 9 . .
9 1 3 . . 7 . . .
. 2 5 4 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 748931256692854371531672498157328649289546713364719825476185932913267584825493167 #1 Easy (258)
Naked Single: r9c1=8
Full House: r7c1=4
Naked Single: r1c1=7
Full House: r2c1=6
Hidden Single: r1c8=5
Hidden Single: r7c6=5
Hidden Single: r8c7=5
Hidden Single: r9c5=9
Hidden Single: r3c8=9
Hidden Single: r8c9=4
Hidden Single: r1c4=9
Hidden Single: r9c8=6
Naked Single: r8c8=8
Naked Single: r7c8=3
Full House: r2c8=7
Naked Single: r9c7=1
Naked Single: r2c9=1
Naked Single: r7c9=2
Full House: r9c9=7
Full House: r9c6=3
Naked Single: r2c3=2
Full House: r3c3=1
Hidden Single: r1c6=1
Naked Single: r1c5=3
Full House: r1c2=4
Full House: r3c2=3
Naked Single: r2c4=8
Naked Single: r3c7=4
Full House: r2c7=3
Full House: r2c6=4
Naked Single: r7c4=1
Full House: r7c5=8
Naked Single: r3c6=2
Full House: r4c6=8
Naked Single: r6c4=7
Full House: r6c5=1
Naked Single: r4c5=2
Full House: r4c4=3
Naked Single: r3c4=6
Full House: r3c5=7
Full House: r8c5=6
Full House: r8c4=2
|
normal_sudoku_3466 | 3....79.6986..4...57..6..2.2.9.1.4734.739.281138.72569.257...1.....5..9.7....16.. | 312587946986124735574963128259618473467395281138472569625739814841256397793841652 | normal_sudoku_3466 | 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 | 9 | 3 . . . . 7 9 . 6
9 8 6 . . 4 . . .
5 7 . . 6 . . 2 .
2 . 9 . 1 . 4 7 3
4 . 7 3 9 . 2 8 1
1 3 8 . 7 2 5 6 9
. 2 5 7 . . . 1 .
. . . . 5 . . 9 .
7 . . . . 1 6 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 312587946986124735574963128259618473467395281138472569625739814841256397793841652 #1 Easy (226)
Full House: r6c4=4
Hidden Single: r1c3=2
Naked Single: r1c5=8
Hidden Single: r7c6=9
Naked Single: r3c6=3
Naked Single: r2c5=2
Hidden Single: r9c2=9
Hidden Single: r3c4=9
Hidden Single: r7c1=6
Full House: r8c1=8
Naked Single: r8c6=6
Naked Single: r5c6=5
Full House: r4c6=8
Full House: r5c2=6
Full House: r4c4=6
Full House: r4c2=5
Naked Single: r8c4=2
Naked Single: r9c4=8
Hidden Single: r9c9=2
Hidden Single: r9c8=5
Naked Single: r1c8=4
Full House: r2c8=3
Naked Single: r1c2=1
Full House: r1c4=5
Full House: r3c3=4
Full House: r8c2=4
Full House: r2c4=1
Naked Single: r3c9=8
Full House: r3c7=1
Naked Single: r9c3=3
Full House: r8c3=1
Full House: r9c5=4
Full House: r7c5=3
Naked Single: r8c9=7
Full House: r8c7=3
Naked Single: r2c7=7
Full House: r7c7=8
Full House: r7c9=4
Full House: r2c9=5
|
normal_sudoku_5143 | ....7...8.6.82.9.1..81.9.43..93.8.14....1..9.....92.3..4.2351....39814..5.1.4.3.. | 914673528365824971278159643759368214432517896186492735847235169623981457591746382 | normal_sudoku_5143 | 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 | 9 | . . . . 7 . . . 8
. 6 . 8 2 . 9 . 1
. . 8 1 . 9 . 4 3
. . 9 3 . 8 . 1 4
. . . . 1 . . 9 .
. . . . 9 2 . 3 .
. 4 . 2 3 5 1 . .
. . 3 9 8 1 4 . .
5 . 1 . 4 . 3 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 914673528365824971278159643759368214432517896186492735847235169623981457591746382 #1 Hard (1340)
Locked Candidates Type 1 (Pointing): 6 in b8 => r9c89<>6
Locked Candidates Type 1 (Pointing): 7 in b8 => r9c289<>7
Naked Triple: 2,6,7 in r7c3,r8c12 => r7c1<>6, r7c1<>7, r9c2<>2
Locked Candidates Type 1 (Pointing): 2 in b7 => r8c89<>2
Naked Triple: 2,6,7 in r348c1 => r15c1<>2, r256c1<>7, r56c1<>6
Naked Pair: 3,4 in r2c16 => r2c3<>4
Naked Triple: 2,5,7 in r2c3,r3c12 => r1c23<>2, r1c23<>5
Naked Single: r1c3=4
Naked Single: r2c1=3
Naked Single: r2c6=4
Hidden Single: r5c3=2
Hidden Single: r1c6=3
Hidden Single: r5c2=3
Hidden Single: r4c7=2
Hidden Single: r9c9=2
Naked Single: r9c8=8
Naked Single: r9c2=9
Naked Single: r1c2=1
Naked Single: r7c1=8
Naked Single: r1c1=9
Naked Single: r5c1=4
Naked Single: r6c1=1
Hidden Single: r1c8=2
Hidden Single: r7c9=9
Hidden Single: r6c2=8
Hidden Single: r5c7=8
Hidden Single: r6c4=4
Locked Candidates Type 1 (Pointing): 6 in b3 => r6c7<>6
Locked Candidates Type 1 (Pointing): 7 in b5 => r5c9<>7
Locked Candidates Type 1 (Pointing): 6 in b6 => r8c9<>6
Locked Candidates Type 1 (Pointing): 7 in b6 => r6c3<>7
X-Wing: 5 c25 r34 => r3c7<>5
X-Wing: 7 r27 c38 => r8c8<>7
Skyscraper: 5 in r1c7,r5c9 (connected by r15c4) => r6c7<>5
Naked Single: r6c7=7
Naked Single: r3c7=6
Full House: r1c7=5
Full House: r1c4=6
Full House: r3c5=5
Full House: r2c8=7
Full House: r4c5=6
Full House: r2c3=5
Naked Single: r9c4=7
Full House: r5c4=5
Full House: r5c6=7
Full House: r9c6=6
Full House: r5c9=6
Full House: r6c9=5
Full House: r6c3=6
Full House: r8c9=7
Full House: r7c3=7
Full House: r7c8=6
Full House: r8c8=5
Naked Single: r4c1=7
Full House: r4c2=5
Naked Single: r8c2=2
Full House: r3c2=7
Full House: r3c1=2
Full House: r8c1=6
|
normal_sudoku_2911 | ......3...57.3.1.493....57...82...6.7938642...6..1.8....9.2...8..6.5.93.3....76.. | 614579382857632194932481576148295763793864251265713849579326418426158937381947625 | normal_sudoku_2911 | 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 | 9 | . . . . . . 3 . .
. 5 7 . 3 . 1 . 4
9 3 . . . . 5 7 .
. . 8 2 . . . 6 .
7 9 3 8 6 4 2 . .
. 6 . . 1 . 8 . .
. . 9 . 2 . . . 8
. . 6 . 5 . 9 3 .
3 . . . . 7 6 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 614579382857632194932481576148295763793864251265713849579326418426158937381947625 #1 Extreme (1842)
Locked Candidates Type 1 (Pointing): 1 in b4 => r4c9<>1
Locked Candidates Type 2 (Claiming): 8 in r3 => r1c56,r2c6<>8
Locked Candidates Type 2 (Claiming): 5 in r5 => r46c9,r6c8<>5
Hidden Pair: 3,6 in r7c46 => r7c46<>1, r7c4<>4
Hidden Pair: 5,7 in r16c4 => r1c4<>1, r1c4<>4, r1c4<>6, r16c4<>9, r6c4<>3
Hidden Single: r7c4=3
Naked Single: r7c6=6
XY-Wing: 4/7/9 in r4c57,r6c8 => r4c9,r6c6<>9
Discontinuous Nice Loop: 1/2/4/8 r1c1 =6= r1c9 =9= r6c9 =7= r6c4 -7- r4c5 -9- r9c5 =9= r9c4 -9- r2c4 -6- r2c1 =6= r1c1 => r1c1<>1, r1c1<>2, r1c1<>4, r1c1<>8
Naked Single: r1c1=6
Hidden Single: r3c9=6
Hidden Single: r2c4=6
Hidden Single: r9c4=9
Locked Candidates Type 1 (Pointing): 1 in b8 => r8c129<>1
Naked Pair: 4,8 in r39c5 => r1c5<>4
Locked Candidates Type 1 (Pointing): 4 in b2 => r3c3<>4
Hidden Pair: 1,5 in r59c9 => r9c9<>2
Uniqueness Test 1: 1/5 in r5c89,r9c89 => r9c8<>1, r9c8<>5
Naked Triple: 2,4,7 in r7c7,r8c9,r9c8 => r7c8<>4
Finned X-Wing: 2 c29 r18 fr9c2 => r8c1<>2
Naked Triple: 1,4,8 in r8c146 => r8c2<>4, r8c2<>8
XY-Chain: 4 4- r8c1 -8- r2c1 -2- r3c3 -1- r3c4 -4- r3c5 -8- r9c5 -4 => r8c4,r9c23<>4
Naked Single: r8c4=1
Naked Single: r3c4=4
Naked Single: r8c6=8
Full House: r9c5=4
Naked Single: r3c5=8
Naked Single: r8c1=4
Naked Single: r9c8=2
Naked Single: r8c9=7
Full House: r8c2=2
Naked Single: r4c9=3
Naked Single: r7c7=4
Full House: r4c7=7
Naked Single: r6c9=9
Naked Single: r4c5=9
Full House: r1c5=7
Naked Single: r1c9=2
Naked Single: r6c8=4
Naked Single: r4c6=5
Naked Single: r1c4=5
Full House: r6c4=7
Full House: r6c6=3
Naked Single: r4c1=1
Full House: r4c2=4
Naked Single: r7c1=5
Naked Single: r6c1=2
Full House: r2c1=8
Full House: r6c3=5
Naked Single: r7c8=1
Full House: r7c2=7
Full House: r9c9=5
Full House: r5c9=1
Full House: r5c8=5
Naked Single: r9c3=1
Full House: r9c2=8
Full House: r1c2=1
Naked Single: r2c8=9
Full House: r1c8=8
Full House: r2c6=2
Naked Single: r1c3=4
Full House: r3c3=2
Full House: r1c6=9
Full House: r3c6=1
|
normal_sudoku_1933 | .7.9813.2...37214.231564978.....7...7.3859....2..36.87.18.......9..1..23..2.....4 | 674981352859372146231564978186247539743859261925136487418623795597418623362795814 | normal_sudoku_1933 | 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 | 9 | . 7 . 9 8 1 3 . 2
. . . 3 7 2 1 4 .
2 3 1 5 6 4 9 7 8
. . . . . 7 . . .
7 . 3 8 5 9 . . .
. 2 . . 3 6 . 8 7
. 1 8 . . . . . .
. 9 . . 1 . . 2 3
. . 2 . . . . . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 674981352859372146231564978186247539743859261925136487418623795597418623362795814 #1 Easy (218)
Naked Single: r9c5=9
Hidden Single: r5c7=2
Hidden Single: r4c8=3
Hidden Single: r8c3=7
Hidden Single: r9c8=1
Naked Single: r5c8=6
Naked Single: r1c8=5
Full House: r2c9=6
Full House: r7c8=9
Naked Single: r5c2=4
Full House: r5c9=1
Naked Single: r7c9=5
Full House: r4c9=9
Naked Single: r7c6=3
Hidden Single: r1c3=4
Full House: r1c1=6
Naked Single: r7c1=4
Naked Single: r7c5=2
Full House: r4c5=4
Naked Single: r8c1=5
Naked Single: r4c7=5
Full House: r6c7=4
Naked Single: r6c4=1
Full House: r4c4=2
Naked Single: r8c6=8
Full House: r9c6=5
Naked Single: r9c1=3
Full House: r9c2=6
Naked Single: r4c3=6
Naked Single: r6c1=9
Full House: r6c3=5
Full House: r2c3=9
Naked Single: r8c7=6
Full House: r8c4=4
Naked Single: r4c2=8
Full House: r2c2=5
Full House: r2c1=8
Full House: r4c1=1
Naked Single: r9c4=7
Full House: r7c4=6
Full House: r7c7=7
Full House: r9c7=8
|
normal_sudoku_4700 | 64.5..9...53...46.1.93.4.5..61.4..3543..5...99.5.3.....1.47..96376289514.94...3.. | 647521983253897461189364752761948235438152679925736148512473896376289514894615327 | normal_sudoku_4700 | 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 | 9 | 6 4 . 5 . . 9 . .
. 5 3 . . . 4 6 .
1 . 9 3 . 4 . 5 .
. 6 1 . 4 . . 3 5
4 3 . . 5 . . . 9
9 . 5 . 3 . . . .
. 1 . 4 7 . . 9 6
3 7 6 2 8 9 5 1 4
. 9 4 . . . 3 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 647521983253897461189364752761948235438152679925736148512473896376289514894615327 #1 Easy (236)
Hidden Single: r3c5=6
Naked Single: r9c5=1
Naked Single: r1c5=2
Full House: r2c5=9
Naked Single: r9c4=6
Naked Single: r9c6=5
Full House: r7c6=3
Hidden Single: r1c9=3
Hidden Single: r4c4=9
Hidden Single: r6c8=4
Hidden Single: r7c1=5
Hidden Single: r1c6=1
Hidden Single: r2c9=1
Hidden Single: r2c1=2
Naked Single: r3c2=8
Full House: r1c3=7
Full House: r6c2=2
Full House: r1c8=8
Naked Single: r9c1=8
Full House: r4c1=7
Full House: r5c3=8
Full House: r7c3=2
Full House: r7c7=8
Naked Single: r4c7=2
Full House: r4c6=8
Naked Single: r3c7=7
Full House: r3c9=2
Naked Single: r5c8=7
Full House: r9c8=2
Full House: r9c9=7
Full House: r6c9=8
Naked Single: r2c6=7
Full House: r2c4=8
Naked Single: r5c4=1
Full House: r6c4=7
Naked Single: r6c6=6
Full House: r5c6=2
Full House: r5c7=6
Full House: r6c7=1
|
normal_sudoku_3742 | 16.5.9.84..8.146.9.4.68.51....1.8.466849..1..7...46..827.4.18.58...6.4..4..8....1 | 163529784528714639947683512395178246684952173712346958279431865831265497456897321 | normal_sudoku_3742 | 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 | 9 | 1 6 . 5 . 9 . 8 4
. . 8 . 1 4 6 . 9
. 4 . 6 8 . 5 1 .
. . . 1 . 8 . 4 6
6 8 4 9 . . 1 . .
7 . . . 4 6 . . 8
2 7 . 4 . 1 8 . 5
8 . . . 6 . 4 . .
4 . . 8 . . . . 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 163529784528714639947683512395178246684952173712346958279431865831265497456897321 #1 Extreme (6636)
Forcing Chain Contradiction in c9 => r1c5<>7
r1c5=7 r1c3<>7 r3c3=7 r3c9<>7
r1c5=7 r4c5<>7 r4c7=7 r5c9<>7
r1c5=7 r2c4<>7 r8c4=7 r8c9<>7
Forcing Net Contradiction in r7c8 => r2c4<>2
r2c4=2 (r1c5<>2 r1c5=3 r1c7<>3) (r6c4<>2 r6c4=3 r6c7<>3) r2c4<>7 (r2c8=7 r9c8<>7) r8c4=7 (r9c5<>7) r9c6<>7 r9c7=7 r9c7<>3 r4c7=3 r4c123<>3 r6c23=3 r6c4<>3 r6c4=2 r2c4<>2
Finned Franken Swordfish: 2 c49b2 r358 fr1c5 fr6c4 => r5c5<>2
Forcing Chain Contradiction in c7 => r9c6<>2
r9c6=2 r3c6<>2 r1c5=2 r1c7<>2
r9c6=2 r5c6<>2 r5c89=2 r4c7<>2
r9c6=2 r5c6<>2 r5c89=2 r6c7<>2
r9c6=2 r9c7<>2
Forcing Net Contradiction in r7c8 => r2c4=7
r2c4<>7 (r8c4=7 r9c6<>7 r9c7=7 r9c7<>2 r9c8=2 r5c8<>2) r2c4=3 (r1c5<>3 r1c5=2 r4c5<>2) (r2c2<>3) r2c1<>3 r2c1=5 r2c2<>5 r2c2=2 r4c2<>2 r4c7=2 r5c9<>2 r5c6=2 r6c4<>2 r6c4=3 r2c4<>3 r2c4=7
Finned Franken Swordfish: 3 r27b2 c358 fr2c1 fr2c2 fr3c6 => r3c3<>3
Finned Franken Swordfish: 3 c49b2 r358 fr1c5 fr6c4 => r5c5<>3
Forcing Chain Contradiction in r8c9 => r4c5<>3
r4c5=3 r1c5<>3 r1c5=2 r9c5<>2 r8c46=2 r8c9<>2
r4c5=3 r6c4<>3 r8c4=3 r8c9<>3
r4c5=3 r4c5<>7 r4c7=7 r1c7<>7 r3c9=7 r8c9<>7
W-Wing: 2/3 in r3c6,r8c4 connected by 3 in r5c6,r6c4 => r8c6<>2
Forcing Chain Contradiction in c9 => r1c7<>3
r1c7=3 r1c7<>7 r3c9=7 r3c9<>2
r1c7=3 r1c5<>3 r1c5=2 r3c6<>2 r5c6=2 r5c9<>2
r1c7=3 r1c5<>3 r1c5=2 r9c5<>2 r8c4=2 r8c9<>2
Discontinuous Nice Loop: 2 r3c3 -2- r3c6 -3- r1c5 =3= r1c3 =7= r3c3 => r3c3<>2
Discontinuous Nice Loop: 3 r6c8 -3- r2c8 -2- r1c7 -7- r4c7 =7= r4c5 -7- r5c5 -5- r5c8 =5= r6c8 => r6c8<>3
Grouped AIC: 3 3- r8c4 =3= r6c4 -3- r5c6 =3= r5c89 -3- r46c7 =3= r9c7 -3 => r8c89,r9c56<>3
Empty Rectangle: 3 in b8 (r1c35) => r8c3<>3
AIC: 2/7 7- r4c5 =7= r4c7 -7- r1c7 =7= r3c9 -7- r8c9 -2- r8c4 =2= r9c5 -2 => r4c5<>2, r9c5<>7
Locked Pair: 5,7 in r45c5 => r5c6,r9c5<>5, r5c6<>7
Naked Pair: 2,3 in r35c6 => r8c6<>3
X-Wing: 3 c69 r35 => r3c1,r5c8<>3
Naked Single: r3c1=9
Naked Single: r3c3=7
Hidden Single: r1c7=7
Hidden Single: r4c5=7
Naked Single: r5c5=5
Hidden Single: r6c8=5
Locked Candidates Type 1 (Pointing): 9 in b6 => r9c7<>9
Remote Pair: 2/3 r2c8 -3- r3c9 -2- r3c6 -3- r5c6 -2- r6c4 -3- r8c4 => r58c8<>2
Naked Single: r5c8=7
Naked Single: r8c8=9
Hidden Single: r8c9=7
Naked Single: r8c6=5
Naked Single: r8c3=1
Naked Single: r9c6=7
Naked Single: r8c2=3
Full House: r8c4=2
Full House: r6c4=3
Full House: r5c6=2
Full House: r3c6=3
Full House: r5c9=3
Full House: r1c5=2
Full House: r3c9=2
Full House: r1c3=3
Full House: r2c8=3
Naked Single: r9c5=9
Full House: r7c5=3
Naked Single: r2c1=5
Full House: r2c2=2
Full House: r4c1=3
Naked Single: r7c8=6
Full House: r7c3=9
Full House: r9c8=2
Full House: r9c7=3
Naked Single: r9c2=5
Full House: r9c3=6
Naked Single: r6c3=2
Full House: r4c3=5
Naked Single: r4c2=9
Full House: r4c7=2
Full House: r6c7=9
Full House: r6c2=1
|
normal_sudoku_2810 | .....38..8.....3.53528469716359.41.7.2.6..5.3.873..69...3....5.....3.4195..461.3. | 796153824814792365352846971635924187921678543487315692143289756268537419579461238 | normal_sudoku_2810 | 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 | 9 | . . . . . 3 8 . .
8 . . . . . 3 . 5
3 5 2 8 4 6 9 7 1
6 3 5 9 . 4 1 . 7
. 2 . 6 . . 5 . 3
. 8 7 3 . . 6 9 .
. . 3 . . . . 5 .
. . . . 3 . 4 1 9
5 . . 4 6 1 . 3 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 796153824814792365352846971635924187921678543487315692143289756268537419579461238 #1 Unfair (940)
Hidden Single: r7c9=6
Hidden Single: r9c9=8
Naked Single: r9c3=9
Naked Single: r9c2=7
Full House: r9c7=2
Full House: r7c7=7
Naked Single: r8c1=2
Naked Single: r8c2=6
Naked Single: r7c4=2
Naked Single: r8c3=8
Hidden Single: r5c1=9
Hidden Single: r1c1=7
Locked Candidates Type 1 (Pointing): 1 in b5 => r12c5<>1
Skyscraper: 2 in r1c9,r2c6 (connected by r6c69) => r1c5,r2c8<>2
2-String Kite: 4 in r1c9,r5c3 (connected by r5c8,r6c9) => r1c3<>4
Sue de Coq: r12c5 - {2579} (r47c5 - {289}, r12c4 - {157}) => r2c6<>7, r5c5<>8, r6c5<>2
XY-Wing: 2/9/5 in r1c5,r26c6 => r6c5<>5
Naked Single: r6c5=1
Naked Single: r5c5=7
Naked Single: r6c1=4
Full House: r5c3=1
Full House: r7c1=1
Full House: r7c2=4
Naked Single: r5c6=8
Full House: r5c8=4
Naked Single: r6c9=2
Full House: r1c9=4
Full House: r4c8=8
Full House: r4c5=2
Full House: r6c6=5
Naked Single: r1c3=6
Full House: r2c3=4
Naked Single: r7c6=9
Full House: r7c5=8
Naked Single: r2c8=6
Full House: r1c8=2
Naked Single: r2c5=9
Full House: r1c5=5
Naked Single: r8c6=7
Full House: r2c6=2
Full House: r8c4=5
Naked Single: r2c2=1
Full House: r1c2=9
Full House: r1c4=1
Full House: r2c4=7
|
normal_sudoku_149 | ....63.....2.5.96865.82...4..3..6.....85.461......2.9...56...49..42157.67.6.4.251 | 841963572372451968659827134413796825298534617567182493125678349934215786786349251 | normal_sudoku_149 | 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 | 9 | . . . . 6 3 . . .
. . 2 . 5 . 9 6 8
6 5 . 8 2 . . . 4
. . 3 . . 6 . . .
. . 8 5 . 4 6 1 .
. . . . . 2 . 9 .
. . 5 6 . . . 4 9
. . 4 2 1 5 7 . 6
7 . 6 . 4 . 2 5 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 841963572372451968659827134413796825298534617567182493125678349934215786786349251 #1 Extreme (2336)
Hidden Single: r6c2=6
Locked Candidates Type 1 (Pointing): 1 in b5 => r12c4<>1
Locked Candidates Type 1 (Pointing): 8 in b5 => r7c5<>8
Locked Candidates Type 1 (Pointing): 9 in b8 => r9c2<>9
Locked Candidates Type 2 (Claiming): 9 in c3 => r1c12<>9
Locked Candidates Type 2 (Claiming): 9 in c5 => r4c4<>9
Locked Candidates Type 2 (Claiming): 3 in c9 => r6c7<>3
Naked Triple: 3,8,9 in r8c12,r9c2 => r7c12<>3, r7c12<>8
XY-Chain: 1 1- r2c6 -7- r7c6 -8- r7c7 -3- r3c7 -1 => r3c6<>1
Hidden Single: r2c6=1
Empty Rectangle: 7 in b4 (r2c24) => r6c4<>7
XY-Chain: 3 3- r2c1 -4- r2c4 -7- r3c6 -9- r9c6 -8- r9c2 -3 => r2c2,r8c1<>3
Hidden Single: r2c1=3
XY-Chain: 7 7- r3c6 -9- r9c6 -8- r7c6 -7- r7c5 -3- r7c7 -8- r8c8 -3- r3c8 -7 => r3c3<>7
XY-Chain: 7 7- r2c2 -4- r2c4 -7- r3c6 -9- r3c3 -1- r6c3 -7 => r1c3,r45c2<>7
Hidden Single: r6c3=7
Locked Pair: 2,9 in r5c12 => r4c12,r5c5<>9, r4c12,r5c9<>2
Hidden Single: r4c5=9
Hidden Single: r6c5=8
Locked Candidates Type 2 (Claiming): 1 in c3 => r1c12<>1
XY-Wing: 1/4/7 in r24c2,r4c4 => r2c4<>7
Naked Single: r2c4=4
Full House: r2c2=7
2-String Kite: 7 in r3c8,r4c4 (connected by r1c4,r3c6) => r4c8<>7
Locked Candidates Type 1 (Pointing): 7 in b6 => r1c9<>7
Hidden Rectangle: 2/7 in r1c89,r4c89 => r4c9<>7
Hidden Single: r4c4=7
Naked Single: r1c4=9
Full House: r3c6=7
Naked Single: r5c5=3
Full House: r6c4=1
Full House: r9c4=3
Full House: r7c5=7
Naked Single: r1c3=1
Full House: r3c3=9
Naked Single: r3c8=3
Full House: r3c7=1
Naked Single: r7c6=8
Full House: r9c6=9
Full House: r9c2=8
Naked Single: r5c9=7
Naked Single: r1c7=5
Naked Single: r8c8=8
Full House: r7c7=3
Naked Single: r1c2=4
Full House: r1c1=8
Naked Single: r8c1=9
Full House: r8c2=3
Naked Single: r1c9=2
Full House: r1c8=7
Full House: r4c8=2
Naked Single: r6c7=4
Full House: r4c7=8
Naked Single: r4c2=1
Naked Single: r5c1=2
Full House: r5c2=9
Full House: r7c2=2
Full House: r7c1=1
Naked Single: r4c9=5
Full House: r4c1=4
Full House: r6c1=5
Full House: r6c9=3
|
normal_sudoku_575 | ..72...3.2....3..438...9.....1.5.....6.93..8...3..67....2.9...51..3...2.....246.. | 957248136216573894384619572891457263765932481423186759672891345148365927539724618 | normal_sudoku_575 | 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 | 9 | . . 7 2 . . . 3 .
2 . . . . 3 . . 4
3 8 . . . 9 . . .
. . 1 . 5 . . . .
. 6 . 9 3 . . 8 .
. . 3 . . 6 7 . .
. . 2 . 9 . . . 5
1 . . 3 . . . 2 .
. . . . 2 4 6 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 957248136216573894384619572891457263765932481423186759672891345148365927539724618 #1 Extreme (15918)
Locked Candidates Type 1 (Pointing): 8 in b4 => r79c1<>8
2-String Kite: 6 in r1c1,r8c5 (connected by r7c1,r8c3) => r1c5<>6
Grouped Discontinuous Nice Loop: 8 r9c4 -8- r9c3 =8= r8c3 =6= r7c1 -6- r1c1 =6= r1c9 =8= r12c7 -8- r7c7 =8= r7c46 -8- r9c4 => r9c4<>8
Forcing Net Contradiction in b9 => r4c2<>4
r4c2=4 (r8c2<>4) (r5c1<>4) r5c3<>4 r5c7=4 (r8c7<>4) r8c7<>4 r8c3=4 (r8c3<>8 r9c3=8 r9c9<>8) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>8 r8c9=8 r8c7<>8 r8c7=9
r4c2=4 (r8c2<>4) (r5c1<>4) r5c3<>4 (r5c3=5 r6c2<>5 r6c8=5 r6c8<>9) r5c7=4 r8c7<>4 r8c3=4 (r3c3<>4 r3c3=6 r2c3<>6 r2c3=9 r2c8<>9) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r4c9<>6 r4c8=6 r4c8<>9 r9c8=9
Forcing Net Contradiction in b9 => r6c2<>4
r6c2=4 (r8c2<>4) (r5c1<>4) r5c3<>4 r5c7=4 (r8c7<>4) r8c7<>4 r8c3=4 (r8c3<>8 r9c3=8 r9c9<>8) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>8 r8c9=8 r8c7<>8 r8c7=9
r6c2=4 (r8c2<>4) (r5c1<>4) r5c3<>4 (r5c3=5 r6c1<>5 r6c8=5 r6c8<>9) r5c7=4 r8c7<>4 r8c3=4 (r3c3<>4 r3c3=6 r2c3<>6 r2c3=9 r2c8<>9) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r4c9<>6 r4c8=6 r4c8<>9 r9c8=9
Forcing Net Contradiction in c8 => r6c8<>1
r6c8=1 (r6c8<>5 r5c7=5 r5c1<>5) (r6c8<>5) r5c9<>1 r5c9=2 r6c9<>2 r6c2=2 r6c2<>5 r6c1=5 (r9c1<>5) r5c3<>5 r5c3=4 r5c1<>4 r5c1=7 r9c1<>7 r9c1=9 (r8c3<>9) r9c3<>9 r2c3=9 r2c8<>9
r6c8=1 (r6c9<>1) r5c9<>1 r5c9=2 r6c9<>2 r6c9=9 r4c8<>9
r6c8=1 r6c8<>9
r6c8=1 (r6c8<>5) r5c9<>1 (r5c6=1 r5c6<>7 r5c1=7 r9c1<>7) r5c9=2 r6c9<>2 r6c2=2 r6c2<>5 r6c1=5 r9c1<>5 r9c1=9 r9c8<>9
Forcing Net Contradiction in r8c7 => r1c9<>1
r1c9=1 (r6c9<>1 r5c7=1 r5c6<>1 r7c6=1 r7c6<>8) r1c9<>6 r1c1=6 r7c1<>6 r7c4=6 r7c4<>8 r7c7=8 (r8c9<>8) r9c9<>8 r1c9=8 r1c9<>1
Forcing Net Contradiction in c7 => r8c3<>4
r8c3=4 (r8c2<>4 r1c2=4 r1c2<>9) (r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>9) (r8c3<>9) r8c3<>8 r9c3=8 r9c3<>9 r2c3=9 r1c1<>9 r1c7=9
r8c3=4 (r8c7<>4) (r8c3<>8 r9c3=8 r9c9<>8) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>8 r8c9=8 r8c7<>8 r8c7=9
Forcing Net Contradiction in b7 => r8c3<>5
r8c3=5 (r8c3<>9) (r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>8 r8c9=8 r8c9<>9) (r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r7c1<>4 r1c1=4 r1c1<>9) (r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>9) (r8c3<>9) r8c3<>8 r9c3=8 r9c3<>9 r2c3=9 r1c2<>9 r1c7=9 r8c7<>9 r8c2=9
r8c3=5 (r8c6<>5) (r8c3<>8 r9c3=8 r9c9<>8) r8c3<>6 r8c5=6 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r1c9<>8 r8c9=8 r8c6<>8 r8c6=7 (r5c6<>7 r5c1=7 r9c1<>7) r8c6<>5 r1c6=5 (r2c4<>5) r3c4<>5 r9c4=5 r9c1<>5 r9c1=9
Forcing Net Contradiction in r3 => r2c2<>5
r2c2=5 (r8c2<>5 r8c6=5 r1c6<>5 r1c7=5 r3c8<>5 r3c4=5 r3c4<>4) (r8c2<>5 r8c6=5 r1c6<>5) r2c2<>1 r1c2=1 (r1c5<>1) r1c6<>1 r1c6=8 r1c5<>8 r1c5=4 r3c5<>4 r3c3=4 r3c3<>6
r2c2=5 (r3c3<>5) (r1c1<>5) (r1c2<>5) r8c2<>5 r8c6=5 r1c6<>5 r1c7=5 (r3c7<>5) r3c8<>5 r3c4=5 r3c4<>6
r2c2=5 (r8c2<>5 r8c6=5 r1c6<>5) r2c2<>1 r1c2=1 r1c6<>1 r1c6=8 (r7c6<>8) (r2c4<>8) r2c5<>8 r2c7=8 r7c7<>8 r7c4=8 r7c4<>6 r23c4=6 r3c5<>6
r2c2=5 (r8c2<>5 r8c6=5 r1c6<>5) r2c2<>1 r1c2=1 r1c6<>1 r1c6=8 (r7c6<>8) (r2c4<>8) r2c5<>8 r2c7=8 r7c7<>8 r7c4=8 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r3c8<>6
r2c2=5 (r8c2<>5 r8c6=5 r1c6<>5) r2c2<>1 r1c2=1 r1c6<>1 r1c6=8 (r7c6<>8) (r2c4<>8) r2c5<>8 r2c7=8 r7c7<>8 r7c4=8 r7c4<>6 r7c1=6 r1c1<>6 r1c9=6 r3c9<>6
Forcing Net Contradiction in r1c1 => r6c2<>5
r6c2=5 (r1c2<>5) (r5c3<>5 r5c7=5 r1c7<>5) r8c2<>5 r8c6=5 r1c6<>5 r1c1=5 (r1c1<>6 r7c1=6 r7c1<>4) r3c3<>5 r3c3=6 r3c3<>4 r5c3=4 (r4c1<>4) (r5c1<>4) (r3c3<>4) r6c1<>4 r1c1=4
r6c2=5 (r1c2<>5) (r5c3<>5 r5c7=5 r1c7<>5) r8c2<>5 r8c6=5 r1c6<>5 r1c1=5
Forcing Net Contradiction in r8 => r1c1<>5
r1c1=5 (r6c1<>5 r6c8=5 r6c8<>4) r1c1<>6 r1c9=6 r4c9<>6 r4c8=6 r4c8<>4 r7c8=4 r8c7<>4 r8c2=4 r8c2<>7
r1c1=5 r1c1<>6 r7c1=6 r8c3<>6 r8c5=6 r8c5<>7
r1c1=5 r1c6<>5 r8c6=5 r8c6<>7
r1c1=5 (r1c1<>6 r1c9=6 r1c9<>8) (r9c1<>5) (r1c6<>5 r8c6=5 r9c4<>5) (r5c1<>5) r6c1<>5 r6c8=5 r5c7<>5 r5c3=5 r9c3<>5 r9c2=5 r9c2<>3 r9c9=3 r9c9<>8 r8c9=8 r8c9<>7
Forcing Chain Contradiction in r1c5 => r2c7<>1
r2c7=1 r2c2<>1 r1c2=1 r1c5<>1
r2c7=1 r2c2<>1 r1c2=1 r1c2<>5 r23c3=5 r5c3<>5 r5c3=4 r3c3<>4 r1c12=4 r1c5<>4
r2c7=1 r2c7<>8 r1c79=8 r1c5<>8
Forcing Net Verity => r2c2=1
r4c7=4 (r8c7<>4 r8c2=4 r8c2<>5) r4c7<>3 r4c9=3 r9c9<>3 r9c2=3 r9c2<>5 r1c2=5 r1c2<>1 r2c2=1
r4c8=4 r4c8<>6 r4c9=6 (r1c9<>6 r1c1=6 r3c3<>6 r8c3=6 r8c3<>9) r4c9<>3 r9c9=3 r9c9<>8 r9c3=8 r9c3<>9 r2c3=9 r2c2<>9 r2c2=1
r5c7=4 r5c3<>4 r5c3=5 (r2c3<>5) r3c3<>5 r1c2=5 r1c2<>1 r2c2=1
r6c8=4 r6c8<>5 r6c1=5 (r9c1<>5) (r5c1<>5) r5c3<>5 r5c3=4 r5c1<>4 r5c1=7 r9c1<>7 r9c1=9 (r8c3<>9) r9c3<>9 r2c3=9 r2c2<>9 r2c2=1
Forcing Net Verity => r1c2<>9
r4c7=4 (r8c7<>4 r8c2=4 r8c2<>5) r4c7<>3 r4c9=3 r9c9<>3 r9c2=3 r9c2<>5 r1c2=5 r1c2<>9
r4c8=4 r4c8<>6 r4c9=6 (r1c9<>6 r1c1=6 r3c3<>6 r8c3=6 r8c3<>9) r4c9<>3 r9c9=3 r9c9<>8 r9c3=8 r9c3<>9 r2c3=9 r1c2<>9
r5c7=4 r5c3<>4 r5c3=5 (r2c3<>5) r3c3<>5 r1c2=5 r1c2<>9
r6c8=4 r6c8<>5 r6c1=5 (r9c1<>5) (r5c1<>5) r5c3<>5 r5c3=4 r5c1<>4 r5c1=7 r9c1<>7 r9c1=9 (r8c3<>9) r9c3<>9 r2c3=9 r1c2<>9
Grouped Discontinuous Nice Loop: 5 r2c3 -5- r1c2 -4- r78c2 =4= r7c1 =6= r1c1 =9= r2c3 => r2c3<>5
Forcing Net Contradiction in c8 => r1c1<>4
r1c1=4 r1c1<>9 r2c3=9 r2c8<>9
r1c1=4 r1c1<>6 r1c9=6 r4c9<>6 r4c8=6 r4c8<>9
r1c1=4 (r6c1<>4) (r4c1<>4) (r1c1<>9 r2c3=9 r8c3<>9 r8c3=8 r8c7<>8) (r1c1<>9) r1c1<>6 r1c9=6 (r4c9<>6 r4c8=6 r4c8<>4) r1c9<>9 r1c7=9 r8c7<>9 r8c7=4 r4c7<>4 r4c4=4 (r6c4<>4) r6c5<>4 r6c8=4 r6c8<>9
r1c1=4 (r6c1<>4) (r4c1<>4) (r1c1<>9 r2c3=9 r8c3<>9 r8c3=8 r8c7<>8) (r1c1<>9) r1c1<>6 r1c9=6 (r4c9<>6 r4c8=6 r4c8<>4) r1c9<>9 r1c7=9 r8c7<>9 r8c7=4 r4c7<>4 r4c4=4 (r6c4<>4) r6c5<>4 r6c8=4 r6c8<>5 r6c1=5 (r5c1<>5) r5c3<>5 (r9c3=5 r9c1<>5) r5c3=4 r5c1<>4 r5c1=7 r9c1<>7 r9c1=9 r9c8<>9
Naked Pair: 6,9 in r1c1,r2c3 => r3c3<>6
Naked Pair: 4,5 in r35c3 => r9c3<>5
2-String Kite: 5 in r3c3,r6c8 (connected by r5c3,r6c1) => r3c8<>5
2-String Kite: 6 in r2c3,r7c4 (connected by r7c1,r8c3) => r2c4<>6
Forcing Chain Contradiction in c8 => r7c2<>4
r7c2=4 r7c2<>3 r7c7=3 r4c7<>3 r4c9=3 r4c9<>6 r4c8=6 r4c8<>4
r7c2=4 r7c1<>4 r456c1=4 r5c3<>4 r5c3=5 r5c7<>5 r6c8=5 r6c8<>4
r7c2=4 r7c8<>4
Forcing Chain Contradiction in r8c7 => r2c7<>9
r2c7=9 r2c3<>9 r2c3=6 r8c3<>6 r7c1=6 r7c1<>4 r8c2=4 r8c7<>4
r2c7=9 r2c3<>9 r2c3=6 r1c1<>6 r1c9=6 r1c9<>8 r12c7=8 r8c7<>8
r2c7=9 r8c7<>9
Forcing Chain Contradiction in r9 => r7c4<>7
r7c4=7 r7c4<>6 r7c1=6 r1c1<>6 r1c1=9 r9c1<>9
r7c4=7 r7c4<>6 r7c1=6 r1c1<>6 r1c1=9 r2c3<>9 r89c3=9 r9c2<>9
r7c4=7 r7c2<>7 r7c2=3 r7c7<>3 r9c9=3 r9c9<>8 r9c3=8 r9c3<>9
r7c4=7 r7c4<>6 r7c1=6 r1c1<>6 r1c1=9 r2c3<>9 r2c8=9 r9c8<>9
r7c4=7 r7c2<>7 r7c2=3 r7c7<>3 r9c9=3 r9c9<>9
Forcing Chain Contradiction in r8c7 => r8c3<>9
r8c3=9 r8c3<>6 r7c1=6 r7c1<>4 r8c2=4 r8c7<>4
r8c3=9 r8c3<>6 r2c3=6 r1c1<>6 r1c9=6 r1c9<>8 r12c7=8 r8c7<>8
r8c3=9 r8c7<>9
Forcing Chain Verity => r9c9<>9
r1c2=5 r1c2<>4 r8c2=4 r8c2<>9 r8c79=9 r9c9<>9
r8c2=5 r8c2<>9 r8c79=9 r9c9<>9
r9c2=5 r9c2<>3 r9c9=3 r9c9<>9
Forcing Net Verity => r6c2=2
r5c7=1 r5c9<>1 r5c9=2 r6c9<>2 r6c2=2
r5c7=2 r6c9<>2 r6c2=2
r5c7=4 (r6c8<>4 r7c8=4 r7c1<>4) (r5c1<>4) r5c3<>4 r5c3=5 (r6c1<>5 r6c8=5 r6c8<>9) r5c1<>5 r5c1=7 r7c1<>7 r7c1=6 (r7c1<>4 r8c2=4 r8c7<>4 r8c7=9 r4c7<>9) r1c1<>6 r1c1=9 (r6c1<>9) (r4c1<>9) r2c3<>9 (r2c8=9 r4c8<>9) r9c3=9 r9c3<>8 r9c9=8 r9c9<>3 r4c9=3 r4c9<>9 r4c2=9 r6c2<>9 r6c9=9 r6c9<>2 r6c2=2
r5c7=5 (r2c7<>5 r2c7=8 r2c4<>8) r6c8<>5 r2c8=5 r2c4<>5 r2c4=7 (r2c5<>7) r3c5<>7 r8c5=7 r8c6<>7 r8c6=8 r7c6<>8 r7c7=8 r2c7<>8 r2c7=5 (r5c7<>5) r3c7<>5 r3c3=5 (r3c4<>5) (r1c2<>5 r1c6=5 r8c6<>5) r5c3<>5 (r5c3=4 r6c1<>4 r7c1=4 r7c1<>6 r7c4=6 r7c4<>8) r5c1=5 r5c1<>7 r5c6=7 r5c6<>2 r4c6=2 r4c2<>2 r6c2=2
Discontinuous Nice Loop: 9 r4c7 -9- r4c2 -7- r7c2 -3- r7c7 =3= r4c7 => r4c7<>9
Discontinuous Nice Loop: 5 r1c7 -5- r1c2 -4- r8c2 =4= r8c7 =9= r1c7 => r1c7<>5
X-Wing: 5 r18 c26 => r9c2<>5
Naked Triple: 3,7,9 in r479c2 => r8c2<>7, r8c2<>9
Locked Candidates Type 1 (Pointing): 9 in b7 => r9c8<>9
Finned Swordfish: 9 r168 c179 fr6c8 => r4c9<>9
Grouped AIC: 7 7- r5c1 =7= r5c6 =1= r5c79 -1- r6c9 -9- r46c8 =9= r2c8 -9- r2c3 =9= r9c3 =8= r9c9 =3= r9c2 -3- r7c2 -7 => r4c2,r79c1<>7
Naked Single: r4c2=9
Hidden Pair: 5,9 in r26c8 => r2c8<>6, r2c8<>7, r6c8<>4
Locked Candidates Type 1 (Pointing): 7 in b3 => r3c45<>7
X-Wing: 6 r28 c35 => r3c5<>6
Naked Triple: 1,4,8 in r136c5 => r28c5<>8
XY-Chain: 1 1- r3c5 -4- r3c3 -5- r1c2 -4- r8c2 -5- r9c1 -9- r1c1 -6- r2c3 -9- r2c8 -5- r6c8 -9- r6c9 -1 => r3c9,r6c5<>1
Locked Candidates Type 2 (Claiming): 1 in c5 => r1c6,r3c4<>1
XY-Chain: 8 8- r1c6 -5- r1c2 -4- r8c2 -5- r9c1 -9- r1c1 -6- r2c3 -9- r2c8 -5- r2c7 -8 => r1c79,r2c4<>8
Hidden Single: r2c7=8
Locked Candidates Type 2 (Claiming): 8 in r7 => r8c6<>8
Naked Pair: 6,9 in r1c19 => r1c7<>9
Naked Single: r1c7=1
Hidden Single: r8c7=9
Hidden Single: r3c5=1
Hidden Single: r8c2=4
Naked Single: r1c2=5
Naked Single: r7c1=6
Naked Single: r1c6=8
Naked Single: r3c3=4
Naked Single: r1c1=9
Full House: r2c3=6
Naked Single: r8c3=8
Naked Single: r1c5=4
Full House: r1c9=6
Naked Single: r5c3=5
Full House: r9c3=9
Naked Single: r9c1=5
Naked Single: r2c5=7
Naked Single: r8c9=7
Naked Single: r6c5=8
Full House: r8c5=6
Full House: r8c6=5
Naked Single: r3c8=7
Naked Single: r2c4=5
Full House: r2c8=9
Full House: r3c4=6
Naked Single: r3c9=2
Full House: r3c7=5
Naked Single: r9c8=1
Naked Single: r6c1=4
Naked Single: r6c8=5
Naked Single: r4c9=3
Naked Single: r5c9=1
Naked Single: r7c8=4
Full House: r4c8=6
Naked Single: r9c4=7
Naked Single: r5c1=7
Full House: r4c1=8
Naked Single: r6c4=1
Full House: r6c9=9
Full House: r9c9=8
Full House: r7c7=3
Full House: r9c2=3
Full House: r7c2=7
Naked Single: r4c4=4
Full House: r7c4=8
Full House: r7c6=1
Naked Single: r5c6=2
Full House: r4c6=7
Full House: r4c7=2
Full House: r5c7=4
|
normal_sudoku_593 | 67.8.4...2.4.16....8.27.46.4..1.2...817469532..2..7.4.12.64...8.487.1...7.6.28..4 | 671834925254916873983275461439152687817469532562387149125643798348791256796528314 | normal_sudoku_593 | 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 | 9 | 6 7 . 8 . 4 . . .
2 . 4 . 1 6 . . .
. 8 . 2 7 . 4 6 .
4 . . 1 . 2 . . .
8 1 7 4 6 9 5 3 2
. . 2 . . 7 . 4 .
1 2 . 6 4 . . . 8
. 4 8 7 . 1 . . .
7 . 6 . 2 8 . . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 671834925254916873983275461439152687817469532562387149125643798348791256796528314 #1 Extreme (5032)
Grouped Discontinuous Nice Loop: 3 r1c7 =2= r8c7 =6= r8c9 =3= r789c7 -3- r1c7 => r1c7<>3
Finned Franken Swordfish: 3 c16b5 r368 fr4c5 fr7c6 => r8c5<>3
W-Wing: 5/3 in r3c6,r6c4 connected by 3 in r7c6,r9c4 => r2c4<>5
Sashimi Swordfish: 5 c146 r368 fr7c6 fr9c4 => r8c5<>5
Naked Single: r8c5=9
Hidden Single: r2c4=9
Forcing Chain Contradiction in r7c3 => r3c1<>3
r3c1=3 r3c6<>3 r7c6=3 r7c3<>3
r3c1=3 r8c1<>3 r8c1=5 r7c3<>5
r3c1=3 r3c1<>9 r13c3=9 r7c3<>9
Skyscraper: 3 in r8c1,r9c4 (connected by r6c14) => r9c2<>3
Grouped Discontinuous Nice Loop: 3 r2c7 -3- r2c2 =3= r46c2 -3- r6c1 =3= r8c1 -3- r8c9 =3= r789c7 -3- r2c7 => r2c7<>3
Locked Candidates Type 1 (Pointing): 3 in b3 => r8c9<>3
Discontinuous Nice Loop: 7 r4c8 -7- r4c9 =7= r2c9 -7- r2c7 -8- r2c8 =8= r4c8 => r4c8<>7
Grouped Discontinuous Nice Loop: 5 r7c8 -5- r7c6 -3- r7c3 =3= r8c1 =5= r8c89 -5- r7c8 => r7c8<>5
Turbot Fish: 5 r1c5 =5= r3c6 -5- r7c6 =5= r7c3 => r1c3<>5
Grouped Discontinuous Nice Loop: 3 r3c9 -3- r3c6 -5- r3c13 =5= r2c2 =3= r2c9 -3- r3c9 => r3c9<>3
Discontinuous Nice Loop: 5 r6c2 -5- r6c4 -3- r9c4 =3= r7c6 -3- r3c6 =3= r3c3 -3- r2c2 -5- r6c2 => r6c2<>5
Discontinuous Nice Loop: 5 r6c5 -5- r1c5 -3- r3c6 =3= r3c3 =1= r3c9 -1- r6c9 =1= r6c7 =8= r6c5 => r6c5<>5
Almost Locked Set XZ-Rule: A=r6c14 {359}, B=r2c2,r3c1 {359}, X=9, Z=3 => r6c2<>3
Forcing Chain Contradiction in r7c3 => r3c1=9
r3c1<>9 r3c1=5 r8c1<>5 r8c1=3 r7c3<>3
r3c1<>9 r3c1=5 r3c6<>5 r7c6=5 r7c3<>5
r3c1<>9 r13c3=9 r7c3<>9
Naked Pair: 3,5 in r6c14 => r6c5<>3
Naked Single: r6c5=8
Swordfish: 3 r689 c147 => r7c7<>3
Locked Pair: 7,9 in r7c78 => r7c3,r9c78<>9
Hidden Single: r4c3=9
Naked Single: r4c8=8
Naked Single: r6c2=6
Hidden Single: r9c2=9
Hidden Single: r2c7=8
X-Wing: 3 r37 c36 => r1c3<>3
Naked Single: r1c3=1
Hidden Single: r9c8=1
Naked Single: r9c7=3
Full House: r9c4=5
Full House: r6c4=3
Full House: r7c6=3
Full House: r4c5=5
Full House: r3c6=5
Full House: r1c5=3
Naked Single: r6c1=5
Full House: r4c2=3
Full House: r8c1=3
Full House: r7c3=5
Full House: r3c3=3
Full House: r3c9=1
Full House: r2c2=5
Naked Single: r6c9=9
Full House: r6c7=1
Naked Single: r2c8=7
Full House: r2c9=3
Naked Single: r1c9=5
Naked Single: r7c8=9
Full House: r7c7=7
Naked Single: r8c9=6
Full House: r4c9=7
Full House: r4c7=6
Naked Single: r1c8=2
Full House: r1c7=9
Full House: r8c7=2
Full House: r8c8=5
|
normal_sudoku_6878 | 28....19.3.9712.587519..2.38.....9..1.267.3....5.....292....8.1.18...5..5..8.1..9 | 286354197349712658751968243874123965192675384635489712923546871418297536567831429 | normal_sudoku_6878 | 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 | 9 | 2 8 . . . . 1 9 .
3 . 9 7 1 2 . 5 8
7 5 1 9 . . 2 . 3
8 . . . . . 9 . .
1 . 2 6 7 . 3 . .
. . 5 . . . . . 2
9 2 . . . . 8 . 1
. 1 8 . . . 5 . .
5 . . 8 . 1 . . 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 286354197349712658751968243874123965192675384635489712923546871418297536567831429 #1 Hard (1206)
Hidden Single: r1c9=7
Naked Pair: 4,6 in r8c19 => r8c4568<>4, r8c568<>6
Skyscraper: 6 in r4c9,r6c1 (connected by r8c19) => r4c23,r6c78<>6
Turbot Fish: 6 r1c3 =6= r2c2 -6- r2c7 =6= r9c7 => r9c3<>6
Empty Rectangle: 6 in b8 (r17c3) => r1c5<>6
W-Wing: 4/6 in r2c2,r8c1 connected by 6 in r6c12 => r9c2<>4
W-Wing: 4/6 in r3c8,r8c9 connected by 6 in r4c89 => r79c8<>4
Turbot Fish: 4 r6c1 =4= r8c1 -4- r8c9 =4= r9c7 => r6c7<>4
Naked Single: r6c7=7
Naked Pair: 4,6 in r8c9,r9c7 => r79c8<>6
Remote Pair: 4/6 r2c2 -6- r2c7 -4- r9c7 -6- r8c9 -4- r8c1 -6- r6c1 => r456c2<>4, r6c2<>6
Naked Single: r5c2=9
Naked Single: r6c2=3
Naked Single: r4c2=7
Naked Single: r4c3=4
Full House: r6c1=6
Full House: r8c1=4
Naked Single: r9c2=6
Full House: r2c2=4
Full House: r1c3=6
Full House: r2c7=6
Full House: r9c7=4
Full House: r3c8=4
Naked Single: r8c9=6
Naked Single: r5c8=8
Naked Single: r4c9=5
Full House: r5c9=4
Full House: r5c6=5
Naked Single: r6c8=1
Full House: r4c8=6
Naked Single: r4c6=3
Naked Single: r6c4=4
Naked Single: r1c6=4
Naked Single: r4c5=2
Full House: r4c4=1
Naked Single: r9c5=3
Naked Single: r1c5=5
Full House: r1c4=3
Naked Single: r7c4=5
Full House: r8c4=2
Naked Single: r8c5=9
Naked Single: r9c3=7
Full House: r7c3=3
Full House: r9c8=2
Naked Single: r6c5=8
Full House: r6c6=9
Naked Single: r8c6=7
Full House: r8c8=3
Full House: r7c8=7
Naked Single: r3c5=6
Full House: r3c6=8
Full House: r7c6=6
Full House: r7c5=4
|
normal_sudoku_918 | 5469.7.8.217..8.9.893..5....8.5...7997..8..5462...981.168.925....9.....8..28..9.. | 546927381217638495893145762384561279971283654625479813168392547439756128752814936 | normal_sudoku_918 | 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 | 9 | 5 4 6 9 . 7 . 8 .
2 1 7 . . 8 . 9 .
8 9 3 . . 5 . . .
. 8 . 5 . . . 7 9
9 7 . . 8 . . 5 4
6 2 . . . 9 8 1 .
1 6 8 . 9 2 5 . .
. . 9 . . . . . 8
. . 2 8 . . 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 546927381217638495893145762384561279971283654625479813168392547439756128752814936 #1 Medium (494)
Naked Single: r5c3=1
Naked Single: r6c9=3
Naked Single: r4c3=4
Full House: r6c3=5
Full House: r4c1=3
Naked Single: r7c9=7
Hidden Single: r2c9=5
Hidden Single: r3c7=7
Locked Candidates Type 1 (Pointing): 3 in b3 => r8c7<>3
Locked Candidates Type 1 (Pointing): 2 in b6 => r18c7<>2
Hidden Single: r8c8=2
Locked Candidates Type 1 (Pointing): 6 in b6 => r28c7<>6
Locked Candidates Type 1 (Pointing): 6 in b3 => r3c45<>6
Locked Candidates Type 1 (Pointing): 6 in b9 => r9c56<>6
Locked Candidates Type 2 (Claiming): 4 in c6 => r78c4,r89c5<>4
Naked Single: r7c4=3
Full House: r7c8=4
Naked Single: r3c8=6
Full House: r9c8=3
Naked Single: r8c7=1
Full House: r9c9=6
Naked Single: r9c2=5
Full House: r8c2=3
Naked Single: r1c7=3
Naked Single: r2c7=4
Naked Single: r2c4=6
Full House: r2c5=3
Naked Single: r5c4=2
Naked Single: r8c4=7
Naked Single: r5c7=6
Full House: r4c7=2
Full House: r5c6=3
Naked Single: r6c4=4
Full House: r3c4=1
Full House: r6c5=7
Naked Single: r8c1=4
Full House: r9c1=7
Naked Single: r9c5=1
Full House: r9c6=4
Naked Single: r1c5=2
Full House: r1c9=1
Full House: r3c9=2
Full House: r3c5=4
Naked Single: r8c6=6
Full House: r4c6=1
Full House: r4c5=6
Full House: r8c5=5
|
normal_sudoku_2144 | .9341..27..7.....15.1..79...75..3...3168.42....9.5.3..138....4675264....964.387.2 | 893415627627389451541267983475923168316874295289156374138792546752641839964538712 | normal_sudoku_2144 | 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 | 9 | . 9 3 4 1 . . 2 7
. . 7 . . . . . 1
5 . 1 . . 7 9 . .
. 7 5 . . 3 . . .
3 1 6 8 . 4 2 . .
. . 9 . 5 . 3 . .
1 3 8 . . . . 4 6
7 5 2 6 4 . . . .
9 6 4 . 3 8 7 . 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 893415627627389451541267983475923168316874295289156374138792546752641839964538712 #1 Easy (160)
Naked Single: r7c7=5
Naked Single: r9c8=1
Full House: r9c4=5
Naked Single: r8c7=8
Naked Single: r1c7=6
Naked Single: r1c1=8
Full House: r1c6=5
Naked Single: r2c7=4
Full House: r4c7=1
Naked Single: r2c2=2
Naked Single: r2c1=6
Full House: r3c2=4
Full House: r6c2=8
Naked Single: r2c6=9
Naked Single: r6c9=4
Naked Single: r2c4=3
Naked Single: r2c5=8
Full House: r2c8=5
Naked Single: r7c6=2
Naked Single: r8c6=1
Full House: r6c6=6
Naked Single: r6c1=2
Full House: r4c1=4
Naked Single: r3c4=2
Full House: r3c5=6
Naked Single: r6c8=7
Full House: r6c4=1
Naked Single: r4c4=9
Full House: r7c4=7
Full House: r7c5=9
Naked Single: r5c8=9
Naked Single: r4c5=2
Full House: r5c5=7
Full House: r5c9=5
Naked Single: r4c9=8
Full House: r4c8=6
Naked Single: r8c8=3
Full House: r3c8=8
Full House: r3c9=3
Full House: r8c9=9
|
normal_sudoku_2223 | ....6....8..4.2..6...7.82...9.2...3.4...856....8....52.1.5.......3..9..12...4.7.. | 342961587857432916169758243695217834421385679738694152914576328573829461286143795 | normal_sudoku_2223 | 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 | 9 | . . . . 6 . . . .
8 . . 4 . 2 . . 6
. . . 7 . 8 2 . .
. 9 . 2 . . . 3 .
4 . . . 8 5 6 . .
. . 8 . . . . 5 2
. 1 . 5 . . . . .
. . 3 . . 9 . . 1
2 . . . 4 . 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 342961587857432916169758243695217834421385679738694152914576328573829461286143795 #1 Extreme (17808)
Locked Candidates Type 2 (Claiming): 8 in r7 => r8c78,r9c89<>8
Hidden Rectangle: 6/8 in r8c24,r9c24 => r9c2<>6
Grouped Discontinuous Nice Loop: 1 r1c8 -1- r1c46 =1= r23c5 -1- r4c5 -7- r8c5 -2- r8c8 =2= r7c8 =8= r1c8 => r1c8<>1
Forcing Chain Contradiction in r5c4 => r6c6<>3
r6c6=3 r1c6<>3 r1c6=1 r9c6<>1 r9c4=1 r5c4<>1
r6c6=3 r5c4<>3
r6c6=3 r6c6<>4 r6c7=4 r6c7<>9 r5c89=9 r5c4<>9
Forcing Net Contradiction in r5c4 => r1c4<>3
r1c4=3 (r5c4<>3 r5c2=3 r6c2<>3 r6c5=3 r6c5<>1) r1c6<>3 r1c6=1 (r6c6<>1) r9c6<>1 r9c4=1 r6c4<>1 r6c7=1 r6c7<>9 r5c89=9 r5c4<>9
r1c4=3 (r5c4<>3) r1c6<>3 r1c6=1 r9c6<>1 r9c4=1 r5c4<>1 r5c4=9
Forcing Net Contradiction in r2c7 => r1c3<>9
r1c3=9 (r1c4<>9 r1c4=1 r1c7<>1) (r1c4<>9 r1c4=1 r5c4<>1) r1c3<>2 r1c2=2 r5c2<>2 r5c3=2 r5c3<>1 r5c8=1 (r4c7<>1) r6c7<>1 r2c7=1
r1c3=9 (r1c7<>9) (r3c1<>9 r7c1=9 r7c7<>9) r1c3<>2 r1c2=2 r5c2<>2 r5c3=2 r5c3<>1 r5c8=1 (r5c8<>9) (r4c7<>1) r6c7<>1 r2c7=1 r2c7<>9 r6c7=9 r5c9<>9 r5c4=9 (r5c4<>3 r5c2=3 r2c2<>3) r1c4<>9 r1c4=1 (r1c7<>1) (r5c4<>1) r1c6<>1 r1c6=3 r2c5<>3 r2c7=3
Forcing Net Contradiction in r7c7 => r1c7<>1
r1c7=1 (r1c4<>1 r1c4=9 r5c4<>9) (r2c8<>1) r3c8<>1 r5c8=1 (r5c8<>7) r5c8<>9 r5c9=9 r5c9<>7 r4c9=7 r4c5<>7 r4c5=1 r23c5<>1 r1c46=1 r1c7<>1
Forcing Chain Contradiction in r5 => r2c3<>1
r2c3=1 r5c3<>1
r2c3=1 r1c13<>1 r1c46=1 r23c5<>1 r46c5=1 r5c4<>1
r2c3=1 r2c7<>1 r46c7=1 r5c8<>1
Forcing Chain Contradiction in r1c7 => r6c6<>1
r6c6=1 r1c6<>1 r1c6=3 r1c7<>3
r6c6=1 r6c6<>4 r6c7=4 r1c7<>4
r6c6=1 r6c6<>4 r6c7=4 r8c7<>4 r8c7=5 r1c7<>5
r6c6=1 r4c5<>1 r4c5=7 r8c5<>7 r8c5=2 r8c8<>2 r7c8=2 r7c8<>8 r1c8=8 r1c7<>8
r6c6=1 r9c6<>1 r9c4=1 r1c4<>1 r1c4=9 r1c7<>9
Forcing Net Verity => r1c8<>9
r2c5=3 r1c6<>3 r1c6=1 r1c4<>1 r1c4=9 r1c8<>9
r3c5=3 r1c6<>3 r1c6=1 r1c4<>1 r1c4=9 r1c8<>9
r6c5=3 (r5c4<>3 r5c2=3 r2c2<>3 r2c7=3 r2c7<>1) (r6c5<>9) (r5c4<>3) r6c4<>3 r9c4=3 (r9c4<>6) r9c4<>8 r9c2=8 r8c2<>8 r8c4=8 r8c4<>6 r6c4=6 r6c4<>9 r6c7=9 r6c7<>1 r4c7=1 r4c5<>1 r4c5=7 r8c5<>7 r8c5=2 r7c5<>2 r7c8=2 r7c8<>8 r1c8=8 r1c8<>9
r7c5=3 r7c5<>2 r7c8=2 r7c8<>8 r1c8=8 r1c8<>9
Forcing Net Contradiction in r2c7 => r4c6<>1
r4c6=1 (r1c6<>1 r1c6=3 r1c7<>3) (r1c6<>1 r1c6=3 r9c6<>3) r9c6<>1 r9c4=1 r9c4<>3 r9c9=3 r7c7<>3 r2c7=3
r4c6=1 (r9c6<>1) r1c6<>1 r1c6=3 r9c6<>3 r9c6=6 (r9c8<>6 r9c8=9 r7c7<>9) r9c6<>1 r9c4=1 r1c4<>1 r1c4=9 (r1c7<>9) (r2c5<>9) r3c5<>9 r6c5=9 r6c7<>9 r2c7=9
Forcing Net Contradiction in c7 => r5c4<>1
r5c4=1 r1c4<>1 r1c4=9 r1c7<>9
r5c4=1 (r5c4<>3 r5c2=3 r2c2<>3) r9c4<>1 r9c6=1 r1c6<>1 r1c6=3 r2c5<>3 r2c7=3 r2c7<>9
r5c4=1 r1c4<>1 r1c4=9 (r2c5<>9) r3c5<>9 r6c5=9 r6c7<>9
r5c4=1 (r1c4<>1 r1c4=9 r1c1<>9) (r5c4<>3 r5c2=3 r6c1<>3) r9c4<>1 r9c6=1 r1c6<>1 r1c6=3 r1c1<>3 r3c1=3 r3c1<>9 r7c1=9 r7c7<>9
Forcing Chain Contradiction in r2 => r5c4=3
r5c4<>3 r5c2=3 r2c2<>3
r5c4<>3 r5c4=9 r1c4<>9 r1c4=1 r1c6<>1 r1c6=3 r2c5<>3
r5c4<>3 r5c2=3 r5c2<>2 r5c3=2 r5c3<>1 r5c8=1 r46c7<>1 r2c7=1 r2c7<>3
Locked Candidates Type 1 (Pointing): 9 in b5 => r6c7<>9
Hidden Rectangle: 2/7 in r1c23,r5c23 => r1c3<>7
Grouped Discontinuous Nice Loop: 1 r1c3 -1- r1c46 =1= r23c5 -1- r4c5 -7- r4c9 =7= r5c89 -7- r5c2 -2- r5c3 =2= r1c3 => r1c3<>1
Almost Locked Set XY-Wing: A=r4c5 {17}, B=r5c23,r6c12 {12367}, C=r6c4567 {14679}, X,Y=6,7, Z=1 => r4c13<>1
Forcing Chain Contradiction in r1c7 => r1c1<>1
r1c1=1 r1c6<>1 r1c6=3 r1c7<>3
r1c1=1 r1c46<>1 r23c5=1 r4c5<>1 r4c7=1 r6c7<>1 r6c7=4 r1c7<>4
r1c1=1 r1c6<>1 r1c6=3 r9c6<>3 r9c9=3 r9c9<>5 r8c7=5 r1c7<>5
r1c1=1 r1c6<>1 r1c6=3 r23c5<>3 r7c5=3 r7c5<>2 r7c8=2 r7c8<>8 r1c8=8 r1c7<>8
r1c1=1 r1c4<>1 r1c4=9 r1c7<>9
Locked Candidates Type 1 (Pointing): 1 in b1 => r3c58<>1
Locked Candidates Type 1 (Pointing): 1 in b3 => r2c5<>1
Locked Candidates Type 2 (Claiming): 1 in c5 => r6c4<>1
Almost Locked Set XY-Wing: A=r6c4 {69}, B=r1478c1 {35679}, C=r1c46 {139}, X,Y=3,9, Z=6 => r6c1<>6
Forcing Chain Contradiction in r2c2 => r1c3<>5
r1c3=5 r1c3<>2 r5c3=2 r5c3<>1 r6c1=1 r6c1<>3 r6c2=3 r2c2<>3
r1c3=5 r2c2<>5
r1c3=5 r1c3<>2 r1c2=2 r5c2<>2 r5c2=7 r2c2<>7
Forcing Chain Contradiction in c1 => r1c8<>4
r1c8=4 r1c8<>8 r7c8=8 r7c8<>2 r7c5=2 r7c5<>3 r23c5=3 r1c6<>3 r1c6=1 r1c4<>1 r1c4=9 r1c1<>9
r1c8=4 r3c8<>4 r3c8=9 r3c1<>9
r1c8=4 r3c8<>4 r3c8=9 r12c7<>9 r7c7=9 r7c1<>9
Forcing Chain Contradiction in c1 => r1c9<>9
r1c9=9 r1c1<>9
r1c9=9 r5c9<>9 r5c8=9 r5c8<>1 r5c3=1 r3c3<>1 r3c1=1 r3c1<>9
r1c9=9 r12c7<>9 r7c7=9 r7c1<>9
Forcing Chain Contradiction in r2 => r3c1<>5
r3c1=5 r3c1<>1 r6c1=1 r6c1<>3 r6c2=3 r2c2<>3
r3c1=5 r3c5<>5 r2c5=5 r2c5<>3
r3c1=5 r3c1<>1 r3c3=1 r5c3<>1 r5c8=1 r2c8<>1 r2c7=1 r2c7<>3
Forcing Chain Contradiction in r9 => r3c3<>4
r3c3=4 r7c3<>4 r8c2=4 r8c2<>8 r9c2=8 r9c2<>5
r3c3=4 r3c8<>4 r3c8=9 r12c7<>9 r7c7=9 r7c13<>9 r9c3=9 r9c3<>5
r3c3=4 r3c8<>4 r78c8=4 r8c7<>4 r8c7=5 r9c9<>5
Discontinuous Nice Loop: 4 r7c7 -4- r7c3 =4= r1c3 =2= r5c3 =1= r5c8 -1- r6c7 -4- r7c7 => r7c7<>4
Forcing Chain Contradiction in r8 => r1c7<>8
r1c7=8 r4c7<>8 r4c9=8 r4c9<>7 r5c89=7 r5c2<>7 r5c2=2 r5c3<>2 r1c3=2 r1c3<>4 r7c3=4 r8c2<>4
r1c7=8 r4c7<>8 r4c9=8 r4c9<>4 r46c7=4 r8c7<>4
r1c7=8 r1c8<>8 r7c8=8 r7c8<>2 r8c8=2 r8c8<>4
Forcing Chain Contradiction in r8 => r4c5=1
r4c5<>1 r4c7=1 r5c8<>1 r5c3=1 r5c3<>2 r1c3=2 r1c3<>4 r7c3=4 r8c2<>4
r4c5<>1 r4c7=1 r6c7<>1 r6c7=4 r8c7<>4
r4c5<>1 r4c7=1 r4c7<>8 r7c7=8 r7c7<>9 r12c7=9 r3c8<>9 r3c8=4 r8c8<>4
Forcing Chain Contradiction in r8 => r4c7=8
r4c7<>8 r4c7=4 r6c7<>4 r6c7=1 r6c1<>1 r5c3=1 r5c3<>2 r1c3=2 r1c3<>4 r7c3=4 r8c2<>4
r4c7<>8 r4c7=4 r8c7<>4
r4c7<>8 r7c7=8 r7c7<>9 r12c7=9 r3c8<>9 r3c8=4 r8c8<>4
Discontinuous Nice Loop: 9 r1c7 -9- r1c4 -1- r1c6 -3- r9c6 =3= r9c9 -3- r7c7 -9- r1c7 => r1c7<>9
Empty Rectangle: 9 in b7 (r27c7) => r2c3<>9
Discontinuous Nice Loop: 9 r7c3 -9- r7c7 =9= r2c7 =1= r2c8 -1- r5c8 =1= r5c3 =2= r1c3 =4= r7c3 => r7c3<>9
Discontinuous Nice Loop: 6 r9c4 -6- r9c8 -9- r9c3 =9= r3c3 -9- r1c1 =9= r1c4 =1= r9c4 => r9c4<>6
Discontinuous Nice Loop: 6 r9c6 -6- r9c8 -9- r7c7 -3- r9c9 =3= r9c6 => r9c6<>6
Naked Pair: 1,3 in r19c6 => r7c6<>3
Discontinuous Nice Loop: 6 r7c3 -6- r7c6 =6= r8c4 =8= r8c2 =4= r7c3 => r7c3<>6
Discontinuous Nice Loop: 6 r7c8 -6- r7c6 -7- r8c5 -2- r8c8 =2= r7c8 => r7c8<>6
Grouped Discontinuous Nice Loop: 4 r7c8 -4- r3c8 -9- r2c78 =9= r2c5 -9- r6c5 -7- r8c5 -2- r8c8 =2= r7c8 => r7c8<>4
Almost Locked Set XZ-Rule: A=r1c2346789 {12345789}, B=r2c235 {3579}, X=9, Z=7 => r1c1<>7
Grouped AIC: 2 2- r1c3 -4- r7c3 -7- r2c3 =7= r12c2 -7- r5c2 -2 => r1c2,r5c3<>2
Hidden Single: r1c3=2
Hidden Single: r5c2=2
Hidden Single: r7c3=4
AIC: 5/9 9- r9c3 =9= r3c3 -9- r3c8 -4- r8c8 =4= r8c7 =5= r9c9 -5 => r9c3<>5, r9c9<>9
Discontinuous Nice Loop: 3 r1c2 -3- r1c6 =3= r9c6 -3- r9c9 -5- r8c7 -4- r8c8 =4= r3c8 -4- r3c2 =4= r1c2 => r1c2<>3
Discontinuous Nice Loop: 5 r1c2 -5- r9c2 =5= r9c9 -5- r8c7 -4- r8c8 =4= r3c8 -4- r3c2 =4= r1c2 => r1c2<>5
Discontinuous Nice Loop: 6 r3c1 -6- r7c1 =6= r7c6 -6- r8c4 -8- r8c2 =8= r9c2 =5= r9c9 -5- r8c7 -4- r6c7 -1- r6c1 =1= r3c1 => r3c1<>6
Discontinuous Nice Loop: 4 r1c9 -4- r1c2 =4= r3c2 =6= r3c3 =1= r3c1 -1- r6c1 =1= r6c7 =4= r4c9 -4- r1c9 => r1c9<>4
Discontinuous Nice Loop: 9 r2c8 -9- r3c8 -4- r3c9 =4= r4c9 -4- r6c7 -1- r2c7 =1= r2c8 => r2c8<>9
Discontinuous Nice Loop: 3 r1c7 -3- r1c6 -1- r1c4 -9- r2c5 =9= r2c7 -9- r7c7 -3- r1c7 => r1c7<>3
Naked Pair: 4,5 in r18c7 => r2c7<>5, r6c7<>4
Naked Single: r6c7=1
Hidden Single: r6c6=4
Hidden Single: r4c9=4
Hidden Single: r2c8=1
Hidden Single: r5c3=1
Hidden Single: r3c1=1
Locked Candidates Type 1 (Pointing): 7 in b3 => r1c2<>7
Naked Single: r1c2=4
Naked Single: r1c7=5
Naked Single: r8c7=4
Hidden Single: r3c8=4
Hidden Single: r9c9=5
Naked Single: r9c2=8
Naked Single: r9c4=1
Naked Single: r1c4=9
Naked Single: r9c6=3
Naked Single: r1c1=3
Naked Single: r6c4=6
Full House: r8c4=8
Naked Single: r1c6=1
Naked Single: r6c1=7
Naked Single: r4c6=7
Full House: r6c5=9
Full House: r6c2=3
Full House: r7c6=6
Naked Single: r7c1=9
Naked Single: r7c7=3
Full House: r2c7=9
Naked Single: r9c3=6
Full House: r9c8=9
Naked Single: r7c9=8
Naked Single: r3c9=3
Naked Single: r4c3=5
Full House: r4c1=6
Full House: r8c1=5
Full House: r8c2=7
Naked Single: r5c8=7
Full House: r5c9=9
Full House: r1c9=7
Full House: r1c8=8
Naked Single: r7c8=2
Full House: r7c5=7
Full House: r8c5=2
Full House: r8c8=6
Naked Single: r3c5=5
Full House: r2c5=3
Naked Single: r2c3=7
Full House: r3c3=9
Full House: r2c2=5
Full House: r3c2=6
|
normal_sudoku_2981 | ..82....642.5.63.7.6...4...2.6..8...853.4..2..14.25...6358.1...14..62..5.8245.... | 578213496429586317361974258296138574853749621714625839635891742147362985982457163 | normal_sudoku_2981 | 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 | 9 | . . 8 2 . . . . 6
4 2 . 5 . 6 3 . 7
. 6 . . . 4 . . .
2 . 6 . . 8 . . .
8 5 3 . 4 . . 2 .
. 1 4 . 2 5 . . .
6 3 5 8 . 1 . . .
1 4 . . 6 2 . . 5
. 8 2 4 5 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 578213496429586317361974258296138574853749621714625839635891742147362985982457163 #1 Extreme (2696)
Naked Pair: 7,9 in r69c1 => r13c1<>7, r13c1<>9
Empty Rectangle: 3 in b5 (r8c48) => r4c8<>3
Finned Franken Swordfish: 9 r27b7 c358 fr7c7 fr7c9 fr9c1 => r9c8<>9
Forcing Chain Contradiction in r1c6 => r4c5<>7
r4c5=7 r4c5<>3 r13c5=3 r1c6<>3
r4c5=7 r4c2<>7 r1c2=7 r1c6<>7
r4c5=7 r5c6<>7 r5c6=9 r1c6<>9
Forcing Chain Contradiction in r8c4 => r1c6<>7
r1c6=7 r1c6<>3 r9c6=3 r8c4<>3
r1c6=7 r5c6<>7 r456c4=7 r8c4<>7
r1c6=7 r1c2<>7 r1c2=9 r23c3<>9 r8c3=9 r8c4<>9
Skyscraper: 7 in r5c6,r6c1 (connected by r9c16) => r6c4<>7
W-Wing: 9/7 in r4c2,r7c5 connected by 7 in r1c25 => r4c5<>9
Discontinuous Nice Loop: 7 r8c4 -7- r8c3 =7= r3c3 -7- r1c2 -9- r1c6 -3- r9c6 =3= r8c4 => r8c4<>7
Multi Colors 2: 7 (r1c2,r6c1,r8c3) / (r1c5,r3c3,r4c2,r9c1), (r5c6,r7c5) / (r9c6) => r1c5,r3c3,r4c2,r9c1<>7
Naked Single: r4c2=9
Full House: r1c2=7
Full House: r6c1=7
Naked Single: r9c1=9
Full House: r8c3=7
XY-Wing: 3/7/9 in r19c6,r7c5 => r123c5<>9
Hidden Single: r7c5=9
Naked Single: r8c4=3
Full House: r9c6=7
Naked Single: r5c6=9
Full House: r1c6=3
Naked Single: r5c9=1
Naked Single: r6c4=6
Naked Single: r1c1=5
Full House: r3c1=3
Naked Single: r1c5=1
Naked Single: r9c9=3
Naked Single: r5c4=7
Full House: r5c7=6
Naked Single: r2c5=8
Naked Single: r4c5=3
Full House: r4c4=1
Full House: r3c4=9
Full House: r3c5=7
Naked Single: r4c9=4
Naked Single: r9c7=1
Full House: r9c8=6
Naked Single: r3c3=1
Full House: r2c3=9
Full House: r2c8=1
Naked Single: r7c9=2
Naked Single: r3c9=8
Full House: r6c9=9
Naked Single: r3c8=5
Full House: r3c7=2
Naked Single: r6c7=8
Full House: r6c8=3
Naked Single: r4c8=7
Full House: r4c7=5
Naked Single: r8c7=9
Full House: r8c8=8
Naked Single: r7c8=4
Full House: r1c8=9
Full House: r1c7=4
Full House: r7c7=7
|
normal_sudoku_1917 | 1...9..5.7.4..86.998........41.73...5.38214.787..6.312..8..2576...7......57...2.. | 136294758724518639985637124241973865563821497879465312398142576412756983657389241 | normal_sudoku_1917 | 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 | 9 | 1 . . . 9 . . 5 .
7 . 4 . . 8 6 . 9
9 8 . . . . . . .
. 4 1 . 7 3 . . .
5 . 3 8 2 1 4 . 7
8 7 . . 6 . 3 1 2
. . 8 . . 2 5 7 6
. . . 7 . . . . .
. 5 7 . . . 2 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 136294758724518639985637124241973865563821497879465312398142576412756983657389241 #1 Easy (240)
Naked Single: r6c3=9
Naked Single: r5c2=6
Full House: r4c1=2
Full House: r5c8=9
Naked Single: r4c7=8
Naked Single: r1c7=7
Naked Single: r4c8=6
Full House: r4c9=5
Full House: r4c4=9
Naked Single: r3c7=1
Full House: r8c7=9
Hidden Single: r3c3=5
Hidden Single: r1c9=8
Hidden Single: r3c6=7
Hidden Single: r7c2=9
Hidden Single: r9c6=9
Hidden Single: r1c3=6
Full House: r8c3=2
Naked Single: r1c6=4
Naked Single: r3c5=3
Naked Single: r6c6=5
Full House: r6c4=4
Full House: r8c6=6
Naked Single: r1c4=2
Full House: r1c2=3
Full House: r2c2=2
Full House: r8c2=1
Naked Single: r3c9=4
Naked Single: r3c4=6
Full House: r3c8=2
Full House: r2c8=3
Naked Single: r8c9=3
Full House: r9c9=1
Naked Single: r8c1=4
Naked Single: r9c4=3
Naked Single: r7c1=3
Full House: r9c1=6
Naked Single: r8c8=8
Full House: r8c5=5
Full House: r9c8=4
Full House: r9c5=8
Naked Single: r7c4=1
Full House: r2c4=5
Full House: r2c5=1
Full House: r7c5=4
|
normal_sudoku_2626 | 1..975.2697......8..6.3.9.....6..59...4.9...3.9...7...425....19861759234..94216.. | 148975326973246158256138947387614592614592873592387461425863719861759234739421685 | normal_sudoku_2626 | 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 | 9 | 1 . . 9 7 5 . 2 6
9 7 . . . . . . 8
. . 6 . 3 . 9 . .
. . . 6 . . 5 9 .
. . 4 . 9 . . . 3
. 9 . . . 7 . . .
4 2 5 . . . . 1 9
8 6 1 7 5 9 2 3 4
. . 9 4 2 1 6 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 148975326973246158256138947387614592614592873592387461425863719861759234739421685 #1 Easy (198)
Naked Single: r9c2=3
Full House: r9c1=7
Naked Single: r9c9=5
Full House: r9c8=8
Full House: r7c7=7
Hidden Single: r2c8=5
Hidden Single: r4c3=7
Hidden Single: r5c8=7
Naked Single: r3c8=4
Full House: r6c8=6
Naked Single: r1c7=3
Naked Single: r1c3=8
Full House: r1c2=4
Naked Single: r2c7=1
Full House: r3c9=7
Naked Single: r3c2=5
Naked Single: r2c4=2
Naked Single: r5c7=8
Full House: r6c7=4
Naked Single: r3c1=2
Full House: r2c3=3
Full House: r6c3=2
Naked Single: r3c6=8
Full House: r3c4=1
Naked Single: r5c2=1
Full House: r4c2=8
Naked Single: r5c6=2
Naked Single: r4c1=3
Naked Single: r6c9=1
Full House: r4c9=2
Naked Single: r5c4=5
Full House: r5c1=6
Full House: r6c1=5
Naked Single: r4c6=4
Full House: r4c5=1
Naked Single: r6c5=8
Full House: r6c4=3
Full House: r7c4=8
Naked Single: r2c6=6
Full House: r2c5=4
Full House: r7c5=6
Full House: r7c6=3
|
normal_sudoku_436 | ...6.9..1.19.2367.....1.3..26.5.....958364712.7.29.5.6.9..3.257735..2.6.82.....43 | 387659421519423678642718395261587934958364712473291586194836257735142869826975143 | normal_sudoku_436 | 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 | 9 | . . . 6 . 9 . . 1
. 1 9 . 2 3 6 7 .
. . . . 1 . 3 . .
2 6 . 5 . . . . .
9 5 8 3 6 4 7 1 2
. 7 . 2 9 . 5 . 6
. 9 . . 3 . 2 5 7
7 3 5 . . 2 . 6 .
8 2 . . . . . 4 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 387659421519423678642718395261587934958364712473291586194836257735142869826975143 #1 Medium (416)
Locked Candidates Type 1 (Pointing): 1 in b5 => r79c6<>1
Locked Candidates Type 1 (Pointing): 4 in b6 => r4c3<>4
Locked Candidates Type 1 (Pointing): 4 in b7 => r7c4<>4
Locked Candidates Type 1 (Pointing): 8 in b9 => r8c45<>8
Naked Single: r8c5=4
Locked Candidates Type 2 (Claiming): 4 in c2 => r1c13,r23c1,r3c3<>4
Naked Single: r2c1=5
Naked Single: r1c1=3
Naked Single: r3c1=6
Hidden Single: r1c5=5
Naked Single: r9c5=7
Full House: r4c5=8
Naked Single: r6c6=1
Full House: r4c6=7
Naked Single: r6c1=4
Full House: r7c1=1
Naked Single: r3c6=8
Naked Single: r6c3=3
Full House: r4c3=1
Full House: r6c8=8
Naked Single: r7c4=8
Naked Single: r9c3=6
Full House: r7c3=4
Full House: r7c6=6
Full House: r9c6=5
Naked Single: r2c4=4
Full House: r2c9=8
Full House: r3c4=7
Naked Single: r3c2=4
Full House: r1c2=8
Naked Single: r1c8=2
Naked Single: r1c7=4
Full House: r1c3=7
Full House: r3c3=2
Naked Single: r8c9=9
Naked Single: r3c8=9
Full House: r3c9=5
Full House: r4c9=4
Full House: r4c8=3
Full House: r4c7=9
Naked Single: r8c4=1
Full House: r8c7=8
Full House: r9c7=1
Full House: r9c4=9
|
normal_sudoku_6349 | 54....38..3184..758.7...4.1.1.....3.38...9.577.5.....44....75...5.69.748.7...4..3 | 542716389931842675867953421619475832384269157725138964498327516253691748176584293 | normal_sudoku_6349 | 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 | 9 | 5 4 . . . . 3 8 .
. 3 1 8 4 . . 7 5
8 . 7 . . . 4 . 1
. 1 . . . . . 3 .
3 8 . . . 9 . 5 7
7 . 5 . . . . . 4
4 . . . . 7 5 . .
. 5 . 6 9 . 7 4 8
. 7 . . . 4 . . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 542716389931842675867953421619475832384269157725138964498327516253691748176584293 #1 Extreme (5696)
Locked Candidates Type 1 (Pointing): 8 in b8 => r46c5<>8
Forcing Net Contradiction in c3 => r3c5<>6
r3c5=6 (r1c5<>6) (r1c6<>6) r2c6<>6 r2c6=2 (r1c4<>2) (r1c5<>2) r1c6<>2 r1c6=1 (r1c4<>1) r1c5<>1 r1c5=7 r1c4<>7 r1c4=9 r1c3<>9
r3c5=6 (r1c5<>6) (r1c6<>6) r2c6<>6 r2c6=2 (r1c5<>2) r1c6<>2 r1c6=1 r1c5<>1 r1c5=7 r4c5<>7 r4c4=7 r4c4<>4 r4c3=4 r4c3<>9
r3c5=6 (r1c6<>6) r2c6<>6 r2c6=2 (r8c6<>2) r1c6<>2 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>9
r3c5=6 (r1c6<>6) r2c6<>6 r2c6=2 (r8c6<>2) r1c6<>2 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>8 r7c5=8 r9c5<>8 r9c3=8 r9c3<>9
Forcing Net Contradiction in c3 => r3c6<>2
r3c6=2 (r1c4<>2) (r1c5<>2) (r1c6<>2) r2c6<>2 r2c6=6 (r1c5<>6) r1c6<>6 r1c6=1 (r1c4<>1) r1c5<>1 r1c5=7 r1c4<>7 r1c4=9 r1c3<>9
r3c6=2 (r1c5<>2) (r1c6<>2) r2c6<>2 r2c6=6 (r1c5<>6) r1c6<>6 r1c6=1 r1c5<>1 r1c5=7 r4c5<>7 r4c4=7 r4c4<>4 r4c3=4 r4c3<>9
r3c6=2 (r8c6<>2) (r1c6<>2) r2c6<>2 r2c6=6 r1c6<>6 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>9
r3c6=2 (r8c6<>2) (r1c6<>2) r2c6<>2 r2c6=6 r1c6<>6 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>8 r7c5=8 r9c5<>8 r9c3=8 r9c3<>9
Forcing Net Contradiction in c3 => r3c6<>6
r3c6=6 (r1c5<>6) (r1c6<>6) r2c6<>6 r2c6=2 (r1c4<>2) (r1c5<>2) r1c6<>2 r1c6=1 (r1c4<>1) r1c5<>1 r1c5=7 r1c4<>7 r1c4=9 r1c3<>9
r3c6=6 (r1c5<>6) (r1c6<>6) r2c6<>6 r2c6=2 (r1c5<>2) r1c6<>2 r1c6=1 r1c5<>1 r1c5=7 r4c5<>7 r4c4=7 r4c4<>4 r4c3=4 r4c3<>9
r3c6=6 (r1c6<>6) r2c6<>6 r2c6=2 (r8c6<>2) r1c6<>2 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>9
r3c6=6 (r1c6<>6) r2c6<>6 r2c6=2 (r8c6<>2) r1c6<>2 r1c6=1 r8c6<>1 r8c6=3 (r7c4<>3) r7c5<>3 r7c3=3 r7c3<>8 r7c5=8 r9c5<>8 r9c3=8 r9c3<>9
Forcing Net Contradiction in r9 => r3c2<>9
r3c2=9 (r3c2<>6 r3c8=6 r1c9<>6 r1c9=2 r1c3<>2 r1c3=6 r2c1<>6) (r3c2<>6 r3c8=6 r1c9<>6 r1c9=2 r4c9<>2) (r6c2<>9) r2c1<>9 r2c7=9 r6c7<>9 r6c8=9 r4c9<>9 r4c9=6 r4c1<>6 r9c1=6
r3c2=9 (r1c3<>9) (r2c1<>9 r2c7=9 r1c9<>9) r3c2<>6 r3c8=6 (r9c8<>6) r1c9<>6 r1c9=2 r1c3<>2 r1c3=6 r9c3<>6 r9c7=6
Finned Franken Swordfish: 9 c29b1 r147 fr2c1 fr6c2 => r4c1<>9
Forcing Net Verity => r2c1=9
r7c2=2 (r7c9<>2) (r3c2<>2 r3c2=6 r1c3<>6) (r8c1<>2) r8c3<>2 r8c6=2 r2c6<>2 r2c6=6 (r1c5<>6) r1c6<>6 r1c9=6 r7c9<>6 r7c9=9 (r4c9<>9) r7c2<>9 r6c2=9 r4c3<>9 r4c7=9 r2c7<>9 r2c1=9
r7c2=6 r3c2<>6 r3c8=6 r3c8<>9 r3c4=9 r1c4<>9 r1c9=9 r2c7<>9 r2c1=9
r7c2=9 r9c1<>9 r2c1=9
W-Wing: 2/6 in r1c3,r2c7 connected by 6 in r3c28 => r1c9<>2
Sashimi X-Wing: 2 c19 r47 fr8c1 fr9c1 => r7c23<>2
Turbot Fish: 2 r2c7 =2= r3c8 -2- r3c2 =2= r6c2 => r6c7<>2
W-Wing: 6/2 in r1c3,r4c1 connected by 2 in r36c2 => r45c3<>6
Skyscraper: 6 in r2c6,r5c5 (connected by r25c7) => r1c5,r46c6<>6
W-Wing: 9/6 in r1c9,r7c2 connected by 6 in r3c28 => r7c9<>9
Hidden Rectangle: 2/4 in r4c34,r5c34 => r4c4<>2
Sashimi Swordfish: 6 c139 r147 fr9c1 fr9c3 => r7c2<>6
Naked Single: r7c2=9
Hidden Single: r4c3=9
Hidden Single: r1c9=9
Hidden Single: r4c4=4
Hidden Single: r5c3=4
Hidden Single: r3c4=9
Hidden Single: r4c5=7
Hidden Single: r1c4=7
Hidden Single: r9c4=5
Hidden Single: r4c6=5
Naked Single: r3c6=3
Hidden Single: r3c5=5
Hidden Single: r4c7=8
Hidden Single: r6c6=8
Hidden Single: r8c3=3
Remote Pair: 2/6 r3c8 -6- r3c2 -2- r6c2 -6- r4c1 -2- r4c9 -6- r7c9 => r79c8<>2, r79c8<>6
Naked Single: r7c8=1
Naked Single: r9c8=9
Hidden Single: r6c7=9
Hidden Single: r5c7=1
Naked Single: r5c4=2
Full House: r5c5=6
Naked Single: r7c4=3
Full House: r6c4=1
Full House: r6c5=3
Remote Pair: 6/2 r1c3 -2- r3c2 -6- r6c2 -2- r4c1 -6- r4c9 -2- r6c8 -6- r3c8 -2- r2c7 -6- r9c7 -2- r7c9 => r9c1<>2, r7c3,r9c1<>6
Naked Single: r7c3=8
Naked Single: r9c1=1
Naked Single: r7c5=2
Full House: r7c9=6
Full House: r4c9=2
Full House: r9c7=2
Full House: r4c1=6
Full House: r8c1=2
Full House: r8c6=1
Full House: r9c5=8
Full House: r1c5=1
Full House: r6c8=6
Full House: r2c7=6
Full House: r9c3=6
Full House: r6c2=2
Full House: r3c8=2
Full House: r2c6=2
Full House: r1c3=2
Full House: r3c2=6
Full House: r1c6=6
|
normal_sudoku_2621 | 16.....294.39...6..296....4.3.19.2..2814579369.......139....61..12.694.36.4.1..92 | 167584329453972168829631754736198245281457936945326871398245617512769483674813592 | normal_sudoku_2621 | 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 | 9 | 1 6 . . . . . 2 9
4 . 3 9 . . . 6 .
. 2 9 6 . . . . 4
. 3 . 1 9 . 2 . .
2 8 1 4 5 7 9 3 6
9 . . . . . . . 1
3 9 . . . . 6 1 .
. 1 2 . 6 9 4 . 3
6 . 4 . 1 . . 9 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 167584329453972168829631754736198245281457936945326871398245617512769483674813592 #1 Extreme (4222)
Hidden Single: r4c8=4
Hidden Single: r6c2=4
Finned Franken Swordfish: 5 c29b4 r247 fr6c3 fr9c2 => r7c3<>5
W-Wing: 7/5 in r2c2,r4c1 connected by 5 in r8c1,r9c2 => r3c1<>7
Sashimi Swordfish: 7 c129 r247 fr8c1 fr9c2 => r7c3<>7
Naked Single: r7c3=8
Hidden Single: r3c1=8
Discontinuous Nice Loop: 5 r1c7 -5- r3c8 -7- r3c5 -3- r3c7 =3= r1c7 => r1c7<>5
Forcing Chain Contradiction in r9c7 => r2c9<>5
r2c9=5 r2c2<>5 r9c2=5 r9c7<>5
r2c9=5 r7c9<>5 r7c9=7 r9c7<>7
r2c9=5 r2c9<>8 r12c7=8 r9c7<>8
Skyscraper: 5 in r7c9,r8c1 (connected by r4c19) => r8c8<>5
Discontinuous Nice Loop: 7 r4c3 -7- r1c3 =7= r2c2 -7- r2c9 -8- r4c9 =8= r4c6 =6= r4c3 => r4c3<>7
Grouped Discontinuous Nice Loop: 7 r9c4 -7- r9c2 -5- r9c7 =5= r7c9 =7= r7c45 -7- r9c4 => r9c4<>7
Turbot Fish: 7 r1c3 =7= r2c2 -7- r9c2 =7= r9c7 => r1c7<>7
Forcing Chain Contradiction in r9c7 => r1c7=3
r1c7<>3 r1c7=8 r2c9<>8 r2c9=7 r7c9<>7 r7c9=5 r9c7<>5
r1c7<>3 r1c7=8 r2c9<>8 r2c9=7 r2c2<>7 r9c2=7 r9c7<>7
r1c7<>3 r1c7=8 r9c7<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r2c56<>8
Discontinuous Nice Loop: 7 r1c5 -7- r1c3 -5- r4c3 -6- r4c6 -8- r6c5 =8= r1c5 => r1c5<>7
Discontinuous Nice Loop: 2 r7c5 -2- r2c5 -7- r2c9 -8- r4c9 =8= r4c6 -8- r6c5 =8= r1c5 =4= r7c5 => r7c5<>2
Grouped AIC: 4/8 8- r1c5 =8= r6c5 -8- r4c6 =8= r4c9 -8- r2c9 -7- r3c78 =7= r3c5 -7- r7c5 -4- r7c6 =4= r1c6 -4 => r1c5<>4, r1c6<>8
Naked Single: r1c5=8
Hidden Single: r1c6=4
Hidden Single: r7c5=4
Locked Candidates Type 1 (Pointing): 7 in b8 => r1c4<>7
Naked Single: r1c4=5
Full House: r1c3=7
Full House: r2c2=5
Full House: r9c2=7
Full House: r8c1=5
Full House: r4c1=7
W-Wing: 5/8 in r4c9,r9c7 connected by 8 in r2c79 => r6c7,r7c9<>5
Naked Single: r7c9=7
Naked Single: r2c9=8
Full House: r4c9=5
Naked Single: r7c4=2
Full House: r7c6=5
Naked Single: r8c8=8
Full House: r8c4=7
Full House: r9c7=5
Naked Single: r4c3=6
Full House: r4c6=8
Full House: r6c3=5
Naked Single: r6c8=7
Full House: r3c8=5
Full House: r6c7=8
Naked Single: r6c4=3
Full House: r9c4=8
Full House: r9c6=3
Naked Single: r6c5=2
Full House: r6c6=6
Naked Single: r3c6=1
Full House: r2c6=2
Naked Single: r2c5=7
Full House: r2c7=1
Full House: r3c7=7
Full House: r3c5=3
|
normal_sudoku_4486 | .1683..7553...7...8475.16..35.7.6.18.7815....6.14..75.78.....4..6..7..9...5.....7 | 916832475532647189847591623354726918278159364691483752789315246463278591125964837 | normal_sudoku_4486 | 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 | 9 | . 1 6 8 3 . . 7 5
5 3 . . . 7 . . .
8 4 7 5 . 1 6 . .
3 5 . 7 . 6 . 1 8
. 7 8 1 5 . . . .
6 . 1 4 . . 7 5 .
7 8 . . . . . 4 .
. 6 . . 7 . . 9 .
. . 5 . . . . . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 916832475532647189847591623354726918278159364691483752789315246463278591125964837 #1 Extreme (2162)
Locked Candidates Type 1 (Pointing): 3 in b5 => r789c6<>3
Naked Pair: 2,9 in r34c5 => r2679c5<>2, r2679c5<>9
Naked Single: r6c5=8
Hidden Pair: 5,8 in r8c67 => r8c67<>2, r8c6<>4, r8c7<>1, r8c7<>3
Locked Candidates Type 1 (Pointing): 4 in b8 => r9c1<>4
AIC: 1 1- r2c7 =1= r2c9 =4= r5c9 -4- r5c1 =4= r8c1 =1= r8c9 -1 => r2c9,r79c7<>1
Hidden Single: r2c7=1
Hidden Single: r2c8=8
AIC: 1/6 1- r7c5 -6- r2c5 -4- r2c9 =4= r5c9 =6= r7c9 -6 => r7c9<>1, r7c5<>6
Naked Single: r7c5=1
Hidden Single: r8c9=1
Hidden Single: r9c1=1
Empty Rectangle: 9 in b3 (r15c1) => r5c9<>9
W-Wing: 2/9 in r2c3,r6c2 connected by 9 in r15c1 => r4c3<>2
Sashimi X-Wing: 2 r34 c57 fr3c8 fr3c9 => r1c7<>2
Turbot Fish: 2 r1c6 =2= r1c1 -2- r5c1 =2= r6c2 => r6c6<>2
W-Wing: 4/9 in r1c7,r4c3 connected by 9 in r15c1 => r4c7<>4
Hidden Single: r4c3=4
Hidden Single: r8c1=4
Skyscraper: 9 in r3c9,r4c7 (connected by r34c5) => r1c7,r6c9<>9
Naked Single: r1c7=4
Hidden Single: r9c6=4
Naked Single: r9c5=6
Naked Single: r2c5=4
Hidden Single: r5c9=4
Hidden Single: r9c7=8
Naked Single: r8c7=5
Naked Single: r8c6=8
Hidden Single: r2c4=6
Hidden Single: r7c9=6
Hidden Single: r5c8=6
Hidden Single: r7c6=5
X-Wing: 2 c16 r15 => r5c7<>2
Remote Pair: 9/2 r4c7 -2- r4c5 -9- r3c5 -2- r1c6 -9- r1c1 -2- r5c1 => r5c7<>9
Naked Single: r5c7=3
Naked Single: r6c9=2
Full House: r4c7=9
Full House: r7c7=2
Full House: r4c5=2
Full House: r9c8=3
Full House: r3c5=9
Full House: r3c8=2
Full House: r1c6=2
Full House: r3c9=3
Full House: r2c9=9
Full House: r1c1=9
Full House: r2c3=2
Full House: r5c1=2
Full House: r6c2=9
Full House: r5c6=9
Full House: r6c6=3
Full House: r9c2=2
Full House: r9c4=9
Naked Single: r8c3=3
Full House: r7c3=9
Full House: r7c4=3
Full House: r8c4=2
|
normal_sudoku_309 | ..61.8349.914376.8348..97...1.....7...4....3..5..1.98..85.4..93.698.3..7.3...186. | 276158349591437628348269751913682475824975136657314982185746293469823517732591864 | normal_sudoku_309 | 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 | 9 | . . 6 1 . 8 3 4 9
. 9 1 4 3 7 6 . 8
3 4 8 . . 9 7 . .
. 1 . . . . . 7 .
. . 4 . . . . 3 .
. 5 . . 1 . 9 8 .
. 8 5 . 4 . . 9 3
. 6 9 8 . 3 . . 7
. 3 . . . 1 8 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 276158349591437628348269751913682475824975136657314982185746293469823517732591864 #1 Hard (1144)
Locked Candidates Type 2 (Claiming): 5 in c6 => r4c45,r5c45<>5
Naked Pair: 2,5 in r18c5 => r3459c5<>2, r39c5<>5
Naked Single: r3c5=6
Naked Triple: 2,3,7 in r46c3,r5c2 => r456c1<>2, r56c1<>7
Naked Single: r6c1=6
Naked Pair: 8,9 in r4c15 => r4c4<>9
Naked Pair: 2,4 in r6c69 => r6c34<>2
Skyscraper: 7 in r6c3,r7c1 (connected by r67c4) => r9c3<>7
Naked Single: r9c3=2
Naked Single: r4c3=3
Full House: r6c3=7
Naked Single: r5c2=2
Full House: r1c2=7
Naked Single: r6c4=3
Naked Triple: 1,5,6 in r5c679 => r5c4<>6
XYZ-Wing: 1/2/5 in r7c7,r8c58 => r8c7<>2
Swordfish: 2 r128 c158 => r3c8<>2
Skyscraper: 2 in r3c4,r6c6 (connected by r36c9) => r4c4<>2
Naked Single: r4c4=6
Naked Single: r5c6=5
Naked Single: r5c7=1
Naked Single: r5c9=6
Naked Single: r7c7=2
Naked Single: r7c4=7
Naked Single: r7c6=6
Full House: r7c1=1
Naked Single: r5c4=9
Naked Single: r9c5=9
Naked Single: r8c1=4
Full House: r9c1=7
Naked Single: r4c5=8
Naked Single: r5c1=8
Full House: r4c1=9
Full House: r5c5=7
Naked Single: r9c4=5
Full House: r3c4=2
Full House: r8c5=2
Full House: r9c9=4
Full House: r1c5=5
Full House: r1c1=2
Full House: r2c1=5
Full House: r2c8=2
Naked Single: r8c7=5
Full House: r4c7=4
Full House: r8c8=1
Full House: r3c8=5
Full House: r3c9=1
Naked Single: r6c9=2
Full House: r4c9=5
Full House: r4c6=2
Full House: r6c6=4
|
normal_sudoku_1610 | .3..2.7.9745.9.621....7.4...6..89572287..519..5.7.28..5.6.3.2...1..579....4...3.. | 631524789745893621928671435463189572287345196159762843576938214312457968894216357 | normal_sudoku_1610 | 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 | 9 | . 3 . . 2 . 7 . 9
7 4 5 . 9 . 6 2 1
. . . . 7 . 4 . .
. 6 . . 8 9 5 7 2
2 8 7 . . 5 1 9 .
. 5 . 7 . 2 8 . .
5 . 6 . 3 . 2 . .
. 1 . . 5 7 9 . .
. . 4 . . . 3 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 631524789745893621928671435463189572287345196159762843576938214312457968894216357 #1 Unfair (578)
Locked Candidates Type 1 (Pointing): 3 in b3 => r3c46<>3
Hidden Single: r2c6=3
Full House: r2c4=8
Locked Candidates Type 2 (Claiming): 4 in c5 => r45c4<>4
Hidden Single: r4c1=4
Discontinuous Nice Loop: 5/6/8 r9c9 =7= r9c2 =2= r9c4 =9= r7c4 -9- r7c2 -7- r7c9 =7= r9c9 => r9c9<>5, r9c9<>6, r9c9<>8
Naked Single: r9c9=7
Hidden Single: r9c8=5
Naked Single: r1c8=8
Naked Single: r1c3=1
Naked Single: r3c8=3
Full House: r3c9=5
Naked Single: r1c1=6
Naked Single: r4c3=3
Full House: r4c4=1
Naked Single: r1c6=4
Full House: r1c4=5
Naked Single: r6c3=9
Full House: r6c1=1
Naked Single: r3c4=6
Full House: r3c6=1
Naked Single: r5c4=3
Naked Single: r7c6=8
Full House: r9c6=6
Naked Single: r7c9=4
Naked Single: r9c5=1
Naked Single: r5c9=6
Full House: r5c5=4
Full House: r6c5=6
Naked Single: r7c4=9
Naked Single: r7c8=1
Full House: r7c2=7
Naked Single: r8c8=6
Full House: r6c8=4
Full House: r6c9=3
Full House: r8c9=8
Naked Single: r9c4=2
Full House: r8c4=4
Naked Single: r8c1=3
Full House: r8c3=2
Full House: r3c3=8
Naked Single: r9c2=9
Full House: r3c2=2
Full House: r3c1=9
Full House: r9c1=8
|
normal_sudoku_3903 | .159..7......5.91........56..638..7....67.34..37..986...18......78.9.1..25...1... | 815946723764253918923718456596384271182675349437129865341867592678592134259431687 | normal_sudoku_3903 | 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 | 9 | . 1 5 9 . . 7 . .
. . . . 5 . 9 1 .
. . . . . . . 5 6
. . 6 3 8 . . 7 .
. . . 6 7 . 3 4 .
. 3 7 . . 9 8 6 .
. . 1 8 . . . . .
. 7 8 . 9 . 1 . .
2 5 . . . 1 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 815946723764253918923718456596384271182675349437129865341867592678592134259431687 #1 Extreme (6512)
Locked Candidates Type 1 (Pointing): 1 in b5 => r6c19<>1
Locked Candidates Type 1 (Pointing): 9 in b6 => r79c9<>9
Naked Pair: 2,5 in r4c7,r6c9 => r45c9<>2, r45c9<>5
2-String Kite: 6 in r2c2,r8c6 (connected by r7c2,r8c1) => r2c6<>6
Locked Candidates Type 1 (Pointing): 6 in b2 => r1c1<>6
Uniqueness Test 4: 1/9 in r4c19,r5c19 => r45c1<>9
Discontinuous Nice Loop: 7 r2c4 -7- r2c1 =7= r3c1 =9= r7c1 -9- r7c8 =9= r9c8 =8= r9c9 =7= r9c4 -7- r2c4 => r2c4<>7
Grouped AIC: 4 4- r2c4 -2- r1c56 =2= r1c89 -2- r3c7 -4 => r2c9,r3c456<>4
Grouped Discontinuous Nice Loop: 5 r4c6 -5- r4c7 =5= r6c9 -5- r6c1 -4- r4c12 =4= r4c6 => r4c6<>5
Almost Locked Set XZ-Rule: A=r2c34 {234}, B=r1456c1 {13458}, X=3, Z=4 => r2c1<>4
Almost Locked Set XZ-Rule: A=r4c67 {245}, B=r7c12578 {234569}, X=5, Z=4 => r7c6<>4
Almost Locked Set XZ-Rule: A=r1456c1 {13458}, B=r235c3 {2349}, X=3, Z=4 => r3c1<>4
Almost Locked Set XY-Wing: A=r2c349 {2348}, B=r145678c1 {1345689}, C=r9c34579 {346789}, X,Y=8,9, Z=3 => r2c1<>3
Almost Locked Set Chain: 24- r2c349 {2348} -8- r9c34579 {346789} -9- r145678c1 {1345689} -6- r3457c2 {24689} -24 => r2c2<>2, r2c2<>4
Grouped Discontinuous Nice Loop: 2 r3c6 -2- r3c2 =2= r45c2 -2- r5c3 -9- r5c9 -1- r5c1 =1= r4c1 =5= r4c7 =2= r6c9 -2- r6c45 =2= r45c6 -2- r3c6 => r3c6<>2
Forcing Chain Contradiction in r7 => r2c2=6
r2c2<>6 r2c2=8 r5c2<>8 r5c1=8 r5c1<>5 r5c6=5 r7c6<>5
r2c2<>6 r2c2=8 r5c2<>8 r5c1=8 r5c1<>1 r4c1=1 r4c1<>5 r4c7=5 r7c7<>5
r2c2<>6 r2c1=6 r2c1<>7 r2c6=7 r7c6<>7 r7c9=7 r7c9<>5
XYZ-Wing: 2/4/9 in r47c2,r5c3 => r5c2<>9
Discontinuous Nice Loop: 4 r7c9 -4- r7c2 -9- r7c8 =9= r9c8 =8= r9c9 =7= r7c9 => r7c9<>4
Forcing Chain Contradiction in r7 => r5c2=8
r5c2<>8 r5c2=2 r5c6<>2 r5c6=5 r7c6<>5
r5c2<>8 r5c1=8 r5c1<>1 r4c1=1 r4c1<>5 r4c7=5 r7c7<>5
r5c2<>8 r5c2=2 r5c3<>2 r5c3=9 r9c3<>9 r9c8=9 r9c8<>8 r9c9=8 r9c9<>7 r7c9=7 r7c9<>5
Locked Triple: 1,4,5 in r456c1 => r178c1,r4c2<>4
Sue de Coq: r1c89 - {2348} (r1c1 - {38}, r3c7 - {24}) => r2c9<>2, r1c56<>3, r1c6<>8
Naked Triple: 2,4,6 in r1c56,r2c4 => r2c6,r3c45<>2, r2c6<>4
Naked Triple: 3,7,8 in r2c169 => r2c3<>3
Skyscraper: 2 in r2c4,r5c6 (connected by r25c3) => r1c6,r6c4<>2
Hidden Rectangle: 7/8 in r2c16,r3c16 => r3c6<>7
Finned Swordfish: 2 r168 c589 fr8c4 fr8c6 => r7c5<>2
W-Wing: 4/2 in r2c4,r4c6 connected by 2 in r16c5 => r1c6,r6c4<>4
Naked Single: r1c6=6
Hidden Single: r8c1=6
XYZ-Wing: 2/3/9 in r7c18,r8c8 => r7c9<>3
Hidden Rectangle: 4/6 in r7c57,r9c57 => r7c5<>4
Finned X-Wing: 3 r28 c69 fr8c8 => r9c9<>3
Sashimi X-Wing: 4 r18 c59 fr8c4 fr8c6 => r9c5<>4
Locked Pair: 3,6 in r79c5 => r3c5,r78c6<>3
Naked Single: r3c5=1
Naked Single: r3c4=7
Naked Single: r9c4=4
Naked Single: r2c4=2
Naked Single: r9c7=6
Naked Single: r1c5=4
Naked Single: r2c3=4
Naked Single: r8c4=5
Full House: r6c4=1
Naked Single: r9c5=3
Naked Single: r6c5=2
Full House: r7c5=6
Naked Single: r8c6=2
Full House: r7c6=7
Naked Single: r9c3=9
Naked Single: r4c6=4
Full House: r5c6=5
Naked Single: r6c9=5
Full House: r6c1=4
Naked Single: r8c8=3
Full House: r8c9=4
Naked Single: r5c3=2
Full House: r3c3=3
Naked Single: r7c1=3
Full House: r7c2=4
Naked Single: r9c8=8
Full House: r9c9=7
Naked Single: r5c1=1
Full House: r5c9=9
Naked Single: r4c7=2
Full House: r4c9=1
Naked Single: r7c9=2
Naked Single: r4c2=9
Full House: r4c1=5
Full House: r3c2=2
Naked Single: r1c1=8
Naked Single: r3c6=8
Full House: r2c6=3
Naked Single: r1c8=2
Full House: r7c8=9
Full House: r7c7=5
Full House: r3c7=4
Full House: r1c9=3
Full House: r3c1=9
Full House: r2c1=7
Full House: r2c9=8
|
normal_sudoku_3455 | 7..8.1.25.1524.8.72.8..541.8.3.....1..6.182..1......8....18.5.2.825.417.5.1.27.48 | 749831625615249837238765419853472961976318254124956783467183592382594176591627348 | normal_sudoku_3455 | 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 | 9 | 7 . . 8 . 1 . 2 5
. 1 5 2 4 . 8 . 7
2 . 8 . . 5 4 1 .
8 . 3 . . . . . 1
. . 6 . 1 8 2 . .
1 . . . . . . 8 .
. . . 1 8 . 5 . 2
. 8 2 5 . 4 1 7 .
5 . 1 . 2 7 . 4 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 749831625615249837238765419853472961976318254124956783467183592382594176591627348 #1 Extreme (9858)
Almost Locked Set XY-Wing: A=r4c25678 {245679}, B=r5c1489 {34579}, C=r13579c2 {345679}, X,Y=4,5, Z=7 => r4c4<>7
Forcing Chain Contradiction in r6c3 => r5c4<>4
r5c4=4 r5c9<>4 r6c9=4 r6c3<>4
r5c4=4 r5c4<>7 r5c2=7 r6c3<>7
r5c4=4 r5c1<>4 r5c1=9 r6c3<>9
Forcing Net Contradiction in c6 => r4c4=4
r4c4<>4 (r6c4=4 r6c4<>3) r4c2=4 (r5c1<>4 r5c1=9 r5c8<>9) (r4c2<>5) r4c2<>2 r4c6=2 r6c6<>2 r6c2=2 r6c2<>5 (r6c5=5 r6c5<>3) r5c2=5 r5c8<>5 r5c8=3 (r6c7<>3) r6c9<>3 r6c6=3
r4c4<>4 r4c2=4 (r1c2<>4 r1c3=4 r7c3<>4 r7c1=4 r7c1<>3) (r4c2<>2 r4c6=2 r6c6<>2 r6c2=2 r6c2<>5 r5c2=5 r5c8<>5 r5c8=3 r7c8<>3) (r6c3<>4) r5c1<>4 r5c1=9 r6c3<>9 r6c3=7 r7c3<>7 r7c2=7 r7c2<>3 r7c6=3
Forcing Net Contradiction in r1 => r4c2<>9
r4c2=9 (r6c3<>9) r5c1<>9 r5c1=4 (r7c1<>4) r6c3<>4 r6c3=7 r7c3<>7 r7c2=7 r7c2<>4 r7c3=4 r1c3<>4 r1c2=4 r1c2<>6
r4c2=9 (r4c2<>2 r4c6=2 r6c6<>2 r6c2=2 r6c2<>5 r6c5=5 r4c5<>5) (r4c5<>9) (r6c3<>9) r5c1<>9 r5c1=4 r6c3<>4 r6c3=7 r5c2<>7 r5c4=7 r4c5<>7 r4c5=6 r1c5<>6
r4c2=9 (r4c2<>2 r4c6=2 r6c6<>2 r6c2=2 r6c2<>5 r6c5=5 r6c5<>6) (r4c2<>2 r4c6=2 r6c6<>2 r6c2=2 r6c2<>5 r6c5=5 r4c5<>5) (r4c5<>9) (r6c3<>9) r5c1<>9 r5c1=4 r6c3<>4 (r6c9=4 r6c9<>6) r6c3=7 r5c2<>7 r5c4=7 r4c5<>7 r4c5=6 (r6c4<>6) r6c6<>6 r6c7=6 r1c7<>6
Forcing Net Contradiction in r7 => r6c7<>3
r6c7=3 (r6c6<>3) (r1c7<>3) (r9c7<>3) (r5c8<>3) r5c9<>3 r5c4=3 r9c4<>3 r9c2=3 r1c2<>3 r1c5=3 r2c6<>3 r7c6=3
r6c7=3 (r9c7<>3) (r5c8<>3) r5c9<>3 r5c4=3 r9c4<>3 r9c2=3 (r7c1<>3) r7c2<>3 r7c8=3
Forcing Chain Contradiction in c5 => r8c9<>3
r8c9=3 r9c7<>3 r1c7=3 r1c5<>3
r8c9=3 r56c9<>3 r5c8=3 r5c8<>5 r5c2=5 r5c2<>7 r5c4=7 r3c4<>7 r3c5=7 r3c5<>3
r8c9=3 r56c9<>3 r5c8=3 r5c8<>5 r5c2=5 r6c2<>5 r6c5=5 r6c5<>3
r8c9=3 r8c5<>3
Finned Franken Swordfish: 3 r18b9 c257 fr7c8 fr8c1 => r7c2<>3
Forcing Net Contradiction in c1 => r5c9<>9
r5c9=9 (r8c9<>9 r8c9=6 r3c9<>6 r3c9=3 r2c8<>3) (r8c9<>9 r8c9=6 r7c8<>6) (r5c9<>3) r5c1<>9 r5c1=4 (r6c2<>4) r6c3<>4 r6c9=4 r6c9<>3 r5c8=3 r7c8<>3 r7c8=9 r2c8<>9 r2c8=6 r2c1<>6
r5c9=9 (r5c1<>9 r5c1=4 r6c3<>4 r6c9=4 r6c9<>3 r5c8=3 r7c8<>3) (r3c9<>9) r8c9<>9 r8c9=6 r3c9<>6 r3c9=3 (r2c8<>3) (r3c2<>3) r1c7<>3 r9c7=3 r9c2<>3 r1c2=3 r2c1<>3 r2c6=3 r7c6<>3 r7c1=3 r7c1<>6
r5c9=9 r8c9<>9 r8c9=6 r8c1<>6
Forcing Net Contradiction in b8 => r3c9<>3
r3c9=3 (r1c7<>3 r9c7=3 r7c8<>3) r5c9<>3 r5c9=4 r5c1<>4 r7c1=4 r7c1<>3 r7c6=3
r3c9=3 r8c5=3
Locked Candidates Type 2 (Claiming): 3 in c9 => r5c8<>3
Naked Pair: 6,9 in r38c9 => r6c9<>6, r6c9<>9
Almost Locked Set XZ-Rule: A=r5c128 {4579}, B=r1379c2 {34679}, X=7, Z=4 => r6c2<>4
Forcing Net Verity => r1c7<>9
r8c1=6 (r8c1<>3 r8c5=3 r1c5<>3) (r2c1<>6) r8c9<>6 r3c9=6 r2c8<>6 r2c6=6 r1c5<>6 r1c5=9 r1c7<>9
r8c5=6 (r9c4<>6) (r8c5<>3 r8c1=3 r9c2<>3) (r1c5<>6) r8c9<>6 r3c9=6 r1c7<>6 r1c2=6 r9c2<>6 r9c2=9 r9c4<>9 r9c4=3 r9c7<>3 r1c7=3 r1c7<>9
r8c9=6 r3c9<>6 r3c9=9 r1c7<>9
Discontinuous Nice Loop: 6 r7c8 -6- r8c9 -9- r3c9 =9= r2c8 =3= r7c8 => r7c8<>6
Finned Franken Swordfish: 9 r18b3 c159 fr1c2 fr1c3 fr2c8 => r2c1<>9
Almost Locked Set XZ-Rule: A=r2c1,r3c2 {369}, B=r1c7,r3c9 {369}, X=9, Z=3 => r1c2<>3
2-String Kite: 3 in r3c2,r8c5 (connected by r8c1,r9c2) => r3c5<>3
Multi Colors 1: 3 (r1c5,r2c8,r9c7) / (r1c7,r7c8), (r8c1) / (r8c5) => r7c1<>3
Forcing Chain Contradiction in c4 => r5c8=5
r5c8<>5 r5c8=9 r2c8<>9 r2c6=9 r3c4<>9
r5c8<>5 r5c8=9 r5c4<>9
r5c8<>5 r5c8=9 r4c78<>9 r4c56=9 r6c4<>9
r5c8<>5 r5c8=9 r46c7<>9 r9c7=9 r9c4<>9
Naked Triple: 4,7,9 in r5c12,r6c3 => r46c2<>7, r6c2<>9
Discontinuous Nice Loop: 6 r4c7 -6- r4c8 =6= r2c8 -6- r2c1 -3- r3c2 =3= r3c4 =7= r3c5 -7- r4c5 =7= r4c7 => r4c7<>6
Forcing Chain Contradiction in b8 => r4c8=6
r4c8<>6 r4c8=9 r2c8<>9 r2c6=9 r7c6<>9
r4c8<>6 r2c8=6 r2c1<>6 r2c1=3 r8c1<>3 r8c5=3 r8c5<>9
r4c8<>6 r4c8=9 r46c7<>9 r9c7=9 r9c4<>9
Locked Candidates Type 1 (Pointing): 9 in b6 => r9c7<>9
XY-Wing: 3/9/6 in r2c18,r3c9 => r3c2<>6
Finned X-Wing: 6 r27 c16 fr7c2 => r8c1<>6
2-String Kite: 6 in r1c7,r8c5 (connected by r8c9,r9c7) => r1c5<>6
W-Wing: 3/9 in r2c8,r8c1 connected by 9 in r38c9 => r2c1<>3
Naked Single: r2c1=6
Hidden Single: r8c1=3
Hidden Single: r3c2=3
Hidden Single: r1c7=6
Naked Single: r3c9=9
Full House: r2c8=3
Full House: r2c6=9
Full House: r7c8=9
Naked Single: r9c7=3
Full House: r8c9=6
Full House: r8c5=9
Naked Single: r1c5=3
Naked Single: r4c6=2
Naked Single: r7c1=4
Full House: r5c1=9
Naked Single: r9c4=6
Full House: r7c6=3
Full House: r9c2=9
Full House: r6c6=6
Naked Single: r4c2=5
Naked Single: r7c3=7
Full House: r7c2=6
Naked Single: r3c4=7
Full House: r3c5=6
Naked Single: r1c2=4
Full House: r1c3=9
Full House: r6c3=4
Naked Single: r4c5=7
Full House: r4c7=9
Full House: r6c5=5
Full House: r6c7=7
Naked Single: r6c2=2
Full House: r5c2=7
Naked Single: r5c4=3
Full House: r5c9=4
Full House: r6c9=3
Full House: r6c4=9
|
normal_sudoku_1462 | 74....19..16...4.22.9..1.679...1.6...72963.4116.5.87.94..1...766.7...91..91...2.4 | 745326198816759432239481567984217653572963841163548729458192376627834915391675284 | normal_sudoku_1462 | 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 | 9 | 7 4 . . . . 1 9 .
. 1 6 . . . 4 . 2
2 . 9 . . 1 . 6 7
9 . . . 1 . 6 . .
. 7 2 9 6 3 . 4 1
1 6 . 5 . 8 7 . 9
4 . . 1 . . . 7 6
6 . 7 . . . 9 1 .
. 9 1 . . . 2 . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 745326198816759432239481567984217653572963841163548729458192376627834915391675284 #1 Extreme (5022)
Forcing Net Verity => r1c9<>3
r3c7=3 r1c9<>3
r3c7=5 (r3c7<>3 r7c7=3 r7c3<>3) (r3c2<>5) r5c7<>5 r5c1=5 r2c1<>5 r1c3=5 r7c3<>5 r7c3=8 r9c1<>8 r2c1=8 (r2c8<>8) r5c1<>8 r5c7=8 (r5c1<>8) r3c7<>8 r1c9=8 r1c9<>3
r3c7=8 (r3c7<>3 r7c7=3 r7c3<>3) (r3c2<>8) r5c7<>8 r5c1=8 r2c1<>8 r1c3=8 (r1c3<>5) r7c3<>8 r7c3=5 (r4c3<>5 r4c2=5 r3c2<>5) r9c1<>5 r2c1=5 r5c1<>5 r5c7=5 (r5c1<>5) r3c7<>5 r3c5=5 (r1c5<>5) r1c6<>5 r1c9=5 r1c9<>3
Discontinuous Nice Loop: 3 r3c4 -3- r3c7 =3= r2c8 -3- r6c8 -2- r6c5 -4- r3c5 =4= r3c4 => r3c4<>3
Grouped Discontinuous Nice Loop: 3 r3c5 -3- r3c7 =3= r2c8 -3- r6c8 =3= r6c3 -3- r1c3 =3= r1c45 -3- r3c5 => r3c5<>3
Almost Locked Set XY-Wing: A=r1c39 {358}, B=r123c5,r2c46,r3c4 {2345789}, C=r6c35 {234}, X,Y=2,3, Z=5,8 => r1c6<>5, r1c4<>8
Grouped Discontinuous Nice Loop: 5 r9c5 =7= r2c5 =9= r2c6 =5= r123c5 -5- r9c5 => r9c5<>5
Forcing Chain Contradiction in r7 => r2c5<>3
r2c5=3 r2c1<>3 r9c1=3 r7c2<>3
r2c5=3 r2c1<>3 r9c1=3 r7c3<>3
r2c5=3 r7c5<>3
r2c5=3 r2c8<>3 r3c7=3 r7c7<>3
Forcing Net Verity => r3c4=4
r4c9=3 r6c8<>3 r6c8=2 r6c5<>2 r6c5=4 r3c5<>4 r3c4=4
r4c9=5 (r4c3<>5) (r5c7<>5 r5c7=8 r7c7<>8) r4c9<>3 r8c9=3 r7c7<>3 r7c7=5 (r3c7<>5) r7c3<>5 r1c3=5 r3c2<>5 r3c5=5 r3c5<>4 r3c4=4
r4c9=8 (r1c9<>8 r1c9=5 r1c5<>5) (r1c9<>8 r1c9=5 r2c8<>5) r5c7<>8 r5c7=5 (r5c1<>5) r4c8<>5 r9c8=5 r9c1<>5 r2c1=5 (r2c5<>5) r2c6<>5 r3c5=5 r3c5<>4 r3c4=4
Forcing Net Verity => r4c3=4
r7c7=3 r3c7<>3 r2c8=3 r6c8<>3 r6c8=2 r6c5<>2 r6c5=4 r4c6<>4 r4c3=4
r7c7=5 (r7c7<>3 r3c7=3 r3c2<>3) (r7c3<>5) r5c7<>5 r5c1=5 (r4c3<>5) (r9c1<>5 r9c6=5 r8c6<>5 r8c2=5 r8c2<>8) (r9c1<>5) r4c3<>5 r1c3=5 (r3c2<>5 r3c2=8 r7c2<>8) r1c3<>3 r2c1=3 r9c1<>3 r9c1=8 (r7c3<>8) r5c1<>8 r5c7=8 (r4c8<>8 r9c8=8 r9c1<>8 r9c1=3 r7c3<>3 r7c3=8 r4c3<>8) r7c7<>8 r7c5=8 (r8c4<>8) r8c5<>8 r8c9=8 r8c9<>3 r4c9=3 r4c3<>3 r4c3=4
r7c7=8 (r7c7<>3 r3c7=3 r3c2<>3) (r7c3<>8) r5c7<>8 r5c1=8 r4c3<>8 r1c3=8 (r1c9<>8 r4c9=8 r4c8<>8 r2c8=8 r2c4<>8) r1c3<>3 r2c1=3 r2c4<>3 r2c4=7 r4c4<>7 r4c6=7 r4c6<>4 r4c3=4
Naked Single: r6c3=3
Naked Single: r6c8=2
Full House: r6c5=4
Hidden Single: r8c6=4
Locked Candidates Type 2 (Claiming): 3 in r1 => r2c4<>3
Naked Pair: 5,8 in r1c39 => r1c5<>5, r1c5<>8
Finned Franken Swordfish: 5 c37b4 r357 fr1c3 fr4c2 => r3c2<>5
W-Wing: 8/5 in r5c1,r7c3 connected by 5 in r1c3,r2c1 => r9c1<>8
Sashimi Swordfish: 8 c137 r357 fr1c3 fr2c1 => r3c2<>8
Naked Single: r3c2=3
Hidden Single: r2c8=3
Hidden Single: r9c1=3
Hidden Single: r7c7=3
Hidden Single: r4c9=3
Remote Pair: 5/8 r3c5 -8- r3c7 -5- r5c7 -8- r5c1 -5- r4c2 -8- r4c8 -5- r9c8 -8- r8c9 => r8c25<>5, r8c25<>8
Naked Single: r8c2=2
Naked Single: r8c5=3
Naked Single: r1c5=2
Naked Single: r8c4=8
Full House: r8c9=5
Full House: r1c9=8
Full House: r9c8=8
Full House: r3c7=5
Full House: r4c8=5
Full House: r3c5=8
Full House: r5c7=8
Full House: r5c1=5
Full House: r4c2=8
Full House: r2c1=8
Full House: r1c3=5
Full House: r7c2=5
Full House: r7c3=8
Naked Single: r1c6=6
Full House: r1c4=3
Naked Single: r2c4=7
Naked Single: r9c5=7
Naked Single: r7c5=9
Full House: r2c5=5
Full House: r7c6=2
Full House: r2c6=9
Naked Single: r4c4=2
Full House: r9c4=6
Full House: r9c6=5
Full House: r4c6=7
|
normal_sudoku_620 | .2.61..3...3.....1....37..4849276513256341897137..5......7.3....9...8.7.3.51..... | 524619738763824951918537624849276513256341897137985246482793165691458372375162489 | normal_sudoku_620 | 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 | 9 | . 2 . 6 1 . . 3 .
. . 3 . . . . . 1
. . . . 3 7 . . 4
8 4 9 2 7 6 5 1 3
2 5 6 3 4 1 8 9 7
1 3 7 . . 5 . . .
. . . 7 . 3 . . .
. 9 . . . 8 . 7 .
3 . 5 1 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 524619738763824951918537624849276513256341897137985246482793165691458372375162489 #1 Easy (198)
Hidden Single: r8c7=3
Hidden Single: r9c2=7
Hidden Single: r8c3=1
Naked Single: r3c3=8
Naked Single: r1c3=4
Full House: r7c3=2
Naked Single: r2c2=6
Naked Single: r1c6=9
Naked Single: r3c2=1
Full House: r7c2=8
Naked Single: r1c7=7
Naked Single: r3c4=5
Naked Single: r1c1=5
Full House: r1c9=8
Naked Single: r3c1=9
Full House: r2c1=7
Naked Single: r8c4=4
Naked Single: r2c4=8
Full House: r6c4=9
Full House: r6c5=8
Naked Single: r8c1=6
Full House: r7c1=4
Naked Single: r9c6=2
Full House: r2c6=4
Full House: r2c5=2
Naked Single: r8c5=5
Full House: r8c9=2
Naked Single: r2c7=9
Full House: r2c8=5
Naked Single: r6c9=6
Naked Single: r7c8=6
Naked Single: r9c9=9
Full House: r7c9=5
Naked Single: r3c8=2
Full House: r3c7=6
Naked Single: r7c5=9
Full House: r7c7=1
Full House: r9c5=6
Naked Single: r9c7=4
Full House: r6c7=2
Full House: r6c8=4
Full House: r9c8=8
|
normal_sudoku_1967 | .6....472...24.56.4....7..1.147....8..3..47.67...8...43....1..5.59.........59.2.. | 865139472137248569492657831914762358583914726726385914378421695259876143641593287 | normal_sudoku_1967 | 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 | 9 | . 6 . . . . 4 7 2
. . . 2 4 . 5 6 .
4 . . . . 7 . . 1
. 1 4 7 . . . . 8
. . 3 . . 4 7 . 6
7 . . . 8 . . . 4
3 . . . . 1 . . 5
. 5 9 . . . . . .
. . . 5 9 . 2 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 865139472137248569492657831914762358583914726726385914378421695259876143641593287 #1 Unfair (1144)
Hidden Single: r2c9=9
Locked Candidates Type 1 (Pointing): 1 in b2 => r1c13<>1
Locked Candidates Type 1 (Pointing): 3 in b3 => r3c245<>3
Hidden Single: r2c2=3
Naked Single: r2c6=8
Naked Single: r2c1=1
Full House: r2c3=7
Hidden Single: r9c3=1
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c23<>8
Locked Candidates Type 2 (Claiming): 3 in c9 => r8c78,r9c8<>3
Naked Pair: 2,9 in r36c2 => r57c2<>2, r5c2<>9
Naked Single: r5c2=8
Hidden Pair: 4,8 in r78c4 => r78c4<>6, r8c4<>3
2-String Kite: 6 in r6c3,r9c6 (connected by r7c3,r9c1) => r6c6<>6
W-Wing: 8/4 in r7c4,r9c8 connected by 4 in r8c48 => r7c78<>8
XY-Chain: 6 6- r7c7 -9- r7c8 -4- r9c8 -8- r9c1 -6 => r7c3<>6
Hidden Single: r6c3=6
Hidden Single: r3c4=6
Naked Single: r3c5=5
Naked Single: r3c3=2
Naked Single: r3c2=9
Naked Single: r7c3=8
Full House: r1c3=5
Full House: r1c1=8
Naked Single: r6c2=2
Naked Single: r7c4=4
Naked Single: r9c1=6
Naked Single: r7c2=7
Full House: r9c2=4
Full House: r8c1=2
Naked Single: r7c8=9
Naked Single: r8c4=8
Naked Single: r9c6=3
Naked Single: r9c8=8
Full House: r9c9=7
Full House: r8c9=3
Naked Single: r7c7=6
Full House: r7c5=2
Naked Single: r1c6=9
Naked Single: r8c6=6
Full House: r8c5=7
Naked Single: r3c8=3
Full House: r3c7=8
Naked Single: r8c7=1
Full House: r8c8=4
Naked Single: r5c5=1
Naked Single: r6c6=5
Full House: r4c6=2
Naked Single: r1c5=3
Full House: r1c4=1
Full House: r4c5=6
Naked Single: r5c4=9
Full House: r6c4=3
Naked Single: r6c8=1
Full House: r6c7=9
Full House: r4c7=3
Naked Single: r4c8=5
Full House: r4c1=9
Full House: r5c1=5
Full House: r5c8=2
|
normal_sudoku_3981 | ......4.22.18.4.79..492.8.....6..14.14539.627....4.9.84.9.1.78..2.4...9181.7.92.4 | 698537412231864579754921836982675143145398627376142958469213785527486391813759264 | normal_sudoku_3981 | 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 | 9 | . . . . . . 4 . 2
2 . 1 8 . 4 . 7 9
. . 4 9 2 . 8 . .
. . . 6 . . 1 4 .
1 4 5 3 9 . 6 2 7
. . . . 4 . 9 . 8
4 . 9 . 1 . 7 8 .
. 2 . 4 . . . 9 1
8 1 . 7 . 9 2 . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 698537412231864579754921836982675143145398627376142958469213785527486391813759264 #1 Extreme (2040)
Full House: r5c6=8
Hidden Single: r8c5=8
Hidden Pair: 8,9 in r14c2 => r14c2<>3, r1c2<>5, r1c2<>6, r14c2<>7
2-String Kite: 5 in r2c7,r9c5 (connected by r8c7,r9c8) => r2c5<>5
Turbot Fish: 5 r2c7 =5= r8c7 -5- r8c1 =5= r7c2 => r2c2<>5
Hidden Single: r2c7=5
Full House: r8c7=3
Skyscraper: 3 in r2c5,r7c6 (connected by r27c2) => r13c6,r9c5<>3
Hidden Single: r7c6=3
Hidden Single: r9c3=3
Hidden Single: r7c4=2
2-String Kite: 5 in r3c2,r8c6 (connected by r7c2,r8c1) => r3c6<>5
Locked Candidates Type 1 (Pointing): 5 in b2 => r1c1<>5
2-String Kite: 5 in r4c9,r9c5 (connected by r7c9,r9c8) => r4c5<>5
Naked Single: r4c5=7
Swordfish: 5 c458 r169 => r16c6<>5
W-Wing: 3/6 in r2c2,r3c9 connected by 6 in r7c29 => r3c12<>3
Locked Candidates Type 2 (Claiming): 3 in r3 => r1c8<>3
Multi Colors 1: 6 (r2c2) / (r2c5), (r3c9,r7c2,r8c6,r9c8) / (r7c9,r9c5) => r1c5,r3c12,r6c2<>6
Locked Pair: 5,7 in r3c12 => r1c13,r3c6<>7
Hidden Single: r1c6=7
2-String Kite: 6 in r3c6,r9c8 (connected by r8c6,r9c5) => r3c8<>6
XY-Chain: 3 3- r1c5 -5- r1c4 -1- r6c4 -5- r4c6 -2- r4c3 -8- r1c3 -6- r2c2 -3 => r1c1,r2c5<>3
Naked Single: r2c5=6
Full House: r2c2=3
Naked Single: r3c6=1
Naked Single: r9c5=5
Full House: r1c5=3
Full House: r1c4=5
Full House: r8c6=6
Full House: r9c8=6
Full House: r6c4=1
Full House: r7c9=5
Full House: r7c2=6
Naked Single: r6c2=7
Naked Single: r3c8=3
Naked Single: r6c6=2
Full House: r4c6=5
Naked Single: r8c3=7
Full House: r8c1=5
Naked Single: r1c8=1
Full House: r3c9=6
Full House: r4c9=3
Full House: r6c8=5
Naked Single: r3c2=5
Full House: r3c1=7
Naked Single: r6c3=6
Full House: r6c1=3
Naked Single: r4c1=9
Full House: r1c1=6
Naked Single: r1c3=8
Full House: r1c2=9
Full House: r4c2=8
Full House: r4c3=2
|
normal_sudoku_1916 | ..2.951371..327...5374.....3.....7.9.5...83....1..36..816759423..3.....6.2563.871 | 462895137198327564537416298384562719659178342271943685816759423743281956925634871 | normal_sudoku_1916 | 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 | 9 | . . 2 . 9 5 1 3 7
1 . . 3 2 7 . . .
5 3 7 4 . . . . .
3 . . . . . 7 . 9
. 5 . . . 8 3 . .
. . 1 . . 3 6 . .
8 1 6 7 5 9 4 2 3
. . 3 . . . . . 6
. 2 5 6 3 . 8 7 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 462895137198327564537416298384562719659178342271943685816759423743281956925634871 #1 Easy (210)
Naked Single: r1c4=8
Naked Single: r9c6=4
Full House: r9c1=9
Hidden Single: r3c7=2
Naked Single: r3c9=8
Hidden Single: r8c5=8
Hidden Single: r3c8=9
Naked Single: r2c7=5
Full House: r8c7=9
Full House: r8c8=5
Naked Single: r2c9=4
Full House: r2c8=6
Naked Single: r5c9=2
Full House: r6c9=5
Hidden Single: r4c4=5
Hidden Single: r6c1=2
Naked Single: r6c4=9
Naked Single: r5c4=1
Full House: r8c4=2
Full House: r8c6=1
Naked Single: r5c8=4
Naked Single: r3c6=6
Full House: r3c5=1
Full House: r4c6=2
Naked Single: r5c3=9
Naked Single: r6c8=8
Full House: r4c8=1
Naked Single: r2c3=8
Full House: r2c2=9
Full House: r4c3=4
Naked Single: r4c5=6
Full House: r4c2=8
Naked Single: r6c2=7
Full House: r5c1=6
Full House: r5c5=7
Full House: r6c5=4
Naked Single: r8c2=4
Full House: r1c2=6
Full House: r1c1=4
Full House: r8c1=7
|
normal_sudoku_3738 | ..8159..4.4.....5......489.7..6......1.3.5..7.869.7..58...96.2..9...1..8..7.3.... | 628159374149783256573264891735618942914325687286947135851496723392571468467832519 | normal_sudoku_3738 | 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 | 9 | . . 8 1 5 9 . . 4
. 4 . . . . . 5 .
. . . . . 4 8 9 .
7 . . 6 . . . . .
. 1 . 3 . 5 . . 7
. 8 6 9 . 7 . . 5
8 . . . 9 6 . 2 .
. 9 . . . 1 . . 8
. . 7 . 3 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 628159374149783256573264891735618942914325687286947135851496723392571468467832519 #1 Unfair (1024)
Hidden Single: r2c6=3
Locked Candidates Type 1 (Pointing): 4 in b5 => r8c5<>4
Finned X-Wing: 7 r27 c47 fr2c5 => r3c4<>7
Naked Single: r3c4=2
Finned Swordfish: 2 c269 r249 fr1c2 => r2c13<>2
Locked Candidates Type 1 (Pointing): 2 in b1 => r1c7<>2
Finned Swordfish: 6 r158 c178 fr1c2 => r23c1<>6
Locked Pair: 1,9 in r2c13 => r2c79,r3c13<>1
Hidden Single: r3c9=1
Naked Single: r7c9=3
Naked Single: r7c2=5
Hidden Single: r4c3=5
Naked Single: r3c3=3
Naked Single: r3c1=5
Hidden Single: r4c2=3
Hidden Single: r8c1=3
Locked Candidates Type 1 (Pointing): 9 in b4 => r5c7<>9
Locked Candidates Type 1 (Pointing): 6 in b7 => r9c789<>6
Naked Single: r9c9=9
Naked Single: r4c9=2
Full House: r2c9=6
Naked Single: r4c6=8
Full House: r9c6=2
Naked Single: r8c5=7
Naked Single: r9c2=6
Naked Single: r2c5=8
Naked Single: r3c5=6
Full House: r3c2=7
Full House: r2c4=7
Full House: r1c2=2
Naked Single: r7c4=4
Naked Single: r2c7=2
Naked Single: r1c1=6
Naked Single: r7c3=1
Full House: r7c7=7
Naked Single: r8c4=5
Full House: r9c4=8
Naked Single: r2c3=9
Full House: r2c1=1
Naked Single: r9c1=4
Full House: r8c3=2
Full House: r5c3=4
Naked Single: r1c7=3
Full House: r1c8=7
Naked Single: r6c1=2
Full House: r5c1=9
Naked Single: r9c8=1
Full House: r9c7=5
Naked Single: r5c5=2
Naked Single: r5c7=6
Full House: r5c8=8
Naked Single: r4c8=4
Naked Single: r8c7=4
Full House: r8c8=6
Full House: r6c8=3
Naked Single: r4c5=1
Full House: r4c7=9
Full House: r6c7=1
Full House: r6c5=4
|
normal_sudoku_169 | 8.......66.....32.1.45...8.49.......7.349...5561278.3.91785264334..1.2..2..643.9. | 872934516659187324134526987498365172723491865561278439917852643346719258285643791 | normal_sudoku_169 | 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 | 9 | 8 . . . . . . . 6
6 . . . . . 3 2 .
1 . 4 5 . . . 8 .
4 9 . . . . . . .
7 . 3 4 9 . . . 5
5 6 1 2 7 8 . 3 .
9 1 7 8 5 2 6 4 3
3 4 . . 1 . 2 . .
2 . . 6 4 3 . 9 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 872934516659187324134526987498365172723491865561278439917852643346719258285643791 #1 Easy (220)
Naked Single: r2c5=8
Hidden Single: r4c6=5
Hidden Single: r5c2=2
Full House: r4c3=8
Naked Single: r9c3=5
Naked Single: r2c3=9
Naked Single: r8c3=6
Full House: r9c2=8
Full House: r1c3=2
Naked Single: r1c5=3
Naked Single: r4c5=6
Full House: r3c5=2
Naked Single: r5c6=1
Full House: r4c4=3
Naked Single: r5c7=8
Full House: r5c8=6
Hidden Single: r4c9=2
Hidden Single: r8c9=8
Hidden Single: r2c2=5
Naked Single: r1c2=7
Full House: r3c2=3
Hidden Single: r8c8=5
Naked Single: r1c8=1
Full House: r4c8=7
Full House: r4c7=1
Naked Single: r1c4=9
Naked Single: r9c7=7
Full House: r9c9=1
Naked Single: r1c6=4
Full House: r1c7=5
Naked Single: r8c4=7
Full House: r2c4=1
Full House: r8c6=9
Naked Single: r3c7=9
Full House: r6c7=4
Full House: r6c9=9
Naked Single: r2c6=7
Full House: r2c9=4
Full House: r3c9=7
Full House: r3c6=6
|
normal_sudoku_89 | ..621...4..1.7629..7294..1.72..54.3..5...9..2..37.2....3.42..5.2.....84.....97.21 | 986213574341576298572948613728654139654139782193782465837421956219365847465897321 | normal_sudoku_89 | 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 | 9 | . . 6 2 1 . . . 4
. . 1 . 7 6 2 9 .
. 7 2 9 4 . . 1 .
7 2 . . 5 4 . 3 .
. 5 . . . 9 . . 2
. . 3 7 . 2 . . .
. 3 . 4 2 . . 5 .
2 . . . . . 8 4 .
. . . . 9 7 . 2 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 986213574341576298572948613728654139654139782193782465837421956219365847465897321 #1 Hard (980)
Locked Candidates Type 1 (Pointing): 5 in b1 => r9c1<>5
Locked Candidates Type 1 (Pointing): 1 in b5 => r8c4<>1
Locked Candidates Type 2 (Claiming): 8 in c5 => r45c4<>8
Locked Candidates Type 2 (Claiming): 6 in c8 => r4c79,r56c7,r6c9<>6
Hidden Single: r4c4=6
Naked Single: r6c5=8
Naked Single: r5c5=3
Full House: r5c4=1
Full House: r8c5=6
Naked Single: r6c8=6
Hidden Single: r4c7=1
Hidden Single: r5c1=6
Hidden Single: r9c2=6
Naked Single: r9c7=3
Locked Candidates Type 1 (Pointing): 8 in b4 => r79c3<>8
Locked Candidates Type 1 (Pointing): 8 in b7 => r123c1<>8
Locked Candidates Type 2 (Claiming): 7 in c9 => r7c7<>7
Naked Triple: 6,7,9 in r7c379 => r7c1<>9
2-String Kite: 9 in r4c3,r7c7 (connected by r4c9,r6c7) => r7c3<>9
Naked Single: r7c3=7
Hidden Single: r8c9=7
W-Wing: 4/8 in r2c2,r9c1 connected by 8 in r29c4 => r2c1<>4
Hidden Single: r2c2=4
Hidden Single: r1c2=8
Naked Single: r1c8=7
Full House: r5c8=8
Naked Single: r1c7=5
Naked Single: r4c9=9
Full House: r4c3=8
Naked Single: r5c3=4
Full House: r5c7=7
Naked Single: r1c6=3
Full House: r1c1=9
Naked Single: r3c7=6
Naked Single: r6c7=4
Full House: r6c9=5
Full House: r7c7=9
Full House: r7c9=6
Naked Single: r9c3=5
Full House: r8c3=9
Naked Single: r6c1=1
Full House: r6c2=9
Full House: r8c2=1
Naked Single: r9c4=8
Full House: r9c1=4
Full House: r7c1=8
Full House: r7c6=1
Naked Single: r8c6=5
Full House: r3c6=8
Full House: r2c4=5
Full House: r8c4=3
Naked Single: r3c9=3
Full House: r2c9=8
Full House: r2c1=3
Full House: r3c1=5
|
normal_sudoku_2285 | ...8..276...7.2..1.2.......28.49.157....85.424.52.78.985.92.7.49.4.78.2..725.4... | 341859276598762431627341985286493157719685342435217869853926714964178523172534698 | normal_sudoku_2285 | 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 | 9 | . . . 8 . . 2 7 6
. . . 7 . 2 . . 1
. 2 . . . . . . .
2 8 . 4 9 . 1 5 7
. . . . 8 5 . 4 2
4 . 5 2 . 7 8 . 9
8 5 . 9 2 . 7 . 4
9 . 4 . 7 8 . 2 .
. 7 2 5 . 4 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 341859276598762431627341985286493157719685342435217869853926714964178523172534698 #1 Unfair (1554)
Skyscraper: 1 in r6c5,r8c4 (connected by r68c2) => r5c4,r9c5<>1
Hidden Single: r6c5=1
Naked Pair: 3,6 in r4c3,r6c2 => r5c123<>3, r5c123<>6
XYZ-Wing: 3/5/6 in r58c7,r8c9 => r9c7<>3
Hidden Rectangle: 1/7 in r3c13,r5c13 => r3c3<>1
Almost Locked Set Chain: 3- r6c2 {36} -6- r6c8 {36} -3- r2379c8 {13689} -6- r8c79,r9c7 {3569} -3 => r8c2<>3
Discontinuous Nice Loop: 6 r3c4 -6- r5c4 =6= r5c7 -6- r6c8 =6= r6c2 -6- r8c2 -1- r8c4 =1= r3c4 => r3c4<>6
W-Wing: 3/6 in r4c6,r9c5 connected by 6 in r58c4 => r7c6<>3
Skyscraper: 3 in r6c2,r7c3 (connected by r67c8) => r4c3<>3
Naked Single: r4c3=6
Full House: r4c6=3
Full House: r5c4=6
Naked Single: r6c2=3
Full House: r6c8=6
Full House: r5c7=3
Hidden Single: r7c6=6
Naked Single: r9c5=3
Full House: r8c4=1
Full House: r3c4=3
Naked Single: r9c9=8
Naked Single: r8c2=6
Naked Single: r3c9=5
Full House: r8c9=3
Full House: r8c7=5
Naked Single: r9c1=1
Full House: r7c3=3
Full House: r7c8=1
Naked Single: r5c1=7
Naked Single: r9c8=9
Full House: r9c7=6
Naked Single: r3c1=6
Naked Single: r3c8=8
Full House: r2c8=3
Naked Single: r3c5=4
Naked Single: r2c1=5
Full House: r1c1=3
Naked Single: r1c5=5
Full House: r2c5=6
Naked Single: r3c7=9
Full House: r2c7=4
Naked Single: r3c3=7
Full House: r3c6=1
Full House: r1c6=9
Naked Single: r2c2=9
Full House: r2c3=8
Naked Single: r1c3=1
Full House: r1c2=4
Full House: r5c2=1
Full House: r5c3=9
|
normal_sudoku_825 | 2....9.3....2..9....9.4...6.....5.1.526391..731....5...4...7..86...8......89.4... | 261859734473216985859743126984675312526391847317428569142537698695182473738964251 | normal_sudoku_825 | 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 | 9 | 2 . . . . 9 . 3 .
. . . 2 . . 9 . .
. . 9 . 4 . . . 6
. . . . . 5 . 1 .
5 2 6 3 9 1 . . 7
3 1 . . . . 5 . .
. 4 . . . 7 . . 8
6 . . . 8 . . . .
. . 8 9 . 4 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 261859734473216985859743126984675312526391847317428569142537698695182473738964251 #1 Extreme (3042)
Locked Pair: 4,7 in r46c3 => r12c3,r4c1<>4, r128c3,r4c12<>7
Hidden Single: r2c1=4
Locked Candidates Type 1 (Pointing): 8 in b4 => r4c47<>8
Locked Candidates Type 1 (Pointing): 9 in b4 => r4c9<>9
Locked Candidates Type 1 (Pointing): 8 in b5 => r6c8<>8
Locked Candidates Type 2 (Claiming): 4 in r5 => r4c79,r6c89<>4
Uniqueness Test 4: 4/7 in r4c34,r6c34 => r46c4<>7
Locked Candidates Type 1 (Pointing): 7 in b5 => r12c5<>7
2-String Kite: 7 in r2c8,r9c1 (connected by r2c2,r3c1) => r9c8<>7
Discontinuous Nice Loop: 6 r6c5 -6- r4c4 -4- r4c3 -7- r4c5 =7= r6c5 => r6c5<>6
Forcing Chain Contradiction in r1 => r3c7<>7
r3c7=7 r2c8<>7 r2c2=7 r2c2<>6 r1c2=6 r1c2<>8
r3c7=7 r3c4<>7 r1c4=7 r1c4<>8
r3c7=7 r89c7<>7 r8c8=7 r8c8<>4 r5c8=4 r5c8<>8 r5c7=8 r1c7<>8
Forcing Chain Contradiction in r2c3 => r7c3<>1
r7c3=1 r2c3<>1
r7c3=1 r7c3<>2 r8c3=2 r8c6<>2 r8c6=3 r3c6<>3 r3c2=3 r2c3<>3
r7c3=1 r1c3<>1 r1c3=5 r2c3<>5
Forcing Chain Contradiction in r2c3 => r7c3<>5
r7c3=5 r1c3<>5 r1c3=1 r2c3<>1
r7c3=5 r7c3<>2 r8c3=2 r8c6<>2 r8c6=3 r3c6<>3 r3c2=3 r2c3<>3
r7c3=5 r2c3<>5
Finned Franken Swordfish: 5 r37b7 c248 fr7c5 fr8c3 => r8c4<>5
Naked Single: r8c4=1
Locked Candidates Type 1 (Pointing): 1 in b7 => r3c1<>1
Hidden Single: r3c7=1
Naked Single: r2c9=5
Naked Single: r1c9=4
Hidden Single: r9c9=1
Naked Single: r9c1=7
Naked Single: r3c1=8
Naked Single: r3c6=3
Naked Single: r4c1=9
Full House: r7c1=1
Naked Single: r8c6=2
Naked Single: r4c2=8
Hidden Single: r3c8=2
Hidden Single: r8c2=9
Naked Single: r8c9=3
Naked Single: r4c9=2
Full House: r6c9=9
Naked Single: r8c3=5
Naked Single: r6c8=6
Naked Single: r1c3=1
Naked Single: r9c2=3
Full House: r7c3=2
Naked Single: r4c7=3
Naked Single: r6c6=8
Full House: r2c6=6
Naked Single: r9c8=5
Naked Single: r2c3=3
Naked Single: r7c7=6
Naked Single: r6c4=4
Naked Single: r1c5=5
Naked Single: r2c2=7
Naked Single: r2c5=1
Full House: r2c8=8
Full House: r1c7=7
Naked Single: r7c8=9
Naked Single: r9c5=6
Full House: r9c7=2
Naked Single: r7c4=5
Full House: r7c5=3
Naked Single: r4c4=6
Naked Single: r6c3=7
Full House: r4c3=4
Full House: r4c5=7
Full House: r6c5=2
Naked Single: r3c4=7
Full House: r3c2=5
Full House: r1c2=6
Full House: r1c4=8
Naked Single: r5c8=4
Full House: r5c7=8
Full House: r8c7=4
Full House: r8c8=7
|
normal_sudoku_917 | ...61..78.1..8..9338..95.16147.......23..17..5..247.31.7.35916....17...9..1.2...7 | 459613278716482593382795416147938625923561784568247931874359162235176849691824357 | normal_sudoku_917 | 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 | 9 | . . . 6 1 . . 7 8
. 1 . . 8 . . 9 3
3 8 . . 9 5 . 1 6
1 4 7 . . . . . .
. 2 3 . . 1 7 . .
5 . . 2 4 7 . 3 1
. 7 . 3 5 9 1 6 .
. . . 1 7 . . . 9
. . 1 . 2 . . . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 459613278716482593382795416147938625923561784568247931874359162235176849691824357 #1 Easy (218)
Naked Single: r5c5=6
Full House: r4c5=3
Naked Single: r4c6=8
Hidden Single: r1c6=3
Hidden Single: r3c4=7
Naked Single: r2c4=4
Full House: r2c6=2
Naked Single: r9c4=8
Naked Single: r2c7=5
Naked Single: r2c3=6
Full House: r2c1=7
Hidden Single: r4c7=6
Hidden Single: r6c2=6
Hidden Single: r4c4=9
Full House: r5c4=5
Naked Single: r5c9=4
Naked Single: r5c8=8
Full House: r5c1=9
Full House: r6c3=8
Full House: r6c7=9
Naked Single: r7c9=2
Full House: r4c9=5
Full House: r4c8=2
Naked Single: r7c3=4
Full House: r7c1=8
Naked Single: r3c3=2
Full House: r3c7=4
Full House: r1c7=2
Naked Single: r9c1=6
Naked Single: r1c1=4
Full House: r8c1=2
Naked Single: r8c3=5
Full House: r1c3=9
Full House: r1c2=5
Naked Single: r9c7=3
Full House: r8c7=8
Naked Single: r9c6=4
Full House: r8c6=6
Naked Single: r8c2=3
Full House: r8c8=4
Full House: r9c2=9
Full House: r9c8=5
|
normal_sudoku_1868 | .4..7.1....52...741..9.4..851..8.7..43...528.6.....5..7..8.6432..4.2..17......8.5 | 942378156385261974176954328519482763437615289628739541751896432894523617263147895 | normal_sudoku_1868 | 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 | 9 | . 4 . . 7 . 1 . .
. . 5 2 . . . 7 4
1 . . 9 . 4 . . 8
5 1 . . 8 . 7 . .
4 3 . . . 5 2 8 .
6 . . . . . 5 . .
7 . . 8 . 6 4 3 2
. . 4 . 2 . . 1 7
. . . . . . 8 . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 942378156385261974176954328519482763437615289628739541751896432894523617263147895 #1 Extreme (3884)
Locked Candidates Type 1 (Pointing): 3 in b6 => r1c9<>3
Naked Triple: 3,6,9 in r1c9,r23c7 => r13c8<>6, r1c8<>9
Discontinuous Nice Loop: 3 r3c5 -3- r3c7 -6- r8c7 =6= r8c2 =5= r8c4 -5- r1c4 =5= r3c5 => r3c5<>3
Discontinuous Nice Loop: 3 r9c5 -3- r8c6 -9- r8c7 =9= r9c8 -9- r6c8 -4- r6c5 =4= r9c5 => r9c5<>3
Almost Locked Set XY-Wing: A=r4c36 {239}, B=r9c8 {69}, C=r8c67 {369}, X,Y=3,6, Z=9 => r4c8<>9
Empty Rectangle: 9 in b4 (r69c8) => r9c3<>9
Almost Locked Set XY-Wing: A=r6c45689 {123479}, B=r134579c3 {1236789}, C=r148c6 {2389}, X,Y=2,8, Z=7,9 => r6c3<>7, r6c3<>9
Almost Locked Set XY-Wing: A=r9c1238 {12369}, B=r1248c6 {12389}, C=r457c3 {1279}, X,Y=1,2, Z=3,9 => r9c6<>3, r9c6<>9
Forcing Chain Contradiction in r5 => r3c7=3
r3c7<>3 r3c3=3 r3c3<>7 r5c3=7 r5c3<>9
r3c7<>3 r3c7=6 r8c7<>6 r8c7=9 r8c6<>9 r79c5=9 r5c5<>9
r3c7<>3 r3c7=6 r1c9<>6 r1c9=9 r5c9<>9
Grouped Discontinuous Nice Loop: 6 r1c3 -6- r1c9 =6= r2c7 -6- r8c7 =6= r8c2 =5= r8c4 -5- r1c4 =5= r3c5 =6= r3c23 -6- r1c3 => r1c3<>6
Empty Rectangle: 6 in b5 (r1c49) => r5c9<>6
Locked Candidates Type 1 (Pointing): 6 in b6 => r4c4<>6
AIC: 7 7- r3c2 =7= r3c3 =6= r9c3 -6- r9c8 =6= r4c8 -6- r4c9 =6= r1c9 -6- r1c4 =6= r5c4 =7= r5c3 -7 => r3c3,r6c2<>7
Hidden Single: r3c2=7
Hidden Single: r5c3=7
2-String Kite: 9 in r5c5,r9c8 (connected by r5c9,r6c8) => r9c5<>9
XY-Wing: 1/9/6 in r15c9,r5c4 => r1c4<>6
Hidden Single: r1c9=6
Naked Single: r2c7=9
Full House: r8c7=6
Full House: r9c8=9
Naked Single: r6c8=4
Naked Single: r4c8=6
Hidden Single: r5c4=6
Hidden Single: r4c4=4
Hidden Single: r9c5=4
Naked Pair: 3,5 in r18c4 => r69c4<>3
Locked Pair: 1,7 in r9c46 => r7c5,r9c3<>1
Hidden Single: r7c3=1
Locked Candidates Type 1 (Pointing): 3 in b8 => r8c1<>3
W-Wing: 6/2 in r3c3,r9c2 connected by 2 in r19c1 => r2c2,r9c3<>6
Naked Single: r2c2=8
Naked Single: r2c1=3
Naked Single: r2c6=1
Full House: r2c5=6
Naked Single: r9c1=2
Naked Single: r9c6=7
Naked Single: r3c5=5
Naked Single: r1c1=9
Full House: r8c1=8
Naked Single: r9c2=6
Naked Single: r9c3=3
Full House: r9c4=1
Naked Single: r1c4=3
Full House: r1c6=8
Naked Single: r3c8=2
Full House: r1c8=5
Full House: r1c3=2
Full House: r3c3=6
Naked Single: r7c5=9
Full House: r7c2=5
Full House: r8c2=9
Full House: r6c2=2
Naked Single: r6c4=7
Full House: r8c4=5
Full House: r8c6=3
Naked Single: r4c3=9
Full House: r6c3=8
Naked Single: r5c5=1
Full House: r5c9=9
Full House: r6c5=3
Naked Single: r6c6=9
Full House: r4c6=2
Full House: r4c9=3
Full House: r6c9=1
|
normal_sudoku_594 | 419..8.3.6734...8.528.....7251..73..9862.37..734..9...3.5...81.1.7.8..298.2.9..7. | 419578632673412985528936147251867394986243751734159268395724816167385429842691573 | normal_sudoku_594 | 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 | 9 | 4 1 9 . . 8 . 3 .
6 7 3 4 . . . 8 .
5 2 8 . . . . . 7
2 5 1 . . 7 3 . .
9 8 6 2 . 3 7 . .
7 3 4 . . 9 . . .
3 . 5 . . . 8 1 .
1 . 7 . 8 . . 2 9
8 . 2 . 9 . . 7 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 419578632673412985528936147251867394986243751734159268395724816167385429842691573 #1 Unfair (986)
Hidden Single: r4c8=9
Hidden Single: r8c4=3
Hidden Single: r9c9=3
Hidden Single: r2c7=9
Hidden Single: r3c4=9
Hidden Single: r7c2=9
Hidden Single: r3c5=3
Locked Candidates Type 1 (Pointing): 4 in b5 => r7c5<>4
Locked Candidates Type 1 (Pointing): 5 in b9 => r16c7<>5
Locked Candidates Type 1 (Pointing): 5 in b3 => r56c9<>5
Hidden Rectangle: 6/8 in r4c49,r6c49 => r6c9<>6
Hidden Rectangle: 6/7 in r1c45,r7c45 => r1c5<>6
Turbot Fish: 6 r1c4 =6= r3c6 -6- r3c8 =6= r6c8 => r6c4<>6
AIC: 6 6- r1c7 -2- r6c7 =2= r6c9 =8= r6c4 -8- r4c4 -6- r1c4 =6= r3c6 -6 => r1c4,r3c78<>6
Naked Single: r3c8=4
Naked Single: r3c7=1
Full House: r3c6=6
Naked Single: r5c8=5
Full House: r6c8=6
Naked Single: r6c7=2
Naked Single: r1c7=6
Hidden Single: r7c9=6
Naked Single: r7c4=7
Naked Single: r1c4=5
Naked Single: r7c5=2
Full House: r7c6=4
Naked Single: r1c9=2
Full House: r1c5=7
Full House: r2c9=5
Naked Single: r2c5=1
Full House: r2c6=2
Naked Single: r8c6=5
Full House: r9c6=1
Full House: r9c4=6
Naked Single: r5c5=4
Full House: r5c9=1
Naked Single: r6c5=5
Full House: r4c5=6
Naked Single: r8c7=4
Full House: r8c2=6
Full House: r9c2=4
Full House: r9c7=5
Naked Single: r4c4=8
Full House: r4c9=4
Full House: r6c9=8
Full House: r6c4=1
|
normal_sudoku_3721 | 526..1..8.97...6...8..6..9......38.....12...3.3.84..2....5..37..4..72..197531..8. | 526491738197238645483765192264953817859127463731846529612589374348672951975314286 | normal_sudoku_3721 | 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 | 9 | 5 2 6 . . 1 . . 8
. 9 7 . . . 6 . .
. 8 . . 6 . . 9 .
. . . . . 3 8 . .
. . . 1 2 . . . 3
. 3 . 8 4 . . 2 .
. . . 5 . . 3 7 .
. 4 . . 7 2 . . 1
9 7 5 3 1 . . 8 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 526491738197238645483765192264953817859127463731846529612589374348672951975314286 #1 Extreme (2772)
Locked Candidates Type 1 (Pointing): 2 in b7 => r7c9<>2
Locked Candidates Type 1 (Pointing): 4 in b8 => r23c6<>4
Locked Candidates Type 1 (Pointing): 8 in b8 => r7c13<>8
Locked Triple: 1,2,6 in r7c123 => r7c69,r8c1<>6
Locked Candidates Type 2 (Claiming): 3 in r3 => r2c1<>3
2-String Kite: 1 in r2c1,r6c7 (connected by r2c8,r3c7) => r6c1<>1
2-String Kite: 6 in r4c4,r9c9 (connected by r8c4,r9c6) => r4c9<>6
Hidden Rectangle: 1/2 in r4c13,r7c13 => r4c1<>1
Discontinuous Nice Loop: 4 r4c1 -4- r2c1 -1- r2c8 =1= r4c8 -1- r4c2 =1= r7c2 =6= r7c1 =2= r4c1 => r4c1<>4
Discontinuous Nice Loop: 5 r4c8 -5- r4c5 =5= r2c5 =3= r2c8 =1= r4c8 => r4c8<>5
Discontinuous Nice Loop: 5 r5c8 -5- r5c2 =5= r4c2 -5- r4c5 -9- r1c5 =9= r1c4 -9- r8c4 -6- r8c8 -5- r5c8 => r5c8<>5
XY-Chain: 5 5- r4c5 -9- r1c5 -3- r1c8 -4- r5c8 -6- r5c2 -5 => r4c2,r5c6<>5
Hidden Single: r5c2=5
XY-Chain: 4 4- r5c8 -6- r8c8 -5- r8c7 -9- r7c9 -4 => r4c9<>4
AIC: 4 4- r7c9 -9- r8c7 -5- r8c8 =5= r2c8 =1= r4c8 -1- r4c2 -6- r4c4 =6= r8c4 -6- r9c6 -4 => r7c6,r9c79<>4
Naked Single: r9c7=2
Naked Single: r9c9=6
Full House: r9c6=4
Naked Single: r8c8=5
Naked Single: r8c7=9
Full House: r7c9=4
Naked Single: r8c4=6
Naked Pair: 4,7 in r15c7 => r3c7<>4, r36c7<>7
Naked Triple: 5,7,9 in r4c459 => r4c1<>7, r4c3<>9
Skyscraper: 7 in r1c7,r4c9 (connected by r14c4) => r3c9,r5c7<>7
Naked Single: r5c7=4
Naked Single: r1c7=7
Naked Single: r5c8=6
Naked Single: r4c8=1
Naked Single: r4c2=6
Full House: r7c2=1
Naked Single: r6c7=5
Full House: r3c7=1
Naked Single: r4c1=2
Naked Single: r6c1=7
Naked Single: r7c3=2
Naked Single: r4c3=4
Naked Single: r7c1=6
Naked Single: r5c1=8
Naked Single: r6c9=9
Full House: r4c9=7
Naked Single: r3c3=3
Naked Single: r5c3=9
Full House: r6c3=1
Full House: r6c6=6
Full House: r8c3=8
Full House: r8c1=3
Full House: r5c6=7
Naked Single: r4c4=9
Full House: r4c5=5
Naked Single: r3c1=4
Full House: r2c1=1
Naked Single: r3c6=5
Naked Single: r1c4=4
Naked Single: r2c6=8
Full House: r7c6=9
Full House: r7c5=8
Naked Single: r3c9=2
Full House: r2c9=5
Full House: r3c4=7
Full House: r2c4=2
Naked Single: r1c8=3
Full House: r1c5=9
Full House: r2c5=3
Full House: r2c8=4
|
normal_sudoku_4857 | .1..28....2315...48.54.312......47...5.9...42.....59..5.13.24...42.8153....54.2.1 | 714628395923157684865493127239814756157936842486275913591362478642781539378549261 | normal_sudoku_4857 | 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 | 9 | . 1 . . 2 8 . . .
. 2 3 1 5 . . . 4
8 . 5 4 . 3 1 2 .
. . . . . 4 7 . .
. 5 . 9 . . . 4 2
. . . . . 5 9 . .
5 . 1 3 . 2 4 . .
. 4 2 . 8 1 5 3 .
. . . 5 4 . 2 . 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 714628395923157684865493127239814756157936842486275913591362478642781539378549261 #1 Extreme (6886)
Naked Pair: 6,7 in r18c4 => r46c4<>6, r6c4<>7
Finned Franken Swordfish: 9 r28b8 c168 fr7c5 fr8c9 => r7c8<>9
Sashimi Swordfish: 9 r378 c259 fr8c1 => r9c2<>9
Forcing Net Verity => r1c1<>9
r8c1=6 (r8c1<>9 r8c9=9 r3c9<>9) (r1c1<>6) (r2c1<>6) r8c4<>6 r1c4=6 (r1c7<>6) (r2c6<>6) r1c3<>6 r3c2=6 r3c2<>9 r3c5=9 r2c6<>9 r2c6=7 (r2c1<>7) r5c6<>7 r5c6=6 r5c7<>6 r2c7=6 r2c1<>6 r2c1=9 r1c1<>9
r8c1=7 (r8c1<>9 r8c9=9 r9c8<>9) (r2c1<>7) r8c4<>7 r1c4=7 r2c6<>7 r2c8=7 r2c8<>9 r1c8=9 r1c1<>9
r8c1=9 r1c1<>9
Forcing Net Verity => r1c3<>7
r8c1=6 (r8c1<>9 r8c9=9 r3c9<>9) (r1c1<>6) (r2c1<>6) r8c4<>6 r1c4=6 (r2c6<>6) r1c3<>6 r3c2=6 r3c2<>9 r3c5=9 r2c6<>9 r2c6=7 (r5c6<>7 r5c6=6 r5c3<>6) (r5c6<>7 r5c6=6 r5c7<>6) r1c4<>7 r1c4=6 (r2c6<>6) r1c7<>6 r1c7=3 r5c7<>3 r5c7=8 r5c3<>8 r5c3=7 r1c3<>7
r8c4=6 r1c4<>6 r1c4=7 r1c3<>7
r8c9=6 (r8c9<>9 r8c1=9 r2c1<>9) (r3c9<>6) r8c4<>6 r1c4=6 r3c5<>6 r3c2=6 r2c1<>6 r2c1=7 r1c3<>7
Forcing Net Verity => r1c1<>6
r8c1=7 (r8c1<>9) (r8c4<>7 r1c4=7 r1c9<>7 r7c9=7 r7c5<>7 r7c5=9 r9c6<>9) (r8c4<>7 r1c4=7 r2c6<>7 r2c8=7 r2c8<>9) (r2c1<>7 r3c2=7 r3c2<>9) r8c1<>9 r8c9=9 (r9c8<>9) r3c9<>9 r3c5=9 r2c6<>9 r2c1=9 (r9c1<>9) r9c1<>9 r9c3=9 r9c6<>9 r2c6=9 r2c1<>9 r4c1=9 r4c1<>2 r4c4=2 r6c4<>2 r6c1=2 r6c1<>4 r6c3=4 r1c3<>4 r1c1=4 r1c1<>6
r8c4=7 r1c4<>7 r1c4=6 r1c1<>6
r8c9=7 (r8c9<>9 r8c1=9 r2c1<>9) (r7c8<>7) (r9c8<>7) r8c4<>7 r1c4=7 r1c8<>7 r2c8=7 r2c1<>7 r2c1=6 r1c1<>6
Hidden Rectangle: 4/7 in r1c13,r6c13 => r6c3<>7
Forcing Chain Contradiction in r2 => r8c1<>7
r8c1=7 r2c1<>7
r8c1=7 r8c4<>7 r1c4=7 r2c6<>7
r8c1=7 r9c3<>7 r5c3=7 r5c3<>8 r5c7=8 r2c7<>8 r2c8=8 r2c8<>7
Forcing Chain Contradiction in r9c6 => r9c3<>9
r9c3=9 r9c3<>7 r5c3=7 r5c6<>7 r5c6=6 r9c6<>6
r9c3=9 r8c1<>9 r8c1=6 r8c4<>6 r8c4=7 r9c6<>7
r9c3=9 r9c6<>9
Forcing Chain Contradiction in r3 => r9c6<>7
r9c6=7 r9c123<>7 r7c2=7 r3c2<>7
r9c6=7 r5c6<>7 r56c5=7 r3c5<>7
r9c6=7 r8c4<>7 r8c9=7 r3c9<>7
Discontinuous Nice Loop: 6 r3c5 -6- r1c4 -7- r8c4 =7= r7c5 =9= r3c5 => r3c5<>6
Grouped Discontinuous Nice Loop: 7 r5c1 -7- r5c6 -6- r5c7 =6= r12c7 -6- r3c9 =6= r3c2 =7= r12c1 -7- r5c1 => r5c1<>7
Grouped Discontinuous Nice Loop: 7 r9c1 -7- r9c3 =7= r5c3 =8= r5c7 =6= r12c7 -6- r3c9 =6= r3c2 =7= r12c1 -7- r9c1 => r9c1<>7
Finned Franken Swordfish: 6 r38b2 c149 fr2c6 fr3c2 => r2c1<>6
Discontinuous Nice Loop: 7 r3c2 -7- r2c1 -9- r8c1 -6- r8c4 =6= r1c4 -6- r1c3 =6= r3c2 => r3c2<>7
Locked Candidates Type 1 (Pointing): 7 in b1 => r6c1<>7
Skyscraper: 7 in r3c5,r8c4 (connected by r38c9) => r1c4,r7c5<>7
Naked Single: r1c4=6
Naked Single: r1c7=3
Naked Single: r8c4=7
Hidden Single: r3c2=6
Naked Pair: 7,9 in r2c16 => r2c8<>7, r2c8<>9
Naked Triple: 6,7,8 in r5c367 => r5c15<>6, r5c5<>7
Turbot Fish: 9 r1c3 =9= r2c1 -9- r8c1 =9= r8c9 => r1c9<>9
Turbot Fish: 9 r2c1 =9= r1c3 -9- r1c8 =9= r9c8 => r9c1<>9
W-Wing: 6/9 in r7c5,r8c9 connected by 9 in r3c59 => r7c89<>6
Hidden Single: r7c5=6
Full House: r9c6=9
Naked Single: r2c6=7
Full House: r3c5=9
Full House: r5c6=6
Full House: r3c9=7
Naked Single: r2c1=9
Naked Single: r5c7=8
Full House: r2c7=6
Full House: r2c8=8
Naked Single: r1c9=5
Full House: r1c8=9
Naked Single: r1c3=4
Full House: r1c1=7
Naked Single: r8c1=6
Full House: r8c9=9
Naked Single: r5c3=7
Naked Single: r7c8=7
Naked Single: r9c1=3
Naked Single: r7c9=8
Full House: r9c8=6
Full House: r7c2=9
Naked Single: r9c3=8
Full House: r9c2=7
Naked Single: r5c1=1
Full House: r5c5=3
Naked Single: r6c8=1
Full House: r4c8=5
Naked Single: r6c3=6
Full House: r4c3=9
Naked Single: r4c1=2
Full House: r6c1=4
Naked Single: r4c5=1
Full House: r6c5=7
Naked Single: r6c9=3
Full House: r4c9=6
Naked Single: r4c4=8
Full House: r4c2=3
Full House: r6c2=8
Full House: r6c4=2
|
normal_sudoku_4525 | .....93589..835.7..38.7.6...9...8.3.21...386..8..1...4.6...7.8.15..8.2..8..5..... | 741269358926835471538471629694758132217943865385612794462197583159386247873524916 | normal_sudoku_4525 | 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 | 9 | . . . . . 9 3 5 8
9 . . 8 3 5 . 7 .
. 3 8 . 7 . 6 . .
. 9 . . . 8 . 3 .
2 1 . . . 3 8 6 .
. 8 . . 1 . . . 4
. 6 . . . 7 . 8 .
1 5 . . 8 . 2 . .
8 . . 5 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 741269358926835471538471629694758132217943865385612794462197583159386247873524916 #1 Hard (642)
Hidden Single: r3c1=5
Hidden Single: r2c3=6
Hidden Single: r1c3=1
Locked Candidates Type 1 (Pointing): 2 in b1 => r9c2<>2
Locked Candidates Type 1 (Pointing): 1 in b2 => r3c89<>1
Hidden Single: r9c8=1
Hidden Single: r7c4=1
Hidden Single: r3c6=1
Hidden Single: r8c4=3
Locked Candidates Type 1 (Pointing): 9 in b8 => r5c5<>9
Locked Candidates Type 2 (Claiming): 4 in c6 => r79c5<>4
Sashimi X-Wing: 4 r27 c27 fr7c1 fr7c3 => r9c2<>4
Naked Single: r9c2=7
Hidden Single: r1c1=7
Hidden Single: r8c9=7
Hidden Single: r8c6=6
Naked Single: r6c6=2
Full House: r9c6=4
Naked Single: r6c8=9
Naked Single: r9c7=9
Naked Single: r5c9=5
Naked Single: r8c8=4
Full House: r3c8=2
Full House: r8c3=9
Naked Single: r9c5=2
Full House: r7c5=9
Naked Single: r5c5=4
Naked Single: r6c7=7
Naked Single: r7c9=3
Naked Single: r7c7=5
Full House: r9c9=6
Full House: r9c3=3
Naked Single: r2c9=1
Naked Single: r3c4=4
Full House: r3c9=9
Full House: r2c7=4
Full House: r4c7=1
Full House: r4c9=2
Full House: r2c2=2
Full House: r1c2=4
Naked Single: r1c5=6
Full House: r1c4=2
Full House: r4c5=5
Naked Single: r5c3=7
Full House: r5c4=9
Naked Single: r6c4=6
Full House: r4c4=7
Naked Single: r7c1=4
Full House: r7c3=2
Naked Single: r6c3=5
Full House: r4c3=4
Full House: r6c1=3
Full House: r4c1=6
|
normal_sudoku_573 | .6.8.49.....2....44....5.8.8..5.1.7.753648219..173...8...18..4.1..45...7.....7... | 367814952985276134412395786896521473753648219241739568679182345128453697534967821 | normal_sudoku_573 | 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 | 9 | . 6 . 8 . 4 9 . .
. . . 2 . . . . 4
4 . . . . 5 . 8 .
8 . . 5 . 1 . 7 .
7 5 3 6 4 8 2 1 9
. . 1 7 3 . . . 8
. . . 1 8 . . 4 .
1 . . 4 5 . . . 7
. . . . . 7 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 367814952985276134412395786896521473753648219241739568679182345128453697534967821 #1 Extreme (13420)
Forcing Chain Contradiction in r2c8 => r8c8<>6
r8c8=6 r8c8<>9 r9c8=9 r9c4<>9 r9c4=3 r3c4<>3 r2c6=3 r2c8<>3
r8c8=6 r6c8<>6 r6c8=5 r2c8<>5
r8c8=6 r2c8<>6
Forcing Net Contradiction in r9 => r1c9<>3
r1c9=3 r4c9<>3 r4c9=6 (r6c7<>6) r6c8<>6 r6c1=6 r9c1<>6
r1c9=3 (r3c9<>3) (r1c8<>3) r4c9<>3 r4c9=6 (r3c9<>6) r6c8<>6 r6c8=5 (r2c8<>5 r2c7=5 r2c7<>1) r1c8<>5 r1c8=2 r3c9<>2 r3c9=1 (r9c9<>1 r9c7=1 r9c7<>8) r1c9<>1 r1c5=1 r2c5<>1 r2c2=1 r2c2<>8 r2c3=8 r9c3<>8 r9c2=8 r9c2<>4 r9c3=4 r9c3<>6
r1c9=3 (r2c8<>3) r4c9<>3 r4c9=6 (r3c9<>6) r6c8<>6 r6c8=5 r2c8<>5 r2c8=6 r3c7<>6 r3c5=6 r9c5<>6
r1c9=3 (r1c9<>5) r4c9<>3 (r4c7=3 r7c7<>3) r4c9=6 r6c8<>6 r6c8=5 (r1c8<>5) r2c8<>5 r2c7=5 r7c7<>5 r7c7=6 r9c7<>6
r1c9=3 (r2c8<>3) r4c9<>3 r4c9=6 r6c8<>6 r6c8=5 r2c8<>5 r2c8=6 r9c8<>6
r1c9=3 r4c9<>3 r4c9=6 r9c9<>6
Forcing Net Verity => r2c1<>3
r2c6=3 r2c1<>3
r2c6=6 (r2c6<>3 r3c4=3 r9c4<>3 r9c4=9 r9c1<>9) (r2c8<>6) (r2c5<>6) r3c5<>6 r9c5=6 (r9c5<>2 r4c5=2 r6c6<>2 r6c6=9 r6c1<>9) (r9c1<>6) r9c8<>6 r6c8=6 r6c1<>6 r7c1=6 r7c1<>9 r2c1=9 r2c1<>3
r2c6=9 (r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c8<>2) r3c4<>9 r9c4=9 r9c8<>9 r8c8=9 r8c8<>2 r1c8=2 r1c8<>3 r1c1=3 r2c1<>3
Forcing Net Contradiction in r8c8 => r2c5<>9
r2c5=9 (r3c4<>9 r9c4=9 r8c6<>9 r6c6=9 r6c1<>9) (r3c4<>9 r9c4=9 r9c1<>9) (r9c5<>9) r4c5<>9 r4c5=2 r9c5<>2 r9c5=6 (r9c1<>6) (r9c8<>6) r8c6<>6 r2c6=6 (r7c6<>6) r2c8<>6 r6c8=6 r6c1<>6 r7c1=6 r7c1<>9 r2c1=9 r2c5<>9
Forcing Net Contradiction in c1 => r2c6<>9
r2c6=9 (r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c8<>2) r3c4<>9 r9c4=9 r9c8<>9 r8c8=9 r8c8<>2 r1c8=2 r1c1<>2
r2c6=9 r6c6<>9 r6c6=2 r6c1<>2
r2c6=9 (r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c9<>2) (r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c8<>2) r3c4<>9 r9c4=9 r9c8<>9 r8c8=9 r8c8<>2 r1c8=2 (r1c9<>2) r3c9<>2 r7c9=2 r7c1<>2
r2c6=9 r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c1<>2
Locked Candidates Type 1 (Pointing): 9 in b2 => r3c23<>9
Almost Locked Set XY-Wing: A=r3c3 {27}, B=r9c14589 {123569}, C=r1c1389 {12357}, X,Y=1,7, Z=2 => r9c3<>2
Almost Locked Set XY-Wing: A=r49c5 {269}, B=r26c8 {356}, C=r123c5,r2c6 {13679}, X,Y=3,9, Z=6 => r9c8<>6
Discontinuous Nice Loop: 3 r9c9 -3- r9c4 =3= r3c4 -3- r2c6 -6- r2c8 =6= r6c8 -6- r4c9 -3- r9c9 => r9c9<>3
Forcing Chain Contradiction in b3 => r4c3<>2
r4c3=2 r4c3<>6 r6c1=6 r6c8<>6 r6c8=5 r1c8<>5
r4c3=2 r3c3<>2 r3c3=7 r1c3<>7 r1c5=7 r1c5<>1 r1c9=1 r1c9<>5
r4c3=2 r3c3<>2 r3c3=7 r3c7<>7 r2c7=7 r2c7<>5
r4c3=2 r4c3<>6 r6c1=6 r6c8<>6 r6c8=5 r2c8<>5
Forcing Chain Contradiction in r8c3 => r7c2<>2
r7c2=2 r8c3<>2
r7c2=2 r46c2<>2 r6c1=2 r6c1<>6 r4c3=6 r8c3<>6
r7c2=2 r7c2<>7 r7c3=7 r1c3<>7 r1c5=7 r1c5<>1 r1c9=1 r9c9<>1 r9c7=1 r9c7<>8 r8c7=8 r8c3<>8
r7c2=2 r4c2<>2 r4c5=2 r4c5<>9 r6c6=9 r7c6<>9 r7c123=9 r8c3<>9
Forcing Chain Contradiction in r9c8 => r9c3<>9
r9c3=9 r7c123<>9 r7c6=9 r6c6<>9 r6c6=2 r4c5<>2 r9c5=2 r9c8<>2
r9c3=9 r9c4<>9 r9c4=3 r9c8<>3
r9c3=9 r9c3<>4 r9c2=4 r6c2<>4 r6c7=4 r6c7<>5 r6c8=5 r9c8<>5
r9c3=9 r9c8<>9
Forcing Chain Verity => r9c7<>3
r8c3=6 r4c3<>6 r6c1=6 r6c8<>6 r2c8=6 r2c6<>6 r2c6=3 r3c4<>3 r9c4=3 r9c7<>3
r8c6=6 r2c6<>6 r2c6=3 r3c4<>3 r9c4=3 r9c7<>3
r8c7=6 r8c7<>8 r9c7=8 r9c7<>3
Forcing Net Verity => r2c1=9
r3c2=3 r3c2<>1 r2c2=1 (r2c2<>9) r2c2<>8 r2c3=8 r2c3<>9 r2c1=9
r3c4=3 (r9c4<>3 r9c4=9 r8c6<>9 r6c6=9 r6c1<>9) (r9c4<>3 r9c4=9 r9c1<>9) r2c6<>3 r2c6=6 (r2c8<>6 r6c8=6 r6c1<>6) (r2c5<>6) r3c5<>6 r9c5=6 r9c1<>6 r7c1=6 r7c1<>9 r2c1=9
r3c7=3 (r3c7<>7 r2c7=7 r2c2<>7) (r1c8<>3 r1c1=3 r7c1<>3) (r7c7<>3) (r3c4<>3 r9c4=3 r7c6<>3) r4c7<>3 r4c9=3 r7c9<>3 r7c2=3 r7c2<>7 r3c2=7 r3c2<>1 r2c2=1 (r2c2<>9) r2c2<>8 r2c3=8 r2c3<>9 r2c1=9
r3c9=3 (r1c8<>3 r1c1=3 r7c1<>3) (r3c4<>3 r9c4=3 r7c6<>3) (r7c9<>3) r4c9<>3 (r4c9=6 r6c8<>6 r6c8=5 r1c8<>5 r1c8=2 r1c3<>2) r4c7=3 r7c7<>3 r7c2=3 r7c2<>7 r7c3=7 r1c3<>7 r1c3=5 r2c1<>5 r2c1=9
Empty Rectangle: 9 in b8 (r6c26) => r9c2<>9
Finned X-Wing: 9 r67 c26 fr7c3 => r8c2<>9
Forcing Chain Contradiction in r8c2 => r1c1<>2
r1c1=2 r6c1<>2 r46c2=2 r8c2<>2
r1c1=2 r1c1<>3 r79c1=3 r8c2<>3
r1c1=2 r3c3<>2 r3c3=7 r1c3<>7 r1c5=7 r1c5<>1 r1c9=1 r9c9<>1 r9c7=1 r9c7<>8 r8c7=8 r8c2<>8
Forcing Chain Contradiction in r8c3 => r2c2<>3
r2c2=3 r2c2<>1 r3c2=1 r3c2<>2 r13c3=2 r8c3<>2
r2c2=3 r2c6<>3 r2c6=6 r2c8<>6 r6c8=6 r6c1<>6 r4c3=6 r8c3<>6
r2c2=3 r2c2<>8 r2c3=8 r8c3<>8
r2c2=3 r2c6<>3 r3c4=3 r3c4<>9 r9c4=9 r9c8<>9 r8c8=9 r8c3<>9
Turbot Fish: 3 r1c1 =3= r3c2 -3- r3c4 =3= r9c4 => r9c1<>3
Forcing Chain Contradiction in r7 => r7c3<>2
r7c3=2 r7c3<>7 r7c2=7 r7c2<>9
r7c3=2 r7c3<>9
r7c3=2 r79c1<>2 r6c1=2 r6c6<>2 r6c6=9 r7c6<>9
Forcing Chain Contradiction in c8 => r7c9<>3
r7c9=3 r7c1<>3 r1c1=3 r1c8<>3
r7c9=3 r4c9<>3 r4c9=6 r6c8<>6 r2c8=6 r2c8<>3
r7c9=3 r8c8<>3
r7c9=3 r9c8<>3
Forcing Chain Verity => r7c7<>5
r7c1=3 r1c1<>3 r1c1=5 r1c9<>5 r79c9=5 r7c7<>5
r7c2=3 r7c2<>7 r7c3=7 r1c3<>7 r1c5=7 r1c5<>1 r1c9=1 r1c9<>5 r79c9=5 r7c7<>5
r7c6=3 r2c6<>3 r2c6=6 r2c8<>6 r6c8=6 r6c8<>5 r6c7=5 r7c7<>5
r7c7=3 r7c7<>5
Almost Locked Set XY-Wing: A=r4c235 {2469}, B=r9c145789 {1235689}, C=r478c7 {3468}, X,Y=4,8, Z=6 => r9c3<>6
Almost Locked Set XY-Wing: A=r9c145789 {1235689}, B=r123478c3 {2456789}, C=r478c7 {3468}, X,Y=4,8, Z=5 => r9c3<>5
Forcing Chain Contradiction in r7c9 => r1c1=3
r1c1<>3 r1c8=3 r1c8<>2 r89c8=2 r7c9<>2
r1c1<>3 r1c1=5 r9c1<>5 r7c13=5 r7c9<>5
r1c1<>3 r7c1=3 r7c7<>3 r7c7=6 r7c9<>6
Locked Candidates Type 1 (Pointing): 5 in b1 => r7c3<>5
AIC: 1 1- r1c9 =1= r1c5 =7= r1c3 =5= r2c3 =8= r2c2 =1= r3c2 -1 => r3c79<>1
Discontinuous Nice Loop: 7 r3c5 -7- r3c7 =7= r2c7 =1= r1c9 -1- r1c5 -7- r3c5 => r3c5<>7
Discontinuous Nice Loop: 8 r8c2 -8- r8c7 =8= r9c7 =1= r9c9 -1- r1c9 =1= r1c5 =7= r1c3 =5= r2c3 =8= r2c2 -8- r8c2 => r8c2<>8
Grouped AIC: 6 6- r7c7 -3- r89c8 =3= r2c8 -3- r2c6 -6- r23c5 =6= r9c5 -6 => r7c6,r9c79<>6
XYZ-Wing: 2/3/9 in r67c6,r9c4 => r8c6<>9
Sashimi Swordfish: 6 c168 r268 fr7c1 fr9c1 => r8c3<>6
Empty Rectangle: 6 in b9 (r47c3) => r4c7<>6
W-Wing: 3/6 in r2c6,r7c7 connected by 6 in r8c67 => r2c7,r7c6<>3
Naked Pair: 2,9 in r67c6 => r8c6<>2
2-String Kite: 3 in r2c8,r9c4 (connected by r2c6,r3c4) => r9c8<>3
X-Wing: 3 c68 r28 => r8c27<>3
Naked Single: r8c2=2
Hidden Single: r4c5=2
Full House: r6c6=9
Naked Single: r6c2=4
Naked Single: r7c6=2
Naked Single: r4c2=9
Naked Single: r4c3=6
Full House: r6c1=2
Naked Single: r4c9=3
Full House: r4c7=4
Hidden Single: r9c3=4
Hidden Single: r7c3=9
Naked Single: r8c3=8
Naked Single: r8c7=6
Naked Single: r9c2=3
Naked Single: r6c7=5
Full House: r6c8=6
Naked Single: r7c7=3
Naked Single: r7c9=5
Naked Single: r8c6=3
Full House: r8c8=9
Full House: r2c6=6
Naked Single: r7c2=7
Full House: r7c1=6
Full House: r9c1=5
Naked Single: r9c4=9
Full House: r3c4=3
Full House: r9c5=6
Naked Single: r3c7=7
Naked Single: r9c8=2
Naked Single: r3c2=1
Full House: r2c2=8
Naked Single: r2c7=1
Full House: r9c7=8
Full House: r9c9=1
Naked Single: r3c3=2
Naked Single: r1c8=5
Full House: r2c8=3
Naked Single: r3c5=9
Full House: r3c9=6
Full House: r1c9=2
Naked Single: r2c5=7
Full House: r1c5=1
Full House: r1c3=7
Full House: r2c3=5
|
normal_sudoku_903 | ..3...9..68...93..91..2..6...9.5861...1.7.5.9.5......74..5..1....8..6.9.....8.4.6 | 523864971684719352917325864279458613341672589856931247462597138138246795795183426 | normal_sudoku_903 | 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 | 9 | . . 3 . . . 9 . .
6 8 . . . 9 3 . .
9 1 . . 2 . . 6 .
. . 9 . 5 8 6 1 .
. . 1 . 7 . 5 . 9
. 5 . . . . . . 7
4 . . 5 . . 1 . .
. . 8 . . 6 . 9 .
. . . . 8 . 4 . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 523864971684719352917325864279458613341672589856931247462597138138246795795183426 #1 Extreme (10858)
Grouped Discontinuous Nice Loop: 2 r7c9 -2- r8c7 -7- r3c7 -8- r13c9 =8= r7c9 => r7c9<>2
Almost Locked Set XY-Wing: A=r6c13678 {123468}, B=r1234589c4 {12346789}, C=r7c35689 {236789}, X,Y=6,9, Z=1,2,3,4 => r6c4<>1, r6c4<>2, r6c4<>3, r6c4<>4
Forcing Chain Verity => r1c9<>5
r1c4=1 r1c4<>8 r3c4=8 r3c4<>3 r3c6=3 r3c6<>5 r1c6=5 r1c9<>5
r2c4=1 r2c9<>1 r1c9=1 r1c9<>5
r8c4=1 r8c4<>4 r8c5=4 r2c5<>4 r2c5=1 r2c9<>1 r1c9=1 r1c9<>5
r9c4=1 r9c1<>1 r8c1=1 r8c1<>5 r8c9=5 r1c9<>5
Forcing Net Contradiction in r2 => r1c5=6
r1c5<>6 (r6c5=6 r6c5<>3) r1c4=6 (r5c4<>6 r5c2=6 r7c2<>6 r7c3=6 r7c3<>7) r6c4<>6 r6c4=9 r6c5<>9 r7c5=9 r7c5<>3 r8c5=3 r8c2<>3 r8c2=7 (r9c3<>7) r8c7<>7 (r8c7=2 r8c2<>2) r3c7=7 r3c3<>7 r2c3=7
r1c5<>6 r1c4=6 (r1c4<>7) r1c4<>8 r3c4=8 (r3c4<>7) (r3c7<>8 r3c7=7 r3c6<>7) r3c4<>3 r3c6=3 r3c6<>5 r1c6=5 r1c6<>7 r2c4=7
Continuous Nice Loop: 2/3/7 9= r7c2 =6= r7c3 -6- r6c3 =6= r6c4 =9= r6c5 -9- r7c5 =9= r7c2 =6 => r7c2<>2, r7c2<>3, r7c2<>7
Forcing Net Verity => r1c6<>7
r7c3=7 r23c3<>7 r1c12=7 r1c6<>7
r7c6=7 r1c6<>7
r7c8=7 (r8c7<>7 r3c7=7 r3c7<>8) r7c8<>8 r7c9=8 r3c9<>8 r3c4=8 r3c4<>3 r3c6=3 r3c6<>5 r1c6=5 r1c6<>7
Empty Rectangle: 7 in b2 (r38c7) => r8c4<>7
Forcing Chain Verity => r1c4<>1
r1c1=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c4<>8 r1c4=8 r1c4<>1
r1c2=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c4<>8 r1c4=8 r1c4<>1
r1c4=7 r1c4<>1
r1c8=7 r3c7<>7 r3c7=8 r3c4<>8 r1c4=8 r1c4<>1
Discontinuous Nice Loop: 8 r1c9 -8- r1c4 =8= r3c4 =3= r3c6 =5= r1c6 =1= r1c9 => r1c9<>8
Forcing Chain Verity => r7c9=8
r1c1=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c9<>8 r7c9=8
r1c2=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c9<>8 r7c9=8
r1c4=7 r1c4<>8 r1c8=8 r7c8<>8 r7c9=8
r1c8=7 r3c7<>7 r3c7=8 r3c9<>8 r7c9=8
Discontinuous Nice Loop: 4 r1c9 -4- r3c9 -5- r3c6 =5= r1c6 =1= r1c9 => r1c9<>4
Almost Locked Set XZ-Rule: A=r1c6,r2c45 {1457}, B=r123c9,r2c8 {12457}, X=7, Z=5 => r1c8<>5
Forcing Chain Contradiction in c3 => r1c9=1
r1c9<>1 r1c9=2 r1c12<>2 r2c3=2 r2c3<>4
r1c9<>1 r1c6=1 r1c6<>5 r3c6=5 r3c9<>5 r3c9=4 r3c3<>4
r1c9<>1 r1c6=1 r6c6<>1 r6c5=1 r6c5<>9 r6c4=9 r6c4<>6 r6c3=6 r6c3<>4
Forcing Chain Contradiction in c3 => r6c6=1
r6c6<>1 r6c5=1 r2c5<>1 r2c5=4 r2c3<>4
r6c6<>1 r9c6=1 r9c1<>1 r8c1=1 r8c1<>5 r8c9=5 r3c9<>5 r3c9=4 r3c3<>4
r6c6<>1 r6c5=1 r6c5<>9 r6c4=9 r6c4<>6 r6c3=6 r6c3<>4
Forcing Chain Verity => r1c4<>4
r1c1=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c4<>8 r1c4=8 r1c4<>4
r1c2=7 r23c3<>7 r79c3=7 r8c12<>7 r8c7=7 r3c7<>7 r3c7=8 r3c4<>8 r1c4=8 r1c4<>4
r1c4=7 r1c4<>4
r1c8=7 r1c8<>8 r1c4=8 r1c4<>4
Forcing Chain Verity => r4c2<>3
r8c1=3 r8c9<>3 r4c9=3 r4c2<>3
r8c2=3 r4c2<>3
r9c1=3 r9c1<>1 r8c1=1 r8c1<>5 r8c9=5 r8c9<>3 r4c9=3 r4c2<>3
r9c2=3 r4c2<>3
Forcing Chain Contradiction in r1c1 => r6c1<>2
r6c1=2 r1c1<>2
r6c1=2 r6c7<>2 r6c7=8 r3c7<>8 r3c4=8 r3c4<>3 r3c6=3 r3c6<>5 r1c6=5 r1c1<>5
r6c1=2 r6c7<>2 r6c7=8 r3c7<>8 r3c4=8 r1c4<>8 r1c4=7 r1c1<>7
Forcing Chain Contradiction in r9c3 => r4c9<>2
r4c9=2 r6c78<>2 r6c3=2 r9c3<>2
r4c9=2 r4c9<>3 r8c9=3 r8c9<>5 r8c1=5 r9c3<>5
r4c9=2 r6c7<>2 r8c7=2 r8c7<>7 r8c12=7 r9c3<>7
Finned Swordfish: 2 c379 r268 fr7c3 fr9c3 => r8c12<>2
XY-Chain: 3 3- r6c1 -8- r6c7 -2- r8c7 -7- r8c2 -3 => r5c2,r89c1<>3
AIC: 3 3- r4c9 =3= r8c9 -3- r8c2 -7- r8c7 -2- r6c7 -8- r6c1 -3 => r4c1,r6c8<>3
Hidden Pair: 3,8 in r56c1 => r5c1<>2
AIC: 3 3- r7c5 -9- r7c2 =9= r9c2 =3= r8c2 -3 => r8c45<>3
Naked Pair: 1,4 in r28c5 => r6c5<>4
Empty Rectangle: 4 in b1 (r6c38) => r1c8<>4
Discontinuous Nice Loop: 4 r3c3 -4- r3c9 -5- r3c6 =5= r1c6 =4= r1c2 -4- r3c3 => r3c3<>4
Sashimi Swordfish: 4 r134 c249 fr1c6 fr3c6 => r2c4<>4
Sashimi Swordfish: 4 c368 r256 fr1c6 fr3c6 => r2c5<>4
Naked Single: r2c5=1
Naked Single: r2c4=7
Naked Single: r8c5=4
Naked Single: r1c4=8
Hidden Single: r3c7=8
Naked Single: r6c7=2
Full House: r8c7=7
Naked Single: r8c2=3
Hidden Single: r3c3=7
Hidden Single: r1c8=7
Hidden Single: r4c9=3
Hidden Single: r7c6=7
Locked Candidates Type 1 (Pointing): 2 in b3 => r2c3<>2
Locked Candidates Type 1 (Pointing): 4 in b6 => r2c8<>4
Locked Candidates Type 2 (Claiming): 2 in c3 => r9c12<>2
Naked Triple: 2,3,5 in r9c368 => r9c1<>5, r9c4<>2, r9c4<>3
X-Wing: 5 c38 r29 => r2c9<>5
Skyscraper: 4 in r1c6,r4c4 (connected by r14c2) => r3c4,r5c6<>4
Naked Single: r3c4=3
W-Wing: 4/2 in r1c2,r4c4 connected by 2 in r14c1 => r4c2<>4
Hidden Single: r4c4=4
Locked Candidates Type 1 (Pointing): 2 in b5 => r5c2<>2
Bivalue Universal Grave + 1 => r9c8<>3, r9c8<>5
Naked Single: r9c8=2
Naked Single: r2c8=5
Naked Single: r7c8=3
Full House: r8c9=5
Naked Single: r9c3=5
Naked Single: r9c6=3
Naked Single: r2c3=4
Full House: r2c9=2
Full House: r3c9=4
Full House: r3c6=5
Full House: r1c6=4
Full House: r5c6=2
Naked Single: r7c5=9
Full House: r6c5=3
Naked Single: r8c1=1
Full House: r8c4=2
Full House: r9c4=1
Naked Single: r1c2=2
Full House: r1c1=5
Naked Single: r6c3=6
Full House: r7c3=2
Full House: r7c2=6
Naked Single: r5c4=6
Full House: r6c4=9
Naked Single: r6c1=8
Full House: r6c8=4
Full House: r5c8=8
Naked Single: r9c1=7
Full House: r9c2=9
Naked Single: r4c2=7
Full House: r5c2=4
Full House: r5c1=3
Full House: r4c1=2
|
normal_sudoku_1123 | 75..6..232.3...5.....3..7.1........7...6....297.8...45592146378187239.5......8219 | 758961423213784596469352781321495867845617932976823145592146378187239654634578219 | normal_sudoku_1123 | 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 | 9 | 7 5 . . 6 . . 2 3
2 . 3 . . . 5 . .
. . . 3 . . 7 . 1
. . . . . . . . 7
. . . 6 . . . . 2
9 7 . 8 . . . 4 5
5 9 2 1 4 6 3 7 8
1 8 7 2 3 9 . 5 .
. . . . . 8 2 1 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 758961423213784596469352781321495867845617932976823145592146378187239654634578219 #1 Hard (708)
Hidden Single: r4c2=2
Hidden Single: r6c6=3
Hidden Single: r6c5=2
Hidden Single: r3c6=2
Hidden Single: r3c5=5
Naked Single: r9c5=7
Full House: r9c4=5
Hidden Single: r2c5=8
Hidden Single: r5c6=7
Hidden Single: r2c4=7
Hidden Single: r5c3=5
Hidden Single: r4c6=5
Hidden Single: r2c8=9
Hidden Single: r1c4=9
Full House: r4c4=4
Hidden Single: r3c3=9
Locked Candidates Type 2 (Claiming): 4 in r3 => r1c3,r2c2<>4
Hidden Single: r9c3=4
Locked Candidates Type 2 (Claiming): 6 in c3 => r4c1<>6
2-String Kite: 8 in r3c8,r4c3 (connected by r1c3,r3c1) => r4c8<>8
W-Wing: 3/8 in r4c1,r5c8 connected by 8 in r3c18 => r4c8,r5c12<>3
Naked Single: r4c8=6
Naked Single: r3c8=8
Full House: r5c8=3
Naked Single: r6c7=1
Full House: r6c3=6
Naked Single: r1c7=4
Full House: r2c9=6
Full House: r8c9=4
Full House: r8c7=6
Naked Single: r1c6=1
Full House: r1c3=8
Full House: r2c6=4
Full House: r2c2=1
Full House: r4c3=1
Naked Single: r5c2=4
Naked Single: r4c5=9
Full House: r5c5=1
Naked Single: r3c2=6
Full House: r3c1=4
Full House: r9c2=3
Full House: r9c1=6
Naked Single: r5c1=8
Full House: r4c1=3
Full House: r4c7=8
Full House: r5c7=9
|
normal_sudoku_618 | ...1..536...786........5....2.41936..41..38..639578241......415174.52..3.5.341... | 897124536315786924462935178528419367741263859639578241283697415174852693956341782 | normal_sudoku_618 | 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 | 9 | . . . 1 . . 5 3 6
. . . 7 8 6 . . .
. . . . . 5 . . .
. 2 . 4 1 9 3 6 .
. 4 1 . . 3 8 . .
6 3 9 5 7 8 2 4 1
. . . . . . 4 1 5
1 7 4 . 5 2 . . 3
. 5 . 3 4 1 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 897124536315786924462935178528419367741263859639578241283697415174852693956341782 #1 Hard (784)
Naked Single: r4c9=7
Naked Single: r1c6=4
Full House: r7c6=7
Naked Single: r5c9=9
Full House: r5c8=5
Naked Single: r5c1=7
Hidden Single: r3c5=3
Hidden Single: r1c3=7
Locked Candidates Type 1 (Pointing): 8 in b3 => r3c123<>8
Locked Candidates Type 1 (Pointing): 2 in b9 => r9c13<>2
Naked Pair: 1,9 in r2c27 => r2c18<>9
Naked Single: r2c8=2
Naked Single: r2c9=4
Naked Single: r3c9=8
Full House: r9c9=2
Hidden Single: r3c1=4
Naked Triple: 6,8,9 in r7c2,r9c13 => r7c13<>8, r7c1<>9, r7c3<>6
Skyscraper: 9 in r7c5,r9c1 (connected by r1c15) => r7c2<>9
Hidden Single: r9c1=9
Locked Candidates Type 1 (Pointing): 9 in b9 => r8c4<>9
XY-Wing: 6/8/9 in r17c2,r7c5 => r1c5<>9
Naked Single: r1c5=2
Full House: r3c4=9
Naked Single: r1c1=8
Full House: r1c2=9
Naked Single: r5c5=6
Full House: r5c4=2
Full House: r7c5=9
Naked Single: r3c8=7
Naked Single: r4c1=5
Full House: r4c3=8
Naked Single: r2c2=1
Naked Single: r3c7=1
Full House: r2c7=9
Naked Single: r9c8=8
Full House: r8c8=9
Naked Single: r2c1=3
Full House: r2c3=5
Full House: r7c1=2
Naked Single: r9c3=6
Full House: r9c7=7
Full House: r8c7=6
Full House: r8c4=8
Full House: r7c4=6
Naked Single: r3c2=6
Full House: r3c3=2
Full House: r7c3=3
Full House: r7c2=8
|
normal_sudoku_2172 | .3....96.94856.....6..39.8..826..7.949......6.7..9..2.82697.41.754.168..3194...57 | 237841965948562371561739284182653749495287136673194528826975413754316892319428657 | normal_sudoku_2172 | 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 | 9 | . 3 . . . . 9 6 .
9 4 8 5 6 . . . .
. 6 . . 3 9 . 8 .
. 8 2 6 . . 7 . 9
4 9 . . . . . . 6
. 7 . . 9 . . 2 .
8 2 6 9 7 . 4 1 .
7 5 4 . 1 6 8 . .
3 1 9 4 . . . 5 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 237841965948562371561739284182653749495287136673194528826975413754316892319428657 #1 Easy (156)
Naked Single: r5c8=3
Naked Single: r7c9=3
Full House: r7c6=5
Naked Single: r2c8=7
Naked Single: r4c8=4
Full House: r8c8=9
Naked Single: r8c9=2
Full House: r8c4=3
Full House: r9c7=6
Naked Single: r4c5=5
Naked Single: r2c9=1
Naked Single: r4c1=1
Full House: r4c6=3
Naked Single: r2c6=2
Full House: r2c7=3
Naked Single: r5c3=5
Naked Single: r9c6=8
Full House: r9c5=2
Naked Single: r5c7=1
Naked Single: r6c1=6
Full House: r6c3=3
Naked Single: r5c5=8
Full House: r1c5=4
Naked Single: r5c6=7
Full House: r5c4=2
Naked Single: r6c7=5
Full House: r3c7=2
Full House: r6c9=8
Naked Single: r6c4=1
Full House: r6c6=4
Full House: r1c6=1
Naked Single: r1c9=5
Full House: r3c9=4
Naked Single: r3c1=5
Full House: r1c1=2
Naked Single: r3c4=7
Full House: r1c4=8
Full House: r1c3=7
Full House: r3c3=1
|
normal_sudoku_5254 | ....263..53.789.2...2.3...92..37..6...32.......41.5.3..4891...6.9.85.1..125647983 | 987426315531789624462531879259378461813264597674195238348912756796853142125647983 | normal_sudoku_5254 | 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 | 9 | . . . . 2 6 3 . .
5 3 . 7 8 9 . 2 .
. . 2 . 3 . . . 9
2 . . 3 7 . . 6 .
. . 3 2 . . . . .
. . 4 1 . 5 . 3 .
. 4 8 9 1 . . . 6
. 9 . 8 5 . 1 . .
1 2 5 6 4 7 9 8 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 987426315531789624462531879259378461813264597674195238348912756796853142125647983 #1 Easy (214)
Hidden Single: r3c6=1
Hidden Single: r4c3=9
Hidden Single: r5c8=9
Naked Single: r5c5=6
Full House: r6c5=9
Hidden Single: r1c1=9
Hidden Single: r1c8=1
Naked Single: r1c3=7
Naked Single: r2c9=4
Naked Single: r1c2=8
Naked Single: r8c3=6
Full House: r2c3=1
Full House: r2c7=6
Naked Single: r1c9=5
Full House: r1c4=4
Full House: r3c4=5
Naked Single: r3c2=6
Full House: r3c1=4
Naked Single: r3c8=7
Full House: r3c7=8
Naked Single: r6c2=7
Naked Single: r7c8=5
Full House: r8c8=4
Naked Single: r5c1=8
Naked Single: r6c7=2
Naked Single: r5c6=4
Full House: r4c6=8
Naked Single: r6c1=6
Full House: r6c9=8
Naked Single: r7c7=7
Full House: r8c9=2
Naked Single: r4c9=1
Full House: r5c9=7
Naked Single: r5c7=5
Full House: r4c7=4
Full House: r4c2=5
Full House: r5c2=1
Naked Single: r7c1=3
Full House: r7c6=2
Full House: r8c6=3
Full House: r8c1=7
|
normal_sudoku_2103 | 342.1...7596..3..481764.9.362.8..7.1..142.3..45.1.7.9...43..8.5.3....47...5..4.39 | 342918567596273184817645923623859741971426358458137692764392815239581476185764239 | normal_sudoku_2103 | 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 | 9 | 3 4 2 . 1 . . . 7
5 9 6 . . 3 . . 4
8 1 7 6 4 . 9 . 3
6 2 . 8 . . 7 . 1
. . 1 4 2 . 3 . .
4 5 . 1 . 7 . 9 .
. . 4 3 . . 8 . 5
. 3 . . . . 4 7 .
. . 5 . . 4 . 3 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 342918567596273184817645923623859741971426358458137692764392815239581476185764239 #1 Easy (176)
Hidden Single: r4c8=4
Hidden Single: r1c7=5
Naked Single: r1c4=9
Naked Single: r3c8=2
Full House: r3c6=5
Naked Single: r1c6=8
Full House: r1c8=6
Naked Single: r2c7=1
Full House: r2c8=8
Naked Single: r4c6=9
Naked Single: r2c5=7
Full House: r2c4=2
Naked Single: r7c8=1
Full House: r5c8=5
Naked Single: r4c3=3
Full House: r4c5=5
Naked Single: r5c6=6
Full House: r6c5=3
Naked Single: r8c4=5
Full House: r9c4=7
Naked Single: r6c3=8
Full House: r8c3=9
Naked Single: r5c9=8
Naked Single: r7c6=2
Full House: r8c6=1
Naked Single: r5c2=7
Full House: r5c1=9
Naked Single: r7c1=7
Naked Single: r8c1=2
Full House: r9c1=1
Naked Single: r7c2=6
Full House: r7c5=9
Full House: r9c2=8
Naked Single: r8c9=6
Full House: r6c9=2
Full House: r8c5=8
Full House: r9c5=6
Full House: r9c7=2
Full House: r6c7=6
|
normal_sudoku_5281 | .....2..9..91..8.33..8...7..1.92...59376854..2...14.....84..6..7...68.3..63..1..8 | 871342569649157823352896174416923785937685412285714396128439657794568231563271948 | normal_sudoku_5281 | 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 | 9 | . . . . . 2 . . 9
. . 9 1 . . 8 . 3
3 . . 8 . . . 7 .
. 1 . 9 2 . . . 5
9 3 7 6 8 5 4 . .
2 . . . 1 4 . . .
. . 8 4 . . 6 . .
7 . . . 6 8 . 3 .
. 6 3 . . 1 . . 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 871342569649157823352896174416923785937685412285714396128439657794568231563271948 #1 Extreme (3858)
Swordfish: 2 r257 c289 => r3c29,r8c29,r9c8<>2
2-String Kite: 7 in r4c6,r7c9 (connected by r4c7,r6c9) => r7c6<>7
Finned X-Wing: 4 c29 r38 fr1c2 fr2c2 => r3c3<>4
Discontinuous Nice Loop: 4 r1c1 -4- r3c2 -5- r6c2 -8- r1c2 =8= r1c1 => r1c1<>4
Discontinuous Nice Loop: 7 r1c5 -7- r2c6 =7= r4c6 =3= r7c6 -3- r7c5 =3= r1c5 => r1c5<>7
Discontinuous Nice Loop: 5 r3c3 -5- r6c3 =5= r6c2 =8= r1c2 =7= r2c2 =2= r3c3 => r3c3<>5
Discontinuous Nice Loop: 1 r7c8 -1- r7c1 =1= r8c3 =2= r3c3 -2- r3c7 =2= r2c8 -2- r5c8 -1- r7c8 => r7c8<>1
Discontinuous Nice Loop: 5 r8c2 -5- r8c4 -2- r8c3 =2= r7c2 =9= r8c2 => r8c2<>5
Discontinuous Nice Loop: 5 r8c3 -5- r8c4 -2- r9c4 =2= r9c7 =7= r7c9 -7- r6c9 -6- r6c3 -5- r8c3 => r8c3<>5
Discontinuous Nice Loop: 1 r1c1 -1- r1c7 -5- r1c3 =5= r6c3 -5- r6c2 -8- r1c2 =8= r1c1 => r1c1<>1
Hidden Single: r7c1=1
XY-Wing: 2/4/5 in r8c34,r9c1 => r9c45<>5
AIC: 5 5- r1c7 -1- r8c7 =1= r8c9 =4= r3c9 -4- r3c2 -5 => r1c123,r3c7<>5
Hidden Single: r6c3=5
Naked Single: r6c2=8
Hidden Single: r1c1=8
Hidden Single: r4c8=8
AIC: 7 7- r1c2 =7= r2c2 =2= r7c2 -2- r8c3 -4- r4c3 -6- r4c1 =6= r2c1 -6- r2c6 -7 => r1c4,r2c2<>7
Hidden Single: r1c2=7
Skyscraper: 7 in r7c9,r9c4 (connected by r6c49) => r7c5,r9c7<>7
Hidden Single: r7c9=7
Naked Single: r6c9=6
Naked Single: r6c8=9
Hidden Single: r5c9=2
Full House: r5c8=1
Naked Pair: 4,5 in r9c18 => r9c7<>5
X-Wing: 5 c47 r18 => r1c58<>5
W-Wing: 5/2 in r7c8,r8c4 connected by 2 in r9c47 => r7c5,r8c7<>5
Hidden Single: r8c4=5
Naked Single: r1c4=3
Naked Single: r1c5=4
Naked Single: r6c4=7
Full House: r4c6=3
Full House: r6c7=3
Full House: r9c4=2
Full House: r4c7=7
Naked Single: r1c8=6
Naked Single: r7c6=9
Naked Single: r9c7=9
Naked Single: r1c3=1
Full House: r1c7=5
Naked Single: r3c6=6
Full House: r2c6=7
Naked Single: r7c5=3
Full House: r9c5=7
Naked Single: r3c3=2
Naked Single: r2c5=5
Full House: r3c5=9
Naked Single: r3c7=1
Full House: r8c7=2
Naked Single: r8c3=4
Full House: r4c3=6
Full House: r4c1=4
Naked Single: r2c2=4
Naked Single: r3c9=4
Full House: r8c9=1
Full House: r8c2=9
Full House: r2c8=2
Full House: r2c1=6
Full House: r9c1=5
Full House: r3c2=5
Full House: r7c2=2
Full House: r7c8=5
Full House: r9c8=4
|
normal_sudoku_5013 | 14693..785874..9..392..8...23158.76.87.3....1...217.8..2..4..5..........41...3..7 | 146935278587462913392178645231584769874396521659217384723849156968751432415623897 | normal_sudoku_5013 | 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 | 9 | 1 4 6 9 3 . . 7 8
5 8 7 4 . . 9 . .
3 9 2 . . 8 . . .
2 3 1 5 8 . 7 6 .
8 7 . 3 . . . . 1
. . . 2 1 7 . 8 .
. 2 . . 4 . . 5 .
. . . . . . . . .
4 1 . . . 3 . . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 146935278587462913392178645231584769874396521659217384723849156968751432415623897 #1 Unfair (1022)
2-String Kite: 2 in r1c6,r8c9 (connected by r1c7,r2c9) => r8c6<>2
Locked Candidates Type 1 (Pointing): 2 in b8 => r2c5<>2
Naked Single: r2c5=6
Naked Single: r5c5=9
Naked Single: r4c6=4
Full House: r4c9=9
Full House: r5c6=6
W-Wing: 2/5 in r1c7,r9c5 connected by 5 in r18c6 => r9c7<>2
Naked Pair: 6,8 in r9c47 => r9c3<>8
Naked Triple: 4,5,9 in r569c3 => r78c3<>9, r8c3<>5
XY-Wing: 3/6/8 in r7c39,r9c7 => r7c7<>8
Finned Swordfish: 5 r359 c357 fr3c9 => r1c7<>5
Naked Single: r1c7=2
Full House: r1c6=5
Naked Single: r2c9=3
Naked Single: r3c5=7
Naked Single: r2c8=1
Full House: r2c6=2
Full House: r3c4=1
Naked Single: r7c9=6
Naked Single: r3c8=4
Naked Single: r9c7=8
Naked Single: r3c9=5
Full House: r3c7=6
Naked Single: r5c8=2
Naked Single: r9c4=6
Naked Single: r6c9=4
Full House: r8c9=2
Naked Single: r9c8=9
Full House: r8c8=3
Naked Single: r5c7=5
Full House: r5c3=4
Full House: r6c7=3
Naked Single: r8c5=5
Full House: r9c5=2
Full House: r9c3=5
Naked Single: r7c7=1
Full House: r8c7=4
Naked Single: r8c3=8
Naked Single: r8c2=6
Full House: r6c2=5
Naked Single: r6c3=9
Full House: r7c3=3
Full House: r6c1=6
Naked Single: r7c6=9
Full House: r8c6=1
Naked Single: r8c4=7
Full House: r7c4=8
Full House: r7c1=7
Full House: r8c1=9
|
normal_sudoku_4742 | ..1.4..257..6..9.192..15..42.7..451.3...714.241.5...7.1.....358..315.2475....8196 | 631849725754623981928715634267384519385971462419562873146297358893156247572438196 | normal_sudoku_4742 | 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 | 9 | . . 1 . 4 . . 2 5
7 . . 6 . . 9 . 1
9 2 . . 1 5 . . 4
2 . 7 . . 4 5 1 .
3 . . . 7 1 4 . 2
4 1 . 5 . . . 7 .
1 . . . . . 3 5 8
. . 3 1 5 . 2 4 7
5 . . . . 8 1 9 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 631849725754623981928715634267384519385971462419562873146297358893156247572438196 #1 Hard (526)
Locked Candidates Type 2 (Claiming): 2 in c4 => r7c56,r9c5<>2
Naked Single: r9c5=3
Naked Pair: 6,8 in r1c1,r3c3 => r1c2<>6, r12c2,r2c3<>8
Naked Single: r1c2=3
Naked Pair: 6,9 in r7c5,r8c6 => r7c46<>9, r7c6<>6
Naked Single: r7c6=7
Naked Single: r1c6=9
Naked Single: r8c6=6
Naked Single: r7c5=9
Naked Single: r8c1=8
Full House: r1c1=6
Full House: r8c2=9
Naked Single: r3c3=8
Hidden Single: r9c2=7
Naked Pair: 6,8 in r4c25 => r4c4<>8
Skyscraper: 8 in r1c4,r6c5 (connected by r16c7) => r2c5,r5c4<>8
Naked Single: r2c5=2
Naked Single: r5c4=9
Naked Single: r2c6=3
Full House: r6c6=2
Naked Single: r4c4=3
Naked Single: r2c8=8
Naked Single: r3c4=7
Full House: r1c4=8
Full House: r1c7=7
Naked Single: r4c9=9
Full House: r6c9=3
Naked Single: r5c8=6
Full House: r3c8=3
Full House: r3c7=6
Full House: r6c7=8
Naked Single: r5c3=5
Full House: r5c2=8
Naked Single: r6c5=6
Full House: r4c5=8
Full House: r4c2=6
Full House: r6c3=9
Naked Single: r2c3=4
Full House: r2c2=5
Full House: r7c2=4
Naked Single: r9c3=2
Full House: r7c3=6
Full House: r7c4=2
Full House: r9c4=4
|
normal_sudoku_4735 | ...36..2....49.....3...8..9.6.8..2.42...345..4.7....1..4..8..56..1......5.6.4.78. | 914367825875492631632518479163875294298134567457629318749283156381756942526941783 | normal_sudoku_4735 | 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 | 9 | . . . 3 6 . . 2 .
. . . 4 9 . . . .
. 3 . . . 8 . . 9
. 6 . 8 . . 2 . 4
2 . . . 3 4 5 . .
4 . 7 . . . . 1 .
. 4 . . 8 . . 5 6
. . 1 . . . . . .
5 . 6 . 4 . 7 8 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 914367825875492631632518479163875294298134567457629318749283156381756942526941783 #1 Extreme (4400)
Locked Candidates Type 1 (Pointing): 3 in b4 => r4c8<>3
XY-Wing: 7/8/9 in r4c8,r5c39 => r4c13,r5c8<>9
Grouped Discontinuous Nice Loop: 2 r8c5 -2- r6c5 -5- r6c2 =5= r4c3 =3= r7c3 =2= r7c46 -2- r8c5 => r8c5<>2
Forcing Chain Contradiction in c7 => r4c8=9
r4c8<>9 r8c8=9 r8c8<>3 r2c8=3 r2c7<>3
r4c8<>9 r6c7=9 r6c7<>3
r4c8<>9 r4c8=7 r5c9<>7 r5c9=8 r5c3<>8 r56c2=8 r8c2<>8 r8c1=8 r8c1<>3 r7c13=3 r7c7<>3
r4c8<>9 r8c8=9 r8c8<>4 r8c7=4 r8c7<>3
Locked Candidates Type 1 (Pointing): 7 in b6 => r5c4<>7
Forcing Chain Contradiction in r3 => r6c5=2
r6c5<>2 r6c5=5 r6c2<>5 r4c3=5 r3c3<>5
r6c5<>2 r6c5=5 r8c5<>5 r8c5=7 r78c4<>7 r3c4=7 r3c4<>5
r6c5<>2 r6c5=5 r3c5<>5
Finned X-Wing: 2 r37 c34 fr7c6 => r89c4<>2
AIC: 9 9- r8c7 =9= r7c7 =1= r9c9 -1- r9c4 -9 => r8c46<>9
Discontinuous Nice Loop: 2 r7c3 -2- r9c2 -9- r9c4 -1- r5c4 =1= r5c2 -1- r4c1 -3- r4c3 =3= r7c3 => r7c3<>2
Locked Candidates Type 1 (Pointing): 2 in b7 => r2c2<>2
Locked Candidates Type 2 (Claiming): 2 in r7 => r89c6<>2
Discontinuous Nice Loop: 8 r5c2 -8- r5c3 -9- r7c3 -3- r4c3 =3= r4c1 =1= r5c2 => r5c2<>8
Grouped AIC: 2 2- r8c9 -3- r6c9 -8- r6c2 =8= r5c3 =9= r56c2 -9- r9c2 -2 => r8c2,r9c9<>2
Hidden Single: r8c9=2
Hidden Single: r9c2=2
Locked Candidates Type 2 (Claiming): 9 in r9 => r7c46<>9
Almost Locked Set XY-Wing: A=r3c1578 {14567}, B=r5689c4 {15679}, C=r8c12578 {345789}, X,Y=5,7, Z=1 => r3c4<>1
Almost Locked Set Chain: 5- r4c156 {1357} -3- r4c3 {35} -5- r12357c3 {234589} -3- r1247c6 {12357} -5 => r6c6<>5
XYZ-Wing: 1/6/9 in r59c4,r6c6 => r6c4<>9
Hidden Rectangle: 5/6 in r6c46,r8c46 => r8c6<>5
Finned Swordfish: 5 r348 c345 fr4c6 => r6c4<>5
Naked Single: r6c4=6
Naked Single: r6c6=9
Naked Single: r5c4=1
Naked Single: r5c2=9
Naked Single: r9c4=9
Naked Single: r5c3=8
Naked Single: r5c9=7
Full House: r5c8=6
Naked Single: r6c2=5
Naked Single: r4c3=3
Full House: r4c1=1
Naked Single: r7c3=9
Hidden Single: r8c6=6
Hidden Single: r3c5=1
Hidden Single: r1c1=9
Hidden Single: r8c7=9
Hidden Single: r8c8=4
Naked Single: r3c8=7
Full House: r2c8=3
Naked Single: r3c1=6
Naked Single: r3c7=4
Hidden Single: r8c1=3
Naked Single: r7c1=7
Full House: r2c1=8
Full House: r8c2=8
Naked Single: r7c4=2
Naked Single: r3c4=5
Full House: r3c3=2
Full House: r8c4=7
Full House: r8c5=5
Full House: r4c5=7
Full House: r4c6=5
Naked Single: r1c6=7
Full House: r2c6=2
Naked Single: r2c3=5
Full House: r1c3=4
Naked Single: r1c2=1
Full House: r2c2=7
Naked Single: r2c9=1
Full House: r2c7=6
Naked Single: r1c7=8
Full House: r1c9=5
Naked Single: r9c9=3
Full House: r6c9=8
Full House: r6c7=3
Full House: r7c7=1
Full House: r9c6=1
Full House: r7c6=3
|
normal_sudoku_6896 | .68..91.2.......7..17....4.8..39.726..3267...6.2..83....69.2517..9..6.837...5..6. | 568479132924183675317625948845391726193267854672548391486932517259716483731854269 | normal_sudoku_6896 | 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 | 9 | . 6 8 . . 9 1 . 2
. . . . . . . 7 .
. 1 7 . . . . 4 .
8 . . 3 9 . 7 2 6
. . 3 2 6 7 . . .
6 . 2 . . 8 3 . .
. . 6 9 . 2 5 1 7
. . 9 . . 6 . 8 3
7 . . . 5 . . 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 568479132924183675317625948845391726193267854672548391486932517259716483731854269 #1 Medium (320)
Hidden Single: r6c2=7
Hidden Single: r1c8=3
Locked Candidates Type 1 (Pointing): 5 in b3 => r56c9<>5
Locked Candidates Type 1 (Pointing): 9 in b4 => r5c789<>9
Naked Single: r5c8=5
Full House: r6c8=9
Hidden Single: r6c4=5
Hidden Single: r1c1=5
Naked Single: r2c3=4
Naked Single: r9c3=1
Full House: r4c3=5
Naked Single: r4c2=4
Full House: r4c6=1
Full House: r6c5=4
Full House: r6c9=1
Naked Single: r5c2=9
Full House: r5c1=1
Naked Single: r1c5=7
Full House: r1c4=4
Naked Single: r8c5=1
Naked Single: r9c4=8
Naked Single: r8c4=7
Naked Single: r3c4=6
Full House: r2c4=1
Naked Single: r7c5=3
Full House: r9c6=4
Naked Single: r7c1=4
Full House: r7c2=8
Naked Single: r9c9=9
Naked Single: r8c1=2
Naked Single: r9c7=2
Full House: r8c7=4
Full House: r8c2=5
Full House: r9c2=3
Full House: r2c2=2
Naked Single: r5c7=8
Full House: r5c9=4
Naked Single: r2c5=8
Full House: r3c5=2
Naked Single: r3c7=9
Full House: r2c7=6
Naked Single: r2c9=5
Full House: r3c9=8
Naked Single: r3c1=3
Full House: r2c1=9
Full House: r2c6=3
Full House: r3c6=5
|
normal_sudoku_6663 | .7..3.8....69.....18.7.4.39..41...2..2..4.9.8..9..6....5..79.8....4..2.5......7.. | 975632814346918572182754639864195327521347968739826451453279186617483295298561743 | normal_sudoku_6663 | 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 | 9 | . 7 . . 3 . 8 . .
. . 6 9 . . . . .
1 8 . 7 . 4 . 3 9
. . 4 1 . . . 2 .
. 2 . . 4 . 9 . 8
. . 9 . . 6 . . .
. 5 . . 7 9 . 8 .
. . . 4 . . 2 . 5
. . . . . . 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 975632814346918572182754639864195327521347968739826451453279186617483295298561743 #1 Extreme (2222)
Hidden Single: r1c1=9
Hidden Single: r4c5=9
Locked Pair: 2,5 in r13c3 => r2c1,r5c3<>5, r2c1,r79c3<>2
Locked Candidates Type 1 (Pointing): 4 in b1 => r2c789<>4
Locked Candidates Type 1 (Pointing): 8 in b4 => r89c1<>8
Sashimi X-Wing: 1 r57 c38 fr7c7 fr7c9 => r89c8<>1
Hidden Rectangle: 6/9 in r8c28,r9c28 => r9c2<>6
2-String Kite: 6 in r5c8,r8c2 (connected by r4c2,r5c1) => r8c8<>6
Naked Single: r8c8=9
Hidden Single: r9c2=9
Hidden Single: r2c2=4
Naked Single: r2c1=3
Hidden Pair: 2,4 in r79c1 => r79c1<>6
Locked Candidates Type 1 (Pointing): 6 in b7 => r8c5<>6
Sue de Coq: r7c79 - {1346} (r7c3 - {13}, r9c8 - {46}) => r9c9<>4, r9c9<>6, r7c4<>3
Continuous Nice Loop: 3/5/6/7 7= r5c3 =1= r5c8 =6= r5c1 -6- r8c1 -7- r8c3 =7= r5c3 =1 => r5c3<>3, r5c8<>5, r4c1<>6, r5c8<>7
Locked Candidates Type 1 (Pointing): 3 in b4 => r8c2<>3
Locked Candidates Type 2 (Claiming): 3 in r5 => r4c6,r6c4<>3
Discontinuous Nice Loop: 5/7 r4c1 =8= r4c6 =7= r5c6 -7- r5c3 =7= r8c3 =8= r9c3 -8- r9c4 =8= r6c4 -8- r6c1 =8= r4c1 => r4c1<>5, r4c1<>7
Naked Single: r4c1=8
Naked Triple: 3,5,7 in r45c6,r5c4 => r6c45<>5
AIC: 2 2- r7c4 -6- r1c4 =6= r3c5 -6- r3c7 -5- r4c7 =5= r4c6 =7= r5c6 -7- r5c3 -1- r5c8 -6- r9c8 -4- r9c1 -2 => r7c1,r9c456<>2
Naked Single: r7c1=4
Naked Single: r9c1=2
Hidden Single: r7c4=2
Naked Single: r6c4=8
Naked Single: r6c5=2
Hidden Single: r6c7=4
Hidden Single: r9c8=4
Hidden Single: r3c3=2
Full House: r1c3=5
Naked Single: r1c4=6
Naked Single: r1c8=1
Naked Single: r3c5=5
Full House: r3c7=6
Naked Single: r1c6=2
Full House: r1c9=4
Naked Single: r2c7=5
Naked Single: r5c8=6
Naked Single: r2c8=7
Full House: r2c9=2
Full House: r6c8=5
Naked Single: r4c7=3
Full House: r7c7=1
Naked Single: r6c1=7
Naked Single: r4c2=6
Naked Single: r4c9=7
Full House: r6c9=1
Full House: r4c6=5
Full House: r6c2=3
Full House: r8c2=1
Naked Single: r7c3=3
Full House: r7c9=6
Full House: r9c9=3
Naked Single: r5c1=5
Full House: r5c3=1
Full House: r8c1=6
Naked Single: r5c4=3
Full House: r9c4=5
Full House: r5c6=7
Naked Single: r8c5=8
Naked Single: r9c3=8
Full House: r8c3=7
Full House: r8c6=3
Naked Single: r2c5=1
Full House: r2c6=8
Full House: r9c6=1
Full House: r9c5=6
|
normal_sudoku_5168 | 1.28.654....3..2..........76.524.79.72.5..6.4...6.7.524.7..5.26...4..97.29.76.4.5 | 132876549974351268856924137615248793728539614349617852487195326563482971291763485 | normal_sudoku_5168 | 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 | 9 | 1 . 2 8 . 6 5 4 .
. . . 3 . . 2 . .
. . . . . . . . 7
6 . 5 2 4 . 7 9 .
7 2 . 5 . . 6 . 4
. . . 6 . 7 . 5 2
4 . 7 . . 5 . 2 6
. . . 4 . . 9 7 .
2 9 . 7 6 . 4 . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 132876549974351268856924137615248793728539614349617852487195326563482971291763485 #1 Extreme (11458)
Discontinuous Nice Loop: 4 r2c2 -4- r2c6 =4= r3c6 =2= r3c5 =5= r2c5 =7= r2c2 => r2c2<>4
Forcing Net Contradiction in r3 => r2c2<>8
r2c2=8 (r2c2<>6) (r2c2<>5) r2c2<>7 r2c5=7 r2c5<>5 r2c1=5 r8c1<>5 r8c2=5 r8c2<>6 r3c2=6
r2c2=8 r2c2<>7 r2c5=7 (r2c5<>1) r1c5<>7 r1c5=9 (r3c4<>9 r3c4=1 r2c6<>1) r1c9<>9 r2c9=9 r2c9<>1 r2c8=1 r2c8<>6 r3c8=6
Forcing Net Contradiction in b5 => r2c5<>1
r2c5=1 (r3c4<>1 r7c4=1 r7c2<>1) r2c5<>7 r2c2=7 r1c2<>7 r1c2=3 (r4c2<>3) r7c2<>3 r7c2=8 r4c2<>8 r4c2=1 r4c6<>1
r2c5=1 r5c5<>1
r2c5=1 r3c4<>1 r3c4=9 (r2c6<>9) r3c6<>9 r5c6=9 r5c6<>1
r2c5=1 r6c5<>1
Forcing Net Contradiction in c3 => r3c3<>3
r3c3=3 r1c2<>3 r1c2=7 r1c5<>7 r1c5=9 (r2c6<>9) r3c4<>9 r3c4=1 r2c6<>1 r2c6=4 r2c3<>4
r3c3=3 r3c3<>4
r3c3=3 (r3c3<>9) r1c2<>3 r1c2=7 r1c5<>7 r1c5=9 (r6c5<>9) (r3c4<>9) (r3c5<>9) r3c6<>9 r3c1=9 r6c1<>9 r6c3=9 r6c3<>4
Forcing Net Contradiction in b5 => r3c5<>1
r3c5=1 r3c4<>1 (r7c4=1 r7c2<>1) r3c4=9 r1c5<>9 r1c5=7 r1c2<>7 r1c2=3 (r4c2<>3) r7c2<>3 r7c2=8 r4c2<>8 r4c2=1 r4c6<>1
r3c5=1 r5c5<>1
r3c5=1 r3c4<>1 r3c4=9 (r2c6<>9) r3c6<>9 r5c6=9 r5c6<>1
r3c5=1 r6c5<>1
Forcing Net Contradiction in r3c7 => r3c8<>1
r3c8=1 r3c4<>1 r3c4=9 (r7c4<>9 r7c5=9 r7c5<>3) r1c5<>9 r1c5=7 r1c2<>7 r1c2=3 (r3c1<>3) (r3c2<>3) r7c2<>3 r7c7=3 r3c7<>3 r3c8=3 r3c8<>1
Forcing Net Contradiction in r6c3 => r6c2<>3
r6c2=3 (r6c5<>3) (r4c2<>3) r1c2<>3 r1c9=3 (r3c7<>3 r7c7=3 r7c5<>3) r4c9<>3 r4c6=3 r5c5<>3 r8c5=3 r8c5<>2 r8c6=2 r3c6<>2 r3c5=2 r3c5<>5 r2c5=5 r2c5<>7 r2c2=7 r1c2<>7 r1c2=3 r6c2<>3
Forcing Net Contradiction in c5 => r7c2<>3
r7c2=3 r1c2<>3 r1c2=7 r2c2<>7 r2c5=7 r2c5<>5 r3c5=5 r3c5<>2
r7c2=3 (r8c1<>3) (r8c2<>3) (r8c3<>3) (r4c2<>3) r1c2<>3 r1c9=3 (r8c9<>3) r4c9<>3 r4c6=3 r8c6<>3 r8c5=3 r8c5<>2
Forcing Net Contradiction in c2 => r3c2<>8
r3c2=8 (r3c7<>8) r7c2<>8 r7c2=1 r7c4<>1 r3c4=1 r3c7<>1 r3c7=3 r1c9<>3 r1c2=3
r3c2=8 (r4c2<>8) r7c2<>8 r7c2=1 r4c2<>1 r4c2=3
Forcing Net Contradiction in b9 => r3c6<>1
r3c6=1 r3c4<>1 r7c4=1 r7c7<>1
r3c6=1 (r3c7<>1) r3c4<>1 (r3c4=9 r1c5<>9 r1c9=9 r2c9<>9) r7c4=1 (r7c2<>1 r7c2=8 r7c7<>8) r7c7<>1 r6c7=1 r6c7<>8 r3c7=8 r2c9<>8 r2c9=1 r8c9<>1
r3c6=1 r3c4<>1 (r7c4=1 r7c2<>1 r7c2=8 r9c3<>8) (r7c4=1 r7c2<>1 r7c2=8 r4c2<>8) r3c4=9 (r1c5<>9 r1c9=9 r1c9<>3) r7c4<>9 r7c5=9 r7c5<>3 r7c7=3 r8c9<>3 r4c9=3 r4c9<>8 r4c6=8 r9c6<>8 r9c8=8 r9c8<>1
Forcing Net Contradiction in c6 => r6c2<>1
r6c2=1 (r4c2<>1) r7c2<>1 r7c2=8 r4c2<>8 r4c2=3 r4c6<>3
r6c2=1 (r6c2<>4 r6c3=4 r2c3<>4 r2c6=4 r2c6<>1 r3c4=1 r3c4<>9) (r4c2<>1) r7c2<>1 r7c2=8 r4c2<>8 r4c2=3 r1c2<>3 (r1c9=3 r3c8<>3 r3c1=3 r3c1<>9) r1c2=7 r1c5<>7 r1c5=9 (r5c5<>9) (r3c5<>9) r3c6<>9 r3c3=9 r5c3<>9 r5c6=9 r5c6<>3
r6c2=1 (r6c7<>1) r6c2<>4 r6c3=4 r2c3<>4 r2c6=4 r2c6<>1 r3c4=1 r3c7<>1 r7c7=1 r7c7<>3 r7c5=3 r8c6<>3
r6c2=1 (r6c7<>1) r6c2<>4 r6c3=4 r2c3<>4 r2c6=4 r2c6<>1 r3c4=1 r3c7<>1 r7c7=1 r7c7<>3 r7c5=3 r9c6<>3
Forcing Net Contradiction in r2c5 => r6c2=4
r6c2<>4 (r6c3=4 r6c3<>1 r5c3=1 r5c5<>1) r6c2=8 r7c2<>8 r7c2=1 (r7c5<>1) (r7c7<>1) r7c4<>1 r3c4=1 r3c7<>1 r6c7=1 r6c5<>1 r8c5=1 r8c5<>2 r8c6=2 r3c6<>2 r3c5=2 r3c5<>5 r2c5=5
r6c2<>4 r6c2=8 (r4c2<>8) r7c2<>8 r7c2=1 r4c2<>1 r4c2=3 r1c2<>3 r1c2=7 r2c2<>7 r2c5=7
Forcing Chain Contradiction in b1 => r3c1<>3
r3c1=3 r1c2<>3 r1c9=3 r1c9<>9 r2c9=9 r2c1<>9
r3c1=3 r1c2<>3 r1c9=3 r1c9<>9 r2c9=9 r2c3<>9
r3c1=3 r3c1<>9
r3c1=3 r1c2<>3 r1c2=7 r1c5<>7 r2c5=7 r2c5<>5 r3c5=5 r3c5<>2 r3c6=2 r3c6<>4 r3c3=4 r3c3<>9
Locked Candidates Type 1 (Pointing): 3 in b1 => r48c2<>3
Naked Pair: 1,8 in r47c2 => r8c2<>1, r8c2<>8
Finned Swordfish: 1 c247 r347 fr6c7 => r4c9<>1
Sashimi Swordfish: 1 c247 r367 fr4c2 => r6c3<>1
Finned Jellyfish: 1 c3689 r2589 fr4c6 => r5c5<>1
Forcing Chain Contradiction in r6 => r7c5<>8
r7c5=8 r7c2<>8 r4c2=8 r6c1<>8
r7c5=8 r7c2<>8 r4c2=8 r6c3<>8
r7c5=8 r6c5<>8
r7c5=8 r7c2<>8 r7c2=1 r4c2<>1 r4c6=1 r6c5<>1 r6c7=1 r6c7<>8
Finned Franken Swordfish: 8 r47b8 c269 fr7c7 fr8c5 => r8c9<>8
Multi Colors 1: 8 (r2c9) / (r4c9), (r4c2,r7c7) / (r7c2,r9c8) => r23c8<>8
Discontinuous Nice Loop: 1 r9c8 -1- r8c9 -3- r4c9 -8- r5c8 =8= r9c8 => r9c8<>1
Skyscraper: 1 in r4c2,r9c3 (connected by r49c6) => r5c3,r7c2<>1
Naked Single: r7c2=8
Naked Single: r4c2=1
Hidden Single: r9c8=8
Naked Triple: 1,3,9 in r7c45,r9c6 => r8c56<>1, r8c56<>3
Turbot Fish: 3 r6c1 =3= r8c1 -3- r8c9 =3= r7c7 => r6c7<>3
Empty Rectangle: 8 in b4 (r36c7) => r3c3<>8
W-Wing: 1/3 in r5c8,r9c6 connected by 3 in r4c69 => r5c6<>1
Hidden Single: r5c8=1
Naked Single: r2c8=6
Full House: r3c8=3
Naked Single: r6c7=8
Full House: r4c9=3
Full House: r4c6=8
Naked Single: r1c9=9
Naked Single: r3c7=1
Full House: r2c9=8
Full House: r8c9=1
Full House: r7c7=3
Naked Single: r8c6=2
Naked Single: r1c5=7
Full House: r1c2=3
Naked Single: r3c4=9
Full House: r7c4=1
Full House: r7c5=9
Naked Single: r8c5=8
Full House: r9c6=3
Full House: r9c3=1
Naked Single: r2c5=5
Naked Single: r3c6=4
Naked Single: r5c5=3
Naked Single: r5c6=9
Full House: r2c6=1
Full House: r3c5=2
Full House: r6c5=1
Full House: r5c3=8
Naked Single: r2c1=9
Naked Single: r2c2=7
Full House: r2c3=4
Naked Single: r3c3=6
Naked Single: r6c1=3
Full House: r6c3=9
Full House: r8c3=3
Naked Single: r3c2=5
Full House: r3c1=8
Full House: r8c1=5
Full House: r8c2=6
|
normal_sudoku_1592 | ..56.8..7...7.581938...256415....78...8571.9....8..651........554.3.9..6..6.5794. | 915648327462735819387912564153496782628571493794823651879264135541389276236157948 | normal_sudoku_1592 | 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 | 9 | . . 5 6 . 8 . . 7
. . . 7 . 5 8 1 9
3 8 . . . 2 5 6 4
1 5 . . . . 7 8 .
. . 8 5 7 1 . 9 .
. . . 8 . . 6 5 1
. . . . . . . . 5
5 4 . 3 . 9 . . 6
. . 6 . 5 7 9 4 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 915648327462735819387912564153496782628571493794823651879264135541389276236157948 #1 Easy (218)
Hidden Single: r2c5=3
Hidden Single: r3c3=7
Hidden Single: r5c7=4
Hidden Single: r8c5=8
Hidden Single: r9c9=8
Naked Single: r9c1=2
Naked Single: r5c1=6
Naked Single: r8c3=1
Naked Single: r9c4=1
Full House: r9c2=3
Naked Single: r2c1=4
Naked Single: r8c7=2
Full House: r8c8=7
Naked Single: r3c4=9
Full House: r3c5=1
Full House: r1c5=4
Naked Single: r5c2=2
Full House: r5c9=3
Full House: r4c9=2
Naked Single: r7c3=9
Naked Single: r1c1=9
Naked Single: r2c3=2
Full House: r2c2=6
Full House: r1c2=1
Naked Single: r1c7=3
Full House: r1c8=2
Full House: r7c8=3
Full House: r7c7=1
Naked Single: r4c4=4
Full House: r7c4=2
Naked Single: r7c2=7
Full House: r6c2=9
Full House: r7c1=8
Full House: r6c1=7
Naked Single: r4c3=3
Full House: r6c3=4
Naked Single: r6c6=3
Full House: r6c5=2
Naked Single: r7c5=6
Full House: r4c5=9
Full House: r4c6=6
Full House: r7c6=4
|
normal_sudoku_790 | 56..381.2..8...6933...6...583..7.5199.51.3..6...8.5327..4....311.3..7.6.68.3..754 | 567938142248751693391264875832476519975123486416895327754689231123547968689312754 | normal_sudoku_790 | 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 | 9 | 5 6 . . 3 8 1 . 2
. . 8 . . . 6 9 3
3 . . . 6 . . . 5
8 3 . . 7 . 5 1 9
9 . 5 1 . 3 . . 6
. . . 8 . 5 3 2 7
. . 4 . . . . 3 1
1 . 3 . . 7 . 6 .
6 8 . 3 . . 7 5 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 567938142248751693391264875832476519975123486416895327754689231123547968689312754 #1 Easy (156)
Full House: r8c9=8
Naked Single: r6c1=4
Naked Single: r6c2=1
Naked Single: r6c5=9
Full House: r6c3=6
Naked Single: r4c3=2
Full House: r5c2=7
Naked Single: r9c3=9
Naked Single: r1c3=7
Full House: r3c3=1
Naked Single: r1c8=4
Full House: r1c4=9
Naked Single: r2c1=2
Full House: r7c1=7
Naked Single: r3c7=8
Full House: r3c8=7
Full House: r5c8=8
Full House: r5c7=4
Full House: r5c5=2
Naked Single: r2c2=4
Full House: r3c2=9
Naked Single: r9c5=1
Full House: r9c6=2
Naked Single: r2c6=1
Naked Single: r2c5=5
Full House: r2c4=7
Naked Single: r3c6=4
Full House: r3c4=2
Naked Single: r7c5=8
Full House: r8c5=4
Naked Single: r4c6=6
Full House: r4c4=4
Full House: r7c6=9
Naked Single: r8c4=5
Full House: r7c4=6
Naked Single: r7c7=2
Full House: r7c2=5
Full House: r8c2=2
Full House: r8c7=9
|
normal_sudoku_1941 | 49.8.1....83.59.1452134....95.4...813.81.5...214..8...8....31..13..84.76..5.1.... | 496871253783259614521346798957462381368195427214738569879623145132584976645917832 | normal_sudoku_1941 | 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 | 9 | 4 9 . 8 . 1 . . .
. 8 3 . 5 9 . 1 4
5 2 1 3 4 . . . .
9 5 . 4 . . . 8 1
3 . 8 1 . 5 . . .
2 1 4 . . 8 . . .
8 . . . . 3 1 . .
1 3 . . 8 4 . 7 6
. . 5 . 1 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 496871253783259614521346798957462381368195427214738569879623145132584976645917832 #1 Extreme (3574)
Naked Pair: 6,7 in r14c3 => r7c3<>6, r7c3<>7
Forcing Chain Contradiction in r9c6 => r2c4<>6
r2c4=6 r2c4<>2 r789c4=2 r9c6<>2
r2c4=6 r2c1<>6 r9c1=6 r9c6<>6
r2c4=6 r3c6<>6 r3c6=7 r9c6<>7
2-String Kite: 6 in r2c7,r4c3 (connected by r1c3,r2c1) => r4c7<>6
Turbot Fish: 6 r3c6 =6= r1c5 -6- r1c3 =6= r4c3 => r4c6<>6
Grouped Discontinuous Nice Loop: 7 r1c7 -7- r1c3 -6- r1c5 =6= r3c6 =7= r3c79 -7- r1c7 => r1c7<>7
Grouped Discontinuous Nice Loop: 7 r1c9 -7- r1c3 -6- r1c5 =6= r3c6 =7= r3c79 -7- r1c9 => r1c9<>7
Turbot Fish: 7 r1c5 =7= r1c3 -7- r4c3 =7= r5c2 => r5c5<>7
Grouped Discontinuous Nice Loop: 9 r7c8 -9- r3c8 -6- r3c6 =6= r9c6 -6- r7c45 =6= r7c2 =4= r7c8 => r7c8<>9
Almost Locked Set XY-Wing: A=r5c2 {67}, B=r9c16 {267}, C=r4c36 {267}, X,Y=2,6, Z=7 => r9c2<>7
Discontinuous Nice Loop: 7 r5c7 -7- r5c2 -6- r9c2 -4- r9c7 =4= r5c7 => r5c7<>7
Forcing Chain Contradiction in r9c6 => r2c4=2
r2c4<>2 r789c4=2 r9c6<>2
r2c4<>2 r2c4=7 r3c6<>7 r3c6=6 r9c6<>6
r2c4<>2 r2c4=7 r2c1<>7 r9c1=7 r9c6<>7
Naked Pair: 6,7 in r1c35 => r1c78<>6
X-Wing: 6 r14 c35 => r567c5<>6
Remote Pair: 7/6 r3c6 -6- r1c5 -7- r1c3 -6- r4c3 => r4c6<>7
Naked Single: r4c6=2
Naked Single: r5c5=9
Hidden Single: r7c5=2
Naked Single: r7c3=9
Naked Single: r7c9=5
Naked Single: r8c3=2
Naked Single: r7c8=4
Naked Single: r8c7=9
Full House: r8c4=5
Hidden Single: r5c7=4
Hidden Single: r9c2=4
Hidden Single: r9c4=9
Remote Pair: 6/7 r2c7 -7- r2c1 -6- r1c3 -7- r4c3 -6- r5c2 -7- r7c2 -6- r7c4 -7- r6c4 => r6c7<>6, r46c7<>7
Naked Single: r4c7=3
Naked Single: r6c7=5
Naked Single: r1c7=2
Naked Single: r1c9=3
Naked Single: r9c7=8
Naked Single: r1c8=5
Naked Single: r9c9=2
Full House: r9c8=3
Naked Single: r5c9=7
Naked Single: r5c2=6
Full House: r4c3=7
Full House: r5c8=2
Full House: r7c2=7
Full House: r1c3=6
Full House: r4c5=6
Full House: r7c4=6
Full House: r9c1=6
Full House: r1c5=7
Full House: r2c1=7
Full House: r6c4=7
Full House: r9c6=7
Full House: r3c6=6
Full House: r6c5=3
Full House: r2c7=6
Full House: r3c7=7
Naked Single: r6c9=9
Full House: r3c9=8
Full House: r3c8=9
Full House: r6c8=6
|
normal_sudoku_199 | ....14..6.5.2...8.4....5..9.2.5...9...3.6...2......1..2.8.59.7.9657....837....9.. | 837914526659237481412685739126578394793461852584392167248159673965743218371826945 | normal_sudoku_199 | 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 | 9 | . . . . 1 4 . . 6
. 5 . 2 . . . 8 .
4 . . . . 5 . . 9
. 2 . 5 . . . 9 .
. . 3 . 6 . . . 2
. . . . . . 1 . .
2 . 8 . 5 9 . 7 .
9 6 5 7 . . . . 8
3 7 . . . . 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 837914526659237481412685739126578394793461852584392167248159673965743218371826945 #1 Extreme (7658)
Finned Swordfish: 6 r347 c347 fr4c1 => r6c3<>6
Discontinuous Nice Loop: 4 r6c8 -4- r5c8 -5- r5c1 =5= r6c1 =6= r6c8 => r6c8<>4
Grouped Discontinuous Nice Loop: 1 r5c2 -1- r5c4 =1= r79c4 -1- r8c6 =1= r8c8 -1- r3c8 =1= r2c9 -1- r2c1 =1= r45c1 -1- r5c2 => r5c2<>1
Turbot Fish: 1 r2c9 =1= r3c8 -1- r3c2 =1= r7c2 => r7c9<>1
AIC: 4 4- r2c7 =4= r2c9 =1= r9c9 =5= r9c8 -5- r5c8 -4 => r45c7<>4
Discontinuous Nice Loop: 4 r7c7 -4- r2c7 =4= r2c9 =1= r9c9 =5= r9c8 =6= r7c7 => r7c7<>4
Almost Locked Set XY-Wing: A=r6c234569 {2345789}, B=r13589c8 {123456}, C=r9c34569 {124568}, X,Y=5,6, Z=3 => r6c8<>3
Grouped Discontinuous Nice Loop: 3 r1c4 -3- r7c4 =3= r7c79 -3- r8c8 =3= r13c8 -3- r2c79 =3= r2c56 -3- r1c4 => r1c4<>3
Discontinuous Nice Loop: 7 r2c3 -7- r1c1 -8- r1c4 -9- r2c5 =9= r2c3 => r2c3<>7
Grouped Discontinuous Nice Loop: 3 r2c7 -3- r4c7 =3= r46c9 -3- r7c9 -4- r2c9 =4= r2c7 => r2c7<>3
Grouped Discontinuous Nice Loop: 3 r3c4 -3- r7c4 =3= r7c79 -3- r8c8 =3= r13c8 -3- r2c9 =3= r2c56 -3- r3c4 => r3c4<>3
Discontinuous Nice Loop: 2 r9c6 -2- r6c6 =2= r6c5 =9= r2c5 -9- r1c4 -8- r3c4 -6- r2c6 =6= r9c6 => r9c6<>2
Grouped Discontinuous Nice Loop: 8 r5c2 -8- r3c2 =8= r1c12 -8- r1c4 -9- r5c4 =9= r5c2 => r5c2<>8
Grouped Discontinuous Nice Loop: 8 r5c4 -8- r3c4 -6- r2c6 =6= r9c6 =8= r456c6 -8- r5c4 => r5c4<>8
Grouped Discontinuous Nice Loop: 8 r6c4 -8- r3c4 -6- r2c6 =6= r9c6 =8= r456c6 -8- r6c4 => r6c4<>8
Grouped Discontinuous Nice Loop: 8 r6c5 -8- r456c6 =8= r9c6 =6= r2c6 -6- r3c4 -8- r1c4 -9- r2c5 =9= r6c5 => r6c5<>8
Almost Locked Set XZ-Rule: A=r1c14 {789}, B=r123c3,r2c1 {12679}, X=7, Z=9 => r1c2<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r6c3<>9
Grouped Discontinuous Nice Loop: 7 r3c3 -7- r6c3 -4- r9c3 =4= r7c2 -4- r7c9 -3- r46c9 =3= r4c7 =8= r5c7 =5= r1c7 =7= r1c13 -7- r3c3 => r3c3<>7
Grouped Discontinuous Nice Loop: 7 r6c5 -7- r6c3 -4- r9c3 -1- r7c2 =1= r3c2 =8= r1c12 -8- r1c4 -9- r2c5 =9= r6c5 => r6c5<>7
Grouped Discontinuous Nice Loop: 7 r6c6 -7- r6c3 -4- r9c3 -1- r7c2 =1= r3c2 =8= r1c12 -8- r1c4 -9- r2c5 =9= r6c5 =2= r6c6 => r6c6<>7
Finned Franken Swordfish: 4 r48b7 c359 fr7c2 fr8c7 fr8c8 => r7c9<>4
Naked Single: r7c9=3
Naked Single: r7c7=6
Hidden Single: r4c7=3
Hidden Single: r6c4=3
Hidden Single: r6c8=6
Hidden Single: r5c7=8
Hidden Single: r1c7=5
Locked Candidates Type 1 (Pointing): 7 in b6 => r2c9<>7
Locked Candidates Type 2 (Claiming): 7 in r1 => r2c1<>7
Locked Candidates Type 2 (Claiming): 3 in r2 => r3c5<>3
Sue de Coq: r45c1 - {15678} (r2c1 - {16}, r56c2,r6c13 - {45789}) => r4c3<>4, r4c3<>7
Sashimi X-Wing: 4 r48 c59 fr8c7 fr8c8 => r9c9<>4
XY-Chain: 8 8- r1c2 -3- r1c8 -2- r3c7 -7- r3c5 -8 => r1c4,r3c2<>8
Naked Single: r1c4=9
Hidden Single: r2c3=9
Hidden Single: r6c5=9
Hidden Single: r5c2=9
Hidden Single: r6c6=2
Locked Candidates Type 1 (Pointing): 4 in b4 => r6c9<>4
Locked Candidates Type 1 (Pointing): 8 in b5 => r4c1<>8
Naked Pair: 1,4 in r57c4 => r9c4<>1, r9c4<>4
XY-Chain: 3 3- r2c5 -7- r2c7 -4- r2c9 -1- r9c9 -5- r6c9 -7- r6c3 -4- r9c3 -1- r7c2 -4- r7c4 -1- r8c6 -3 => r2c6,r8c5<>3
Hidden Single: r2c5=3
Hidden Single: r8c6=3
Hidden Single: r8c8=1
Naked Single: r9c9=5
Naked Single: r6c9=7
Naked Single: r4c9=4
Full House: r2c9=1
Full House: r5c8=5
Naked Single: r6c3=4
Naked Single: r2c1=6
Naked Single: r6c2=8
Full House: r6c1=5
Naked Single: r9c3=1
Full House: r7c2=4
Full House: r7c4=1
Naked Single: r2c6=7
Full House: r2c7=4
Naked Single: r1c2=3
Full House: r3c2=1
Naked Single: r3c3=2
Naked Single: r4c3=6
Full House: r1c3=7
Full House: r1c1=8
Full House: r1c8=2
Naked Single: r5c4=4
Naked Single: r3c5=8
Full House: r3c4=6
Full House: r9c4=8
Naked Single: r5c6=1
Full House: r5c1=7
Full House: r4c1=1
Naked Single: r8c7=2
Full House: r3c7=7
Full House: r3c8=3
Full House: r9c8=4
Full House: r8c5=4
Naked Single: r4c5=7
Full House: r4c6=8
Full House: r9c6=6
Full House: r9c5=2
|
normal_sudoku_896 | .8...9......74.6..7.6..5..1........686395....2.1..65.....5..1.7.3....2.55.7..2.6. | 485619372312748659796325481954273816863951724271486593628594137139867245547132968 | normal_sudoku_896 | 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 | 9 | . 8 . . . 9 . . .
. . . 7 4 . 6 . .
7 . 6 . . 5 . . 1
. . . . . . . . 6
8 6 3 9 5 . . . .
2 . 1 . . 6 5 . .
. . . 5 . . 1 . 7
. 3 . . . . 2 . 5
5 . 7 . . 2 . 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 485619372312748659796325481954273816863951724271486593628594137139867245547132968 #1 Extreme (12140)
Locked Candidates Type 1 (Pointing): 2 in b5 => r4c8<>2
Grouped Discontinuous Nice Loop: 4 r4c7 -4- r5c7 -7- r1c7 =7= r1c8 =5= r1c3 -5- r4c3 =5= r4c2 =7= r6c2 =4= r4c123 -4- r4c7 => r4c7<>4
Grouped Discontinuous Nice Loop: 4 r4c8 -4- r5c7 -7- r1c7 =7= r1c8 =5= r1c3 -5- r4c3 =5= r4c2 =7= r6c2 =4= r4c123 -4- r4c8 => r4c8<>4
Forcing Net Contradiction in b2 => r1c4<>2
r1c4=2 r1c4<>1
r1c4=2 r1c4<>6 r1c5=6 r1c5<>1
r1c4=2 (r4c4<>2 r4c5=2 r4c5<>7) (r1c4<>1) r1c4<>6 (r8c4=6 r8c4<>1) r1c5=6 r1c5<>1 r1c1=1 (r8c1<>1) (r2c1<>1) r2c2<>1 r2c6=1 r8c6<>1 r8c5=1 r8c5<>7 (r8c6=7 r5c6<>7) r6c5=7 r6c2<>7 r4c2=7 r4c2<>5 r4c3=5 r1c3<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c8=7 r5c8<>1 r5c6=1 r2c6<>1
Forcing Net Contradiction in r9 => r1c8<>3
r1c8=3 (r1c9<>3) r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 (r3c7<>4) r5c9<>4 r5c9=2 r1c9<>2 r1c9=4 r3c8<>4 r3c2=4 r9c2<>4
r1c8=3 (r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r6c8<>4) (r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r6c9<>4) r1c8<>5 r1c3=5 r4c3<>5 r4c2=5 r4c2<>7 r6c2=7 r6c2<>4 r6c4=4 r9c4<>4
r1c8=3 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r9c7<>4
r1c8=3 (r1c9<>3) r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r5c9<>4 r5c9=2 r1c9<>2 r1c9=4 r9c9<>4
Forcing Net Verity => r2c8<>3
r1c8=2 r1c8<>5 r1c3=5 (r2c2<>5) r2c3<>5 r2c8=5 r2c8<>3
r2c8=2 r2c8<>3
r3c8=2 (r3c5<>2) r3c4<>2 r4c4=2 r4c5<>2 r1c5=2 (r1c5<>1) r1c5<>6 r1c4=6 r1c4<>1 r1c1=1 r1c1<>3 r2c1=3 r2c8<>3
r5c8=2 r5c9<>2 r5c9=4 r5c7<>4 r5c7=7 r1c7<>7 r1c8=7 r1c8<>5 r1c3=5 (r2c2<>5) r2c3<>5 r2c8=5 r2c8<>3
Forcing Net Contradiction in b3 => r2c8<>9
r2c8=9 r2c8<>5 r1c8=5 r1c8<>2
r2c8=9 r2c8<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r5c9<>4 r5c9=2 r1c9<>2
r2c8=9 r2c8<>2
r2c8=9 r2c8<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r5c9<>4 r5c9=2 r2c9<>2
r2c8=9 (r3c8<>9 r3c2=9 r3c2<>4) r2c8<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r3c7<>4 r3c8=4 r3c8<>2
Forcing Net Contradiction in r7c8 => r2c9<>2
r2c9=2 r5c9<>2 r5c9=4 (r1c9<>4 r1c9=3 r1c1<>3 r2c1=3 r2c1<>1) (r1c9<>4 r1c9=3 r1c1<>3) (r1c9<>4 r1c9=3 r1c7<>3) r5c7<>4 r5c7=7 r1c7<>7 r1c7=4 r1c1<>4 r1c1=1 r2c2<>1 r2c6=1 r5c6<>1 r5c8=1 r5c8<>2 r5c9=2 r2c9<>2
Forcing Net Contradiction in r7c8 => r4c4<>4
r4c4=4 (r4c4<>2 r4c5=2 r1c5<>2) (r4c4<>2 r3c4=2 r3c2<>2 r3c2=9 r2c3<>9 r2c3=2 r1c3<>2) (r4c3<>4) r4c1<>4 r4c1=9 r4c3<>9 r4c3=5 r1c3<>5 r1c8=5 r1c8<>2 r1c9=2 r5c9<>2 r5c9=4 r5c7<>4 r5c7=7 r1c7<>7 r1c8=7 r1c8<>5 r1c3=5 r4c3<>5 r4c2=5 r4c2<>7 r6c2=7 r6c2<>4 r4c123=4 r4c4<>4
Forcing Net Contradiction in r1c9 => r4c7<>7
r4c7=7 (r4c2<>7 r6c2=7 r6c2<>4 r6c4=4 r9c4<>4) r5c7<>7 r5c7=4 (r9c7<>4) (r1c7<>4 r1c7=3 r1c9<>3) r5c9<>4 r5c9=2 r1c9<>2 r1c9=4 r9c9<>4 r9c2=4 r3c2<>4 r1c13=4 r1c9<>4
r4c7=7 r5c7<>7 r5c7=4 (r1c7<>4 r1c7=3 r1c9<>3) r5c9<>4 r5c9=2 r1c9<>2 r1c9=4
Forcing Net Contradiction in r1c1 => r5c8<>4
r5c8=4 r5c8<>1 r5c6=1 r2c6<>1 r1c45=1 r1c1<>1
r5c8=4 (r5c9<>4 r5c9=2 r1c9<>2) r5c7<>4 r5c7=7 r1c7<>7 r1c8=7 (r1c8<>2) r1c8<>5 r1c3=5 r1c3<>2 r1c5=2 (r1c5<>1) r1c5<>6 r1c4=6 r1c4<>1 r1c1=1
Forcing Net Contradiction in b8 => r6c8<>4
r6c8=4 (r5c7<>4) r5c9<>4 r5c6=4 r7c6<>4
r6c8=4 (r5c9<>4 r5c9=2 r1c9<>2) r5c7<>4 r5c7=7 r1c7<>7 r1c8=7 (r1c8<>2) r1c8<>5 r1c3=5 (r2c3<>5 r2c8=5 r2c8<>2 r3c8=2 r3c4<>2 r4c4=2 r4c4<>1) r1c3<>2 r1c5=2 (r1c5<>1) r1c5<>6 r1c4=6 r1c4<>1 r1c1=1 (r8c1<>1) (r2c1<>1) r2c2<>1 r2c6=1 (r8c6<>1) r5c6<>1 r5c8=1 r4c8<>1 r4c5=1 (r4c6<>1) r8c5<>1 r8c4=1 r8c4<>4
r6c8=4 (r5c7<>4) r5c9<>4 r5c6=4 r8c6<>4
r6c8=4 r78c8<>4 r9c79=4 r9c4<>4
Forcing Net Contradiction in c4 => r1c9<>4
r1c9=4 (r6c9<>4) (r3c7<>4) r3c8<>4 r3c2=4 r6c2<>4 r6c4=4
r1c9=4 (r3c8<>4 r3c2=4 r9c2<>4) (r9c9<>4) (r5c9<>4) r6c9<>4 r5c7=4 r9c7<>4 r9c4=4
Almost Locked Set XY-Wing: A=r1c9 {23}, B=r2c6,r3c45 {1238}, C=r5c679 {1247}, X,Y=1,2, Z=3 => r1c45<>3
Forcing Chain Contradiction in c9 => r4c7<>9
r4c7=9 r4c123<>9 r6c2=9 r3c2<>9 r2c123=9 r2c9<>9
r4c7=9 r6c9<>9
r4c7=9 r4c123<>9 r6c2=9 r6c2<>7 r4c2=7 r4c2<>5 r4c3=5 r1c3<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r56c9<>4 r9c9=4 r9c9<>9
Forcing Chain Contradiction in c9 => r4c8<>9
r4c8=9 r4c123<>9 r6c2=9 r3c2<>9 r2c123=9 r2c9<>9
r4c8=9 r6c9<>9
r4c8=9 r4c123<>9 r6c2=9 r6c2<>7 r4c2=7 r4c2<>5 r4c3=5 r1c3<>5 r1c8=5 r1c8<>7 r1c7=7 r5c7<>7 r5c7=4 r56c9<>4 r9c9=4 r9c9<>9
Locked Candidates Type 1 (Pointing): 9 in b6 => r6c2<>9
Forcing Chain Contradiction in r2 => r8c6<>1
r8c6=1 r5c6<>1 r5c8=1 r5c8<>2 r5c9=2 r1c9<>2 r1c9=3 r1c1<>3 r2c1=3 r2c1<>1
r8c6=1 r8c1<>1 r9c2=1 r2c2<>1
r8c6=1 r2c6<>1
Forcing Chain Contradiction in r1c5 => r4c4<>1
r4c4=1 r89c4<>1 r89c5=1 r1c5<>1
r4c4=1 r4c4<>2 r4c5=2 r1c5<>2
r4c4=1 r1c4<>1 r1c4=6 r1c5<>6
Forcing Net Verity => r6c2=7
r6c4=4 r6c2<>4 r6c2=7
r8c4=4 (r8c4<>1) (r8c4<>1) r8c4<>6 r1c4=6 r1c4<>1 r9c4=1 r8c5<>1 r8c1=1 r9c2<>1 r2c2=1 r2c2<>5 r4c2=5 r4c2<>7 r6c2=7
r9c4=4 r9c9<>4 r56c9=4 r5c7<>4 r5c7=7 r1c7<>7 r1c8=7 r1c8<>5 r1c3=5 r4c3<>5 r4c2=5 r4c2<>7 r6c2=7
Locked Candidates Type 1 (Pointing): 4 in b4 => r4c6<>4
Forcing Net Contradiction in r9 => r2c1=3
r2c1<>3 r1c1=3 (r1c7<>3) r1c9<>3 r1c9=2 r5c9<>2 r5c9=4 r5c7<>4 r5c7=7 r1c7<>7 r1c7=4 (r3c7<>4) r3c8<>4 r3c2=4 r9c2<>4
r2c1<>3 r1c1=3 r1c9<>3 r1c9=2 r5c9<>2 r5c9=4 r6c9<>4 r6c4=4 r9c4<>4
r2c1<>3 r1c1=3 (r1c7<>3) r1c9<>3 r1c9=2 r5c9<>2 r5c9=4 r5c7<>4 r5c7=7 r1c7<>7 r1c7=4 r9c7<>4
r2c1<>3 r1c1=3 r1c9<>3 r1c9=2 r5c9<>2 r5c9=4 r9c9<>4
Locked Candidates Type 1 (Pointing): 3 in b2 => r3c78<>3
Finned X-Wing: 1 c14 r18 fr9c4 => r8c5<>1
Finned X-Wing: 3 c68 r47 fr6c8 => r4c7<>3
Naked Single: r4c7=8
Sashimi X-Wing: 8 c69 r29 fr7c6 fr8c6 => r9c45<>8
Hidden Single: r9c9=8
Naked Single: r2c9=9
Naked Single: r3c7=4
Naked Single: r5c7=7
Naked Single: r1c7=3
Full House: r9c7=9
Naked Single: r1c9=2
Naked Single: r8c8=4
Full House: r7c8=3
Naked Single: r3c8=8
Naked Single: r5c9=4
Full House: r6c9=3
Naked Single: r4c8=1
Naked Single: r6c8=9
Full House: r5c8=2
Full House: r5c6=1
Naked Single: r2c8=5
Full House: r1c8=7
Naked Single: r6c5=8
Full House: r6c4=4
Naked Single: r2c6=8
Naked Single: r2c3=2
Full House: r2c2=1
Naked Single: r7c6=4
Naked Single: r8c6=7
Full House: r4c6=3
Naked Single: r3c2=9
Naked Single: r1c1=4
Full House: r1c3=5
Naked Single: r9c2=4
Naked Single: r4c4=2
Full House: r4c5=7
Naked Single: r7c2=2
Full House: r4c2=5
Naked Single: r4c1=9
Full House: r4c3=4
Naked Single: r3c4=3
Full House: r3c5=2
Naked Single: r7c1=6
Full House: r8c1=1
Naked Single: r9c4=1
Full House: r9c5=3
Naked Single: r7c5=9
Full House: r7c3=8
Full House: r8c3=9
Naked Single: r1c4=6
Full House: r1c5=1
Full House: r8c5=6
Full House: r8c4=8
|
normal_sudoku_889 | 7..3...6..6..57..8.3..6.7..652...849847529613319846527.7..1.9..4......8...3..5.72 | 785394261264157398931268754652731849847529613319846527578412936426973185193685472 | normal_sudoku_889 | 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 | 9 | 7 . . 3 . . . 6 .
. 6 . . 5 7 . . 8
. 3 . . 6 . 7 . .
6 5 2 . . . 8 4 9
8 4 7 5 2 9 6 1 3
3 1 9 8 4 6 5 2 7
. 7 . . 1 . 9 . .
4 . . . . . . 8 .
. . 3 . . 5 . 7 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 785394261264157398931268754652731849847529613319846527578412936426973185193685472 #1 Medium (242)
Hidden Single: r9c4=6
Hidden Single: r9c7=4
Hidden Single: r9c1=1
Locked Candidates Type 1 (Pointing): 9 in b7 => r1c2<>9
Hidden Single: r1c5=9
Naked Single: r9c5=8
Full House: r9c2=9
Naked Single: r8c2=2
Full House: r1c2=8
Naked Single: r7c1=5
Naked Single: r8c6=3
Naked Single: r7c8=3
Naked Single: r7c9=6
Naked Single: r8c3=6
Full House: r7c3=8
Naked Single: r4c6=1
Naked Single: r8c5=7
Full House: r4c5=3
Full House: r4c4=7
Naked Single: r8c7=1
Full House: r8c9=5
Full House: r8c4=9
Naked Single: r2c8=9
Full House: r3c8=5
Naked Single: r1c7=2
Full House: r2c7=3
Naked Single: r2c1=2
Full House: r3c1=9
Naked Single: r1c6=4
Naked Single: r1c9=1
Full House: r1c3=5
Full House: r3c9=4
Naked Single: r2c4=1
Full House: r2c3=4
Full House: r3c3=1
Naked Single: r7c6=2
Full House: r3c6=8
Full House: r3c4=2
Full House: r7c4=4
|
normal_sudoku_1019 | 4...6.7.1....1..2..1..7..3.3..957.1....1823.612.643....38524...9..731....51896..3 | 493268751867315924215479638386957412574182396129643587638524179942731865751896243 | normal_sudoku_1019 | 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 | 9 | 4 . . . 6 . 7 . 1
. . . . 1 . . 2 .
. 1 . . 7 . . 3 .
3 . . 9 5 7 . 1 .
. . . 1 8 2 3 . 6
1 2 . 6 4 3 . . .
. 3 8 5 2 4 . . .
9 . . 7 3 1 . . .
. 5 1 8 9 6 . . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 493268751867315924215479638386957412574182396129643587638524179942731865751896243 #1 Medium (358)
Hidden Single: r4c2=8
Naked Single: r1c2=9
Hidden Single: r7c7=1
Hidden Single: r4c3=6
Locked Candidates Type 1 (Pointing): 6 in b3 => r8c7<>6
Locked Candidates Type 1 (Pointing): 4 in b4 => r5c8<>4
Locked Candidates Type 1 (Pointing): 4 in b7 => r8c789<>4
Hidden Single: r9c8=4
Naked Single: r9c7=2
Full House: r9c1=7
Naked Single: r4c7=4
Full House: r4c9=2
Naked Single: r5c1=5
Naked Single: r7c1=6
Naked Single: r2c1=8
Full House: r3c1=2
Naked Single: r8c2=4
Full House: r8c3=2
Naked Single: r3c3=5
Naked Single: r3c4=4
Naked Single: r5c2=7
Full House: r2c2=6
Naked Single: r1c3=3
Full House: r2c3=7
Naked Single: r2c4=3
Full House: r1c4=2
Naked Single: r5c8=9
Full House: r5c3=4
Full House: r6c3=9
Naked Single: r7c8=7
Full House: r7c9=9
Naked Single: r3c9=8
Naked Single: r1c8=5
Full House: r1c6=8
Naked Single: r3c6=9
Full House: r2c6=5
Full House: r3c7=6
Naked Single: r8c9=5
Naked Single: r2c7=9
Full House: r2c9=4
Full House: r6c9=7
Naked Single: r6c8=8
Full House: r6c7=5
Full House: r8c7=8
Full House: r8c8=6
|
normal_sudoku_730 | ......5..5..2.3.....9.4...8..74...8...3.26..7.9.37824..3.1598.........1...876...2 | 386917524574283961129645738257491683843526197691378245432159876765832419918764352 | normal_sudoku_730 | 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 | 9 | . . . . . . 5 . .
5 . . 2 . 3 . . .
. . 9 . 4 . . . 8
. . 7 4 . . . 8 .
. . 3 . 2 6 . . 7
. 9 . 3 7 8 2 4 .
. 3 . 1 5 9 8 . .
. . . . . . . 1 .
. . 8 7 6 . . . 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 386917524574283961129645738257491683843526197691378245432159876765832419918764352 #1 Unfair (1144)
Naked Single: r8c4=8
Naked Single: r9c6=4
Naked Single: r8c5=3
Full House: r8c6=2
Locked Candidates Type 1 (Pointing): 1 in b5 => r4c1279<>1
Naked Pair: 5,9 in r5c48 => r5c2<>5, r5c7<>9
Naked Single: r5c7=1
XY-Chain: 9 9- r5c8 -5- r6c9 -6- r6c1 -1- r9c1 -9 => r9c8<>9
XY-Wing: 3/5/9 in r59c8,r9c7 => r4c7<>9
2-String Kite: 9 in r1c4,r4c9 (connected by r4c5,r5c4) => r1c9<>9
XY-Chain: 6 6- r4c7 -3- r9c7 -9- r9c1 -1- r6c1 -6 => r4c12,r6c9<>6
Naked Single: r4c1=2
Naked Single: r6c9=5
Naked Single: r4c2=5
Naked Single: r5c8=9
Naked Single: r4c6=1
Naked Single: r9c2=1
Naked Single: r5c4=5
Full House: r4c5=9
Naked Single: r1c6=7
Full House: r3c6=5
Naked Single: r9c1=9
Naked Single: r3c4=6
Full House: r1c4=9
Naked Single: r9c7=3
Full House: r9c8=5
Naked Single: r3c7=7
Naked Single: r4c7=6
Full House: r4c9=3
Naked Single: r2c8=6
Naked Single: r3c2=2
Naked Single: r7c8=7
Naked Single: r3c8=3
Full House: r1c8=2
Full House: r3c1=1
Naked Single: r2c3=4
Naked Single: r6c1=6
Full House: r6c3=1
Naked Single: r1c3=6
Naked Single: r2c7=9
Full House: r8c7=4
Naked Single: r7c1=4
Naked Single: r1c2=8
Naked Single: r7c3=2
Full House: r8c3=5
Full House: r7c9=6
Full House: r8c9=9
Naked Single: r2c9=1
Full House: r1c9=4
Naked Single: r8c1=7
Full House: r8c2=6
Naked Single: r5c1=8
Full House: r1c1=3
Full House: r1c5=1
Full House: r2c2=7
Full House: r5c2=4
Full House: r2c5=8
|
normal_sudoku_1328 | 75213.4.8...52...11.3.....5618.5.....9.7836123274615892...4..5....3......4....9.6 | 752136498984527361163894275618952743495783612327461589239648157576319824841275936 | normal_sudoku_1328 | 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 | 9 | 7 5 2 1 3 . 4 . 8
. . . 5 2 . . . 1
1 . 3 . . . . . 5
6 1 8 . 5 . . . .
. 9 . 7 8 3 6 1 2
3 2 7 4 6 1 5 8 9
2 . . . 4 . . 5 .
. . . 3 . . . . .
. 4 . . . . 9 . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 752136498984527361163894275618952743495783612327461589239648157576319824841275936 #1 Unfair (1284)
Hidden Single: r3c6=4
Hidden Single: r7c2=3
Naked Single: r7c9=7
Naked Single: r8c9=4
Full House: r4c9=3
Naked Single: r8c8=2
Naked Single: r4c7=7
Full House: r4c8=4
Naked Single: r9c8=3
Naked Single: r2c7=3
Naked Single: r3c7=2
Hidden Single: r8c2=7
Locked Candidates Type 1 (Pointing): 9 in b1 => r2c68<>9
Locked Candidates Type 1 (Pointing): 6 in b7 => r2c3<>6
Locked Candidates Type 1 (Pointing): 8 in b7 => r2c1<>8
XY-Chain: 9 9- r3c5 -7- r9c5 -1- r9c3 -5- r9c1 -8- r9c4 -2- r4c4 -9 => r3c4<>9
Naked Pair: 6,8 in r3c24 => r3c8<>6
XY-Chain: 2 2- r4c6 -9- r1c6 -6- r3c4 -8- r9c4 -2 => r4c4,r9c6<>2
Naked Single: r4c4=9
Full House: r4c6=2
Hidden Single: r9c4=2
XYZ-Wing: 6/8/9 in r17c6,r7c4 => r8c6<>6
Hidden Single: r8c3=6
W-Wing: 9/1 in r7c3,r8c5 connected by 1 in r9c35 => r7c6,r8c1<>9
Hidden Single: r7c3=9
Naked Single: r2c3=4
Naked Single: r2c1=9
Naked Single: r5c3=5
Full House: r5c1=4
Full House: r9c3=1
Naked Single: r9c5=7
Naked Single: r3c5=9
Full House: r8c5=1
Naked Single: r1c6=6
Full House: r1c8=9
Naked Single: r3c8=7
Full House: r2c8=6
Naked Single: r8c7=8
Full House: r7c7=1
Naked Single: r3c4=8
Full House: r2c6=7
Full House: r2c2=8
Full House: r3c2=6
Full House: r7c4=6
Full House: r7c6=8
Naked Single: r8c1=5
Full House: r8c6=9
Full House: r9c6=5
Full House: r9c1=8
|
normal_sudoku_2433 | ..1.5......9..76..4561..378..2745...164..8537975......6.3...8.2597.....32.83..795 | 731856429829437651456192378382745916164928537975613284613579842597284163248361795 | normal_sudoku_2433 | 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 | 9 | . . 1 . 5 . . . .
. . 9 . . 7 6 . .
4 5 6 1 . . 3 7 8
. . 2 7 4 5 . . .
1 6 4 . . 8 5 3 7
9 7 5 . . . . . .
6 . 3 . . . 8 . 2
5 9 7 . . . . . 3
2 . 8 3 . . 7 9 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 731856429829437651456192378382745916164928537975613284613579842597284163248361795 #1 Easy (224)
Hidden Single: r1c1=7
Hidden Single: r6c8=8
Hidden Single: r7c5=7
Hidden Single: r7c4=5
Hidden Single: r2c8=5
Hidden Single: r8c8=6
Naked Single: r4c8=1
Naked Single: r4c7=9
Naked Single: r7c8=4
Full House: r1c8=2
Full House: r8c7=1
Naked Single: r4c9=6
Naked Single: r7c2=1
Full House: r7c6=9
Full House: r9c2=4
Naked Single: r1c7=4
Full House: r6c7=2
Full House: r6c9=4
Naked Single: r3c6=2
Full House: r3c5=9
Naked Single: r1c9=9
Full House: r2c9=1
Naked Single: r6c4=6
Naked Single: r8c6=4
Naked Single: r5c5=2
Full House: r5c4=9
Naked Single: r1c4=8
Naked Single: r8c5=8
Full House: r8c4=2
Full House: r2c4=4
Naked Single: r1c2=3
Full House: r1c6=6
Full House: r2c5=3
Naked Single: r2c1=8
Full House: r2c2=2
Full House: r4c2=8
Full House: r4c1=3
Naked Single: r9c6=1
Full House: r6c6=3
Full House: r6c5=1
Full House: r9c5=6
|
normal_sudoku_5351 | .1.....4...3..7..94..3..2..1..8....2..4.9.7...5..6..3......28...6..5..2.3..9....1 | 612589347583427169497316285176834592834295716259761438941672853768153924325948671 | normal_sudoku_5351 | 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 | 9 | . 1 . . . . . 4 .
. . 3 . . 7 . . 9
4 . . 3 . . 2 . .
1 . . 8 . . . . 2
. . 4 . 9 . 7 . .
. 5 . . 6 . . 3 .
. . . . . 2 8 . .
. 6 . . 5 . . 2 .
3 . . 9 . . . . 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 612589347583427169497316285176834592834295716259761438941672853768153924325948671 #1 Extreme (14382)
Locked Candidates Type 1 (Pointing): 2 in b5 => r12c4<>2
Discontinuous Nice Loop: 8 r5c8 -8- r6c9 -4- r6c6 -1- r6c7 =1= r5c8 => r5c8<>8
Locked Candidates Type 1 (Pointing): 8 in b6 => r13c9<>8
Almost Locked Set XZ-Rule: A=r12349c5 {123478}, B=r456c6 {1345}, X=3, Z=1 => r3c6<>1
Forcing Chain Contradiction in c2 => r2c4<>1
r2c4=1 r3c5<>1 r3c5=8 r3c8<>8 r2c8=8 r2c2<>8
r2c4=1 r3c5<>1 r3c5=8 r3c2<>8
r2c4=1 r23c5<>1 r7c5=1 r7c5<>3 r4c5=3 r4c2<>3 r5c2=3 r5c2<>8
r2c4=1 r23c5<>1 r7c5=1 r7c5<>3 r8c6=3 r8c6<>8 r8c13=8 r9c2<>8
Locked Candidates Type 1 (Pointing): 1 in b2 => r7c5<>1
Forcing Net Contradiction in c9 => r1c7<>5
r1c7=5 (r3c9<>5) (r1c4<>5 r1c4=6 r7c4<>6) r1c7<>3 r8c7=3 r8c7<>9 r7c8=9 r7c8<>6 r7c9=6 r3c9<>6 r3c9=7
r1c7=5 (r1c7<>3 r1c9=3 r8c9<>3) (r9c7<>5) r1c4<>5 r1c4=6 (r1c6<>6) r3c6<>6 r9c6=6 r9c7<>6 r9c7=4 r8c9<>4 r8c9=7
Forcing Net Contradiction in r7 => r6c4<>4
r6c4=4 (r6c6<>4 r6c6=1 r8c6<>1) (r2c4<>4 r2c5=4 r9c5<>4) r6c4<>7 r4c5=7 (r7c5<>7 r7c5=3 r8c6<>3) r9c5<>7 r9c5=8 (r9c6<>8) r8c6<>8 r8c6=4 r9c6<>4 r9c6=6 r7c4<>6
r6c4=4 (r6c7<>4) r6c6<>4 r6c6=1 r6c7<>1 r6c7=9 r4c8<>9 r7c8=9 r7c8<>6
r6c4=4 (r6c9<>4) (r6c6<>4 r6c6=1 r8c6<>1) (r2c4<>4 r2c5=4 r9c5<>4) r6c4<>7 r4c5=7 (r7c5<>7 r7c5=3 r8c6<>3) r9c5<>7 r9c5=8 r8c6<>8 r8c6=4 r8c9<>4 r7c9=4 r7c9<>6
Forcing Net Contradiction in r7c8 => r7c5<>4
r7c5=4 (r7c2<>4 r9c2=4 r9c2<>8) (r7c2<>4 r9c2=4 r9c2<>2) r7c5<>3 r4c5=3 r5c6<>3 r5c2=3 (r5c2<>8) r5c2<>2 r2c2=2 (r2c5<>2) r2c2<>8 r3c2=8 (r3c5<>8 r3c5=1 r2c5<>1) r3c8<>8 r2c8=8 r2c5<>8 r2c5=4 r7c5<>4
Forcing Net Verity => r7c9<>5
r3c3=5 (r1c1<>5) r2c1<>5 r7c1=5 r7c9<>5
r3c6=5 (r1c4<>5 r1c4=6 r1c6<>6 r9c6=6 r9c7<>6) (r1c4<>5 r1c4=6 r2c4<>6 r2c4=4 r2c5<>4) (r1c4<>5) r2c4<>5 r5c4=5 r5c4<>2 r6c4=2 r6c4<>7 r4c5=7 r4c5<>4 r9c5=4 r9c7<>4 r9c7=5 r7c9<>5
r3c8=5 (r9c8<>5) r3c8<>8 r2c8=8 r2c2<>8 r2c2=2 r9c2<>2 r9c3=2 r9c3<>5 r9c7=5 r7c9<>5
r3c9=5 r7c9<>5
Forcing Net Contradiction in r8 => r2c7<>5
r2c7=5 (r9c7<>5) r2c7<>1 r6c7=1 (r5c8<>1 r5c8=6 r7c8<>6) r6c6<>1 r6c6=4 (r4c5<>4) r4c6<>4 r4c7=4 r9c7<>4 r9c7=6 r7c9<>6 r7c4=6 (r2c4<>6) r1c4<>6 r1c4=5 r2c4<>5 r2c4=4 r8c4<>4
r2c7=5 r2c7<>1 r6c7=1 r6c6<>1 r6c6=4 r8c6<>4
r2c7=5 r2c7<>1 r6c7=1 r6c6<>1 r6c6=4 (r4c5<>4) r4c6<>4 r4c7=4 r8c7<>4
r2c7=5 (r2c7<>1 r6c7=1 r5c8<>1 r5c8=6 r7c8<>6) (r2c1<>5) (r2c4<>5) (r1c9<>5) r3c9<>5 r5c9=5 r5c4<>5 r1c4=5 r1c1<>5 r7c1=5 r7c8<>5 r7c8=7 (r7c5<>7 r7c5=3 r8c6<>3) r7c8<>9 r4c8=9 (r4c7<>9) (r7c8<>9) r6c7<>9 r8c7=9 r8c7<>3 r8c9=3 r8c9<>4
Forcing Net Contradiction in r3 => r3c5=1
r3c5<>1 r3c8=1 r2c7<>1 (r2c7=6 r4c7<>6) (r2c7=6 r1c7<>6 r1c7=3 r8c7<>3) r6c7=1 r6c6<>1 r6c6=4 (r4c5<>4) r4c6<>4 r4c7=4 r8c7<>4 r8c7=9 r7c8<>9 r4c8=9 r4c8<>6 r4c3=6 r3c3<>6
r3c5<>1 r3c5=8 r3c8<>8 r2c8=8 r2c2<>8 r2c2=2 (r2c1<>2 r2c1=5 r1c3<>5) (r2c1<>2 r2c1=5 r3c3<>5) r9c2<>2 r9c3=2 r9c3<>5 r7c3=5 r7c3<>1 r7c4=1 r7c4<>6 r9c6=6 r3c6<>6
r3c5<>1 r3c8=1 r3c8<>6
r3c5<>1 r3c8=1 r2c7<>1 r2c7=6 r3c9<>6
Forcing Net Contradiction in c6 => r5c8<>6
r5c8=6 (r3c8<>6) (r4c8<>6 r4c3=6 r3c3<>6) r5c8<>1 r2c8=1 r2c7<>1 r2c7=6 r3c9<>6 r3c6=6
r5c8=6 (r9c8<>6) r5c8<>1 r2c8=1 r2c7<>1 r2c7=6 r9c7<>6 r9c6=6
Forcing Net Contradiction in r3 => r1c6<>5
r1c6=5 (r1c4<>5 r1c4=6 r1c7<>6) (r1c4<>5 r1c4=6 r3c6<>6 r9c6=6 r9c7<>6) (r1c4<>5) r2c4<>5 r5c4=5 (r5c4<>2 r6c4=2 r6c4<>7 r4c5=7 r4c3<>7) r5c8<>5 r5c8=1 (r5c6<>1 r5c6=3 r4c6<>3 r4c2=3 r4c2<>9) r2c8<>1 r2c7=1 r2c7<>6 r4c7=6 r4c3<>6 r4c3=9 r4c8<>9 r7c8=9 r7c2<>9 r3c2=9
r1c6=5 r1c6<>9 r3c6=9
Forcing Net Contradiction in r4 => r2c8<>5
r2c8=5 (r2c8<>1 r2c7=1 r2c7<>6) (r2c8<>6) (r1c9<>5) r3c9<>5 r5c9=5 r5c9<>6 r5c1=6 r2c1<>6 r2c4=6 r2c4<>4 r2c5=4 r4c5<>4
r2c8=5 (r4c8<>5) (r1c9<>5) r3c9<>5 r5c9=5 r4c7<>5 r4c6=5 r4c6<>4
r2c8=5 (r2c8<>1 r2c7=1 r2c7<>6) (r2c8<>6) (r2c8<>8 r3c8=8 r3c8<>6) (r2c8<>1 r2c7=1 r2c7<>6) (r2c8<>6) (r1c9<>5) r3c9<>5 r5c9=5 (r4c7<>5 r4c6=5 r3c6<>5 r3c3=5 r3c3<>6) r5c9<>6 r5c1=6 (r4c3<>6) r2c1<>6 r2c4=6 r3c6<>6 r3c9=6 (r7c9<>6) r5c9<>6 r5c1=6 (r4c3<>6) r2c1<>6 r2c4=6 r7c4<>6 r7c8=6 r4c8<>6 r4c7=6 r4c7<>4
Forcing Chain Contradiction in c7 => r2c1<>6
r2c1=6 r2c1<>5 r2c4=5 r1c4<>5 r1c4=6 r1c7<>6
r2c1=6 r2c7<>6
r2c1=6 r5c1<>6 r5c9=6 r4c7<>6
r2c1=6 r2c1<>5 r2c4=5 r1c4<>5 r1c4=6 r7c4<>6 r9c6=6 r9c7<>6
Grouped Discontinuous Nice Loop: 5 r3c3 -5- r2c1 =5= r2c4 -5- r1c4 -6- r1c13 =6= r3c3 => r3c3<>5
Forcing Chain Contradiction in c9 => r1c6<>6
r1c6=6 r1c9<>6
r1c6=6 r2c4<>6 r2c78=6 r3c9<>6
r1c6=6 r1c1<>6 r5c1=6 r5c9<>6
r1c6=6 r9c6<>6 r7c4=6 r7c9<>6
Forcing Net Contradiction in r7c3 => r1c7=3
r1c7<>3 (r1c9=3 r7c9<>3 r7c5=3 r4c5<>3) r1c7=6 (r2c7<>6 r2c7=1 r2c8<>1 r5c8=1 r5c4<>1 r5c4=2 r6c4<>2) (r2c7<>6) r2c8<>6 r2c4=6 r2c4<>4 r2c5=4 r4c5<>4 r4c5=7 r6c4<>7 r6c4=1 r7c4<>1 r7c3=1
r1c7<>3 (r1c7=6 r1c4<>6 r1c4=5 r2c4<>5 r2c1=5 r7c1<>5) r8c7=3 r8c7<>9 r7c8=9 r7c8<>5 r7c3=5
Almost Locked Set XY-Wing: A=r4c23568 {345679}, B=r68c7 {149}, C=r6c6 {14}, X,Y=1,4, Z=9 => r4c7<>9
Almost Locked Set XY-Wing: A=r8c7 {49}, B=r13578c9 {345678}, C=r6c679 {1489}, X,Y=8,9, Z=4 => r9c7<>4
Forcing Chain Contradiction in r6c7 => r6c4<>1
r6c4=1 r6c7<>1
r6c4=1 r6c6<>1 r6c6=4 r6c7<>4
r6c4=1 r6c6<>1 r6c6=4 r6c9<>4 r46c7=4 r8c7<>4 r8c7=9 r6c7<>9
Forcing Chain Verity => r9c8<>5
r1c3=5 r1c4<>5 r1c4=6 r7c4<>6 r9c6=6 r9c7<>6 r9c7=5 r9c8<>5
r7c3=5 r7c3<>1 r7c4=1 r7c4<>6 r9c6=6 r9c7<>6 r9c7=5 r9c8<>5
r9c3=5 r9c8<>5
Forcing Chain Contradiction in b7 => r9c8=7
r9c8<>7 r9c8=6 r9c6<>6 r3c6=6 r1c4<>6 r1c4=5 r1c3<>5 r12c1=5 r7c1<>5
r9c8<>7 r9c8=6 r9c6<>6 r7c4=6 r7c4<>1 r7c3=1 r7c3<>5
r9c8<>7 r9c8=6 r9c7<>6 r9c7=5 r9c3<>5
Naked Triple: 2,4,8 in r129c5 => r4c5<>4
Locked Candidates Type 1 (Pointing): 4 in b5 => r89c6<>4
Sue de Coq: r5c46 - {1235} (r5c8 - {15}, r4c5,r6c4 - {237}) => r4c6<>3, r5c9<>5
Locked Candidates Type 2 (Claiming): 5 in c9 => r3c8<>5
Naked Triple: 1,6,8 in r2c78,r3c8 => r13c9<>6
Discontinuous Nice Loop: 7 r4c3 -7- r4c5 -3- r7c5 =3= r7c9 =6= r5c9 -6- r5c1 =6= r4c3 => r4c3<>7
Hidden Pair: 3,7 in r4c25 => r4c2<>9
2-String Kite: 9 in r4c3,r8c7 (connected by r4c8,r6c7) => r8c3<>9
Discontinuous Nice Loop: 9 r1c1 -9- r8c1 =9= r8c7 -9- r6c7 =9= r4c8 -9- r4c3 -6- r5c1 =6= r1c1 => r1c1<>9
Grouped Discontinuous Nice Loop: 6 r4c8 -6- r23c8 =6= r2c7 =1= r6c7 =9= r4c8 => r4c8<>6
Finned Swordfish: 6 r349 c367 fr3c8 => r2c7<>6
Naked Single: r2c7=1
Hidden Single: r5c8=1
Hidden Single: r6c6=1
Hidden Single: r4c6=4
Locked Candidates Type 1 (Pointing): 6 in b3 => r7c8<>6
XY-Wing: 3/8/4 in r8c69,r9c5 => r8c4<>4
Locked Candidates Type 2 (Claiming): 4 in r8 => r7c9<>4
Hidden Rectangle: 1/7 in r7c34,r8c34 => r7c3<>7
Sue de Coq: r7c45 - {13467} (r7c1238 - {14579}, r89c6 - {368}) => r9c5<>8
Naked Single: r9c5=4
Hidden Single: r2c4=4
Hidden Single: r7c2=4
Hidden Single: r2c1=5
Hidden Single: r2c8=6
Naked Single: r3c8=8
Hidden Single: r3c2=9
Hidden Single: r1c6=9
Hidden Single: r4c2=7
Naked Single: r4c5=3
Naked Single: r5c6=5
Naked Single: r7c5=7
Naked Single: r3c6=6
Naked Single: r5c4=2
Full House: r6c4=7
Naked Single: r7c1=9
Naked Single: r8c4=1
Naked Single: r1c4=5
Full House: r7c4=6
Naked Single: r3c3=7
Full House: r3c9=5
Full House: r1c9=7
Naked Single: r9c6=8
Full House: r8c6=3
Naked Single: r7c8=5
Full House: r4c8=9
Naked Single: r7c9=3
Full House: r7c3=1
Naked Single: r8c3=8
Naked Single: r9c2=2
Naked Single: r8c9=4
Naked Single: r9c7=6
Full House: r9c3=5
Full House: r8c1=7
Full House: r8c7=9
Naked Single: r4c3=6
Full House: r4c7=5
Full House: r6c7=4
Naked Single: r2c2=8
Full House: r2c5=2
Full House: r5c2=3
Full House: r1c5=8
Naked Single: r6c9=8
Full House: r5c9=6
Full House: r5c1=8
Naked Single: r1c3=2
Full House: r1c1=6
Full House: r6c1=2
Full House: r6c3=9
|
normal_sudoku_2491 | .1.642..3...17........9.1....62.4..1.27.16.3.14..87256.71.......6.72.31.2..4.1..7 | 715642983392178645684395172856234791927516438143987256471863529568729314239451867 | normal_sudoku_2491 | 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 | 9 | . 1 . 6 4 2 . . 3
. . . 1 7 . . . .
. . . . 9 . 1 . .
. . 6 2 . 4 . . 1
. 2 7 . 1 6 . 3 .
1 4 . . 8 7 2 5 6
. 7 1 . . . . . .
. 6 . 7 2 . 3 1 .
2 . . 4 . 1 . . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 715642983392178645684395172856234791927516438143987256471863529568729314239451867 #1 Extreme (7316)
Locked Candidates Type 1 (Pointing): 9 in b5 => r7c4<>9
Naked Triple: 3,5,8 in r3c246 => r3c13<>3, r3c139<>5, r3c1389<>8
Naked Pair: 2,4 in r3c39 => r3c18<>4, r3c8<>2
Hidden Pair: 2,4 in r27c8 => r27c8<>6, r27c8<>8, r27c8<>9
Naked Pair: 2,4 in r2c8,r3c9 => r2c79<>4, r2c9<>2
Forcing Chain Verity => r1c1<>5
r2c1=3 r2c1<>6 r3c1=6 r3c1<>7 r1c1=7 r1c1<>5
r4c1=3 r4c5<>3 r4c5=5 r4c2<>5 r45c1=5 r1c1<>5
r7c1=3 r7c456<>3 r9c5=3 r4c5<>3 r4c5=5 r4c2<>5 r45c1=5 r1c1<>5
Forcing Chain Verity => r2c1<>5
r2c1=3 r2c1<>5
r4c1=3 r4c5<>3 r4c5=5 r4c2<>5 r45c1=5 r2c1<>5
r7c1=3 r7c456<>3 r9c5=3 r4c5<>3 r4c5=5 r4c2<>5 r45c1=5 r2c1<>5
Forcing Chain Verity => r4c7<>8
r2c1=3 r2c1<>6 r2c7=6 r3c8<>6 r3c8=7 r4c8<>7 r4c7=7 r4c7<>8
r4c1=3 r4c5<>3 r4c5=5 r5c4<>5 r5c1=5 r5c1<>8 r4c12=8 r4c7<>8
r7c1=3 r7c456<>3 r9c5=3 r4c5<>3 r4c5=5 r5c4<>5 r5c1=5 r5c1<>8 r4c12=8 r4c7<>8
Forcing Chain Verity => r7c5<>5
r2c1=3 r2c1<>6 r2c7=6 r7c7<>6 r7c5=6 r7c5<>5
r4c1=3 r4c5<>3 r4c5=5 r7c5<>5
r7c1=3 r7c456<>3 r9c5=3 r9c5<>6 r7c5=6 r7c5<>5
Forcing Chain Contradiction in c2 => r9c7<>5
r9c7=5 r1c7<>5 r1c3=5 r2c2<>5
r9c7=5 r1c7<>5 r1c3=5 r3c2<>5
r9c7=5 r9c5<>5 r4c5=5 r4c2<>5
r9c7=5 r9c2<>5
Forcing Net Verity => r1c1<>9
r2c3=3 (r2c3<>4) r2c3<>2 r2c8=2 r2c8<>4 r2c1=4 r2c1<>6 r2c7=6 r3c8<>6 r3c8=7 (r1c7<>7) r1c8<>7 r1c1=7 r1c1<>9
r6c3=3 (r4c1<>3) (r9c3<>3) (r4c1<>3) r4c2<>3 r4c5=3 r9c5<>3 r9c2=3 r7c1<>3 r2c1=3 r2c1<>6 r2c7=6 r3c8<>6 r3c8=7 (r1c7<>7) r1c8<>7 r1c1=7 r1c1<>9
r9c3=3 (r9c3<>5) r6c3<>3 (r6c3=9 r4c2<>9) r6c4=3 r4c5<>3 r4c5=5 r9c5<>5 r9c2=5 r9c2<>9 r2c2=9 r1c1<>9
Forcing Chain Verity => r2c7<>9
r2c1=3 r2c1<>6 r2c7=6 r2c7<>9
r4c1=3 r6c3<>3 r6c3=9 r1c3<>9 r1c78=9 r2c7<>9
r7c1=3 r7c456<>3 r9c5=3 r4c5<>3 r6c4=3 r6c4<>9 r6c3=9 r1c3<>9 r1c78=9 r2c7<>9
Forcing Chain Verity => r9c8<>9
r1c8=8 r1c1<>8 r1c1=7 r3c1<>7 r3c1=6 r3c8<>6 r9c8=6 r9c8<>9
r4c8=8 r4c2<>8 r45c1=8 r1c1<>8 r1c1=7 r3c1<>7 r3c1=6 r3c8<>6 r9c8=6 r9c8<>9
r9c8=8 r9c8<>9
Forcing Net Verity => r1c1=7
r9c5=3 (r7c6<>3 r7c1=3 r4c1<>3) r4c5<>3 (r4c5=5 r4c1<>5) r6c4=3 r6c3<>3 r6c3=9 r4c1<>9 r4c1=8 r1c1<>8 r1c1=7
r9c5=5 (r9c5<>3) r4c5<>5 r4c5=3 (r4c1<>3) r6c4<>3 r6c3=3 r9c3<>3 r9c2=3 r7c1<>3 r2c1=3 r2c1<>6 r2c7=6 r3c8<>6 r3c8=7 (r1c7<>7) r1c8<>7 r1c1=7
r9c5=6 (r9c8<>6 r3c8=6 r3c1<>6 r3c1=7 r1c1<>7 r1c1=8 r1c7<>8 r1c7=5 r1c3<>5) (r9c8<>6 r9c8=8 r9c7<>8 r9c7=9 r7c9<>9) (r9c8<>6 r9c8=8 r9c7<>8 r9c7=9 r8c9<>9) r9c5<>5 r4c5=5 r5c4<>5 r5c4=9 r5c9<>9 r2c9=9 (r2c2<>9) r1c8<>9 (r1c3=9 r6c3<>9 r6c3=3 r9c3<>3) r4c8=9 r4c2<>9 r9c2=9 (r9c2<>5) r9c2<>3 r9c5=3 r9c5<>5 r9c3=5 r9c5<>5 r4c5=5 r4c5<>3 r6c4=3 r6c3<>3 r6c3=9 r1c3<>9 r1c3=8 r1c1<>8 r1c1=7
Naked Single: r3c1=6
Naked Single: r3c8=7
Hidden Single: r4c7=7
Hidden Single: r2c7=6
Hidden Single: r9c8=6
Hidden Single: r7c5=6
2-String Kite: 3 in r6c3,r9c5 (connected by r4c5,r6c4) => r9c3<>3
Turbot Fish: 3 r4c5 =3= r9c5 -3- r9c2 =3= r7c1 => r4c1<>3
X-Wing: 3 r49 c25 => r23c2<>3
Locked Candidates Type 1 (Pointing): 3 in b1 => r2c6<>3
Naked Triple: 5,8,9 in r1c3,r23c2 => r2c13<>8, r2c13<>9, r2c3<>5
2-String Kite: 9 in r2c2,r4c8 (connected by r1c8,r2c9) => r4c2<>9
Empty Rectangle: 8 in b1 (r14c8) => r4c2<>8
Locked Candidates Type 1 (Pointing): 8 in b4 => r78c1<>8
Naked Pair: 3,5 in r4c25 => r4c1<>5
Sashimi X-Wing: 5 c37 r17 fr8c3 fr9c3 => r7c1<>5
XY-Chain: 8 8- r1c8 -9- r4c8 -8- r4c1 -9- r6c3 -3- r4c2 -5- r3c2 -8 => r1c3<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r9c2<>8
Locked Candidates Type 2 (Claiming): 8 in r1 => r2c9<>8
W-Wing: 9/8 in r4c8,r9c7 connected by 8 in r1c78 => r5c7<>9
XY-Wing: 3/9/5 in r16c3,r4c2 => r23c2<>5
Naked Single: r3c2=8
Naked Single: r2c2=9
Naked Single: r1c3=5
Naked Single: r2c9=5
Naked Single: r2c6=8
Hidden Single: r7c4=8
Hidden Single: r7c7=5
Hidden Single: r5c7=4
Remote Pair: 9/8 r4c1 -8- r4c8 -9- r1c8 -8- r1c7 -9- r9c7 -8- r9c3 => r6c3,r78c1<>9
Naked Single: r6c3=3
Full House: r6c4=9
Naked Single: r4c2=5
Full House: r9c2=3
Naked Single: r5c4=5
Full House: r4c5=3
Full House: r9c5=5
Full House: r3c4=3
Full House: r3c6=5
Naked Single: r7c1=4
Naked Single: r8c6=9
Full House: r7c6=3
Naked Single: r2c1=3
Naked Single: r7c8=2
Full House: r7c9=9
Naked Single: r8c1=5
Naked Single: r8c3=8
Full House: r8c9=4
Full House: r9c7=8
Full House: r9c3=9
Full House: r1c7=9
Full House: r1c8=8
Naked Single: r2c8=4
Full House: r3c9=2
Full House: r5c9=8
Full House: r4c8=9
Full House: r2c3=2
Full House: r3c3=4
Full House: r5c1=9
Full House: r4c1=8
|
normal_sudoku_3146 | ..7...3.6..8.37..43.........39861..28.297..3117.2.38...917.8.2328.39.1..7.312.9.. | 417582396928637514365419287539861742842975631176243859691758423284396175753124968 | normal_sudoku_3146 | 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 | 9 | . . 7 . . . 3 . 6
. . 8 . 3 7 . . 4
3 . . . . . . . .
. 3 9 8 6 1 . . 2
8 . 2 9 7 . . 3 1
1 7 . 2 . 3 8 . .
. 9 1 7 . 8 . 2 3
2 8 . 3 9 . 1 . .
7 . 3 1 2 . 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 417582396928637514365419287539861742842975631176243859691758423284396175753124968 #1 Hard (1300)
Locked Candidates Type 1 (Pointing): 6 in b8 => r3c6<>6
Locked Candidates Type 2 (Claiming): 4 in c4 => r1c56,r3c56<>4
Locked Candidates Type 2 (Claiming): 5 in c4 => r1c56,r3c56<>5
Skyscraper: 6 in r5c2,r7c1 (connected by r57c7) => r9c2<>6
Swordfish: 6 r689 c368 => r3c3<>6
Empty Rectangle: 4 in b9 (r67c5) => r6c8<>4
W-Wing: 5/4 in r4c1,r5c6 connected by 4 in r6c35 => r5c2<>5
2-String Kite: 5 in r5c7,r7c5 (connected by r5c6,r6c5) => r7c7<>5
Turbot Fish: 5 r6c3 =5= r4c1 -5- r7c1 =5= r7c5 => r6c5<>5
Naked Single: r6c5=4
Full House: r5c6=5
Naked Single: r7c5=5
Naked Pair: 4,6 in r57c7 => r4c7<>4
Remote Pair: 4/6 r5c2 -6- r5c7 -4- r7c7 -6- r7c1 => r4c1,r9c2<>4
Naked Single: r4c1=5
Naked Single: r9c2=5
Naked Single: r4c7=7
Full House: r4c8=4
Naked Single: r6c3=6
Full House: r5c2=4
Full House: r5c7=6
Naked Single: r9c9=8
Naked Single: r8c3=4
Full House: r3c3=5
Full House: r7c1=6
Full House: r7c7=4
Naked Single: r9c8=6
Full House: r9c6=4
Full House: r8c6=6
Naked Single: r3c7=2
Full House: r2c7=5
Naked Single: r2c1=9
Full House: r1c1=4
Naked Single: r3c6=9
Full House: r1c6=2
Naked Single: r2c4=6
Naked Single: r2c8=1
Full House: r2c2=2
Naked Single: r1c4=5
Full House: r3c4=4
Naked Single: r3c9=7
Naked Single: r1c2=1
Full House: r3c2=6
Naked Single: r3c8=8
Full House: r1c8=9
Full House: r1c5=8
Full House: r3c5=1
Naked Single: r8c9=5
Full House: r6c9=9
Full House: r6c8=5
Full House: r8c8=7
|
normal_sudoku_3832 | 45692...1....4..........2....451.92.17.692...529.84..6.3.4.......52...8.9.1.6...2 | 456923871217845369398176245684517923173692458529384716832451697765239184941768532 | normal_sudoku_3832 | 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 | 9 | 4 5 6 9 2 . . . 1
. . . . 4 . . . .
. . . . . . 2 . .
. . 4 5 1 . 9 2 .
1 7 . 6 9 2 . . .
5 2 9 . 8 4 . . 6
. 3 . 4 . . . . .
. . 5 2 . . . 8 .
9 . 1 . 6 . . . 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 456923871217845369398176245684517923173692458529384716832451697765239184941768532 #1 Hard (1122)
Locked Candidates Type 1 (Pointing): 1 in b8 => r23c6<>1
Naked Triple: 4,6,8 in r489c2 => r23c2<>8
Hidden Pair: 1,9 in r78c6 => r7c6<>5, r78c6<>7, r7c6<>8, r8c6<>3
Locked Candidates Type 1 (Pointing): 8 in b8 => r9c2<>8
Naked Single: r9c2=4
Naked Single: r8c2=6
Naked Single: r4c2=8
Naked Single: r8c1=7
Naked Single: r5c3=3
Full House: r4c1=6
Naked Single: r8c5=3
W-Wing: 8/7 in r3c3,r9c4 connected by 7 in r37c5 => r3c4<>8
Uniqueness Test 4: 2/8 in r2c13,r7c13 => r2c13<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r3c69<>8
Sashimi X-Wing: 3 r14 c69 fr1c7 fr1c8 => r23c9<>3
Hidden Single: r4c9=3
Full House: r4c6=7
Full House: r6c4=3
Locked Candidates Type 2 (Claiming): 7 in r1 => r2c789,r3c89<>7
Hidden Single: r7c9=7
Naked Single: r7c5=5
Full House: r3c5=7
Naked Single: r9c6=8
Naked Single: r3c3=8
Naked Single: r3c4=1
Naked Single: r1c6=3
Naked Single: r9c4=7
Full House: r2c4=8
Naked Single: r3c1=3
Naked Single: r7c3=2
Full House: r2c3=7
Full House: r7c1=8
Full House: r2c1=2
Naked Single: r3c2=9
Full House: r2c2=1
Naked Single: r1c8=7
Full House: r1c7=8
Naked Single: r6c8=1
Full House: r6c7=7
Hidden Single: r5c9=8
Locked Candidates Type 2 (Claiming): 5 in c9 => r2c78,r3c8<>5
Bivalue Universal Grave + 1 => r2c8<>3, r2c8<>9
Naked Single: r2c8=6
Naked Single: r2c6=5
Full House: r3c6=6
Naked Single: r2c7=3
Full House: r2c9=9
Naked Single: r3c8=4
Full House: r3c9=5
Full House: r8c9=4
Naked Single: r7c8=9
Naked Single: r9c7=5
Full House: r9c8=3
Full House: r5c8=5
Full House: r5c7=4
Naked Single: r8c7=1
Full House: r7c7=6
Full House: r7c6=1
Full House: r8c6=9
|
normal_sudoku_1447 | .6732.14.2.4....3.13...67.274.2.3..135671.2.4.2165437.....3......35.2......86...3 | 867325149294187635135946782748293561356718294921654378612439857483572916579861423 | normal_sudoku_1447 | 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 | 9 | . 6 7 3 2 . 1 4 .
2 . 4 . . . . 3 .
1 3 . . . 6 7 . 2
7 4 . 2 . 3 . . 1
3 5 6 7 1 . 2 . 4
. 2 1 6 5 4 3 7 .
. . . . 3 . . . .
. . 3 5 . 2 . . .
. . . 8 6 . . . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 867325149294187635135946782748293561356718294921654378612439857483572916579861423 #1 Extreme (1864)
Naked Pair: 8,9 in r5c8,r6c9 => r4c78<>8, r4c78<>9
XYZ-Wing: 4/8/9 in r3c45,r4c5 => r2c5<>9
Finned Swordfish: 5 r349 c378 fr9c1 => r7c3<>5
Almost Locked Set XY-Wing: A=r9c12367 {124579}, B=r35c8 {589}, C=r347c3 {2589}, X,Y=2,5, Z=9 => r9c8<>9
Almost Locked Set Chain: 9- r3c45 {489} -8- r4c5 {89} -9- r5c6 {89} -8- r5c8 {89} -9 => r3c8<>9
XYZ-Wing: 5/8/9 in r16c9,r3c8 => r2c9<>8
Discontinuous Nice Loop: 9 r1c1 -9- r6c1 -8- r6c9 =8= r5c8 -8- r3c8 -5- r3c3 =5= r1c1 => r1c1<>9
Skyscraper: 9 in r1c9,r5c8 (connected by r15c6) => r6c9<>9
Naked Single: r6c9=8
Full House: r6c1=9
Full House: r4c3=8
Naked Single: r5c8=9
Full House: r5c6=8
Full House: r4c5=9
Hidden Single: r1c1=8
Naked Single: r2c2=9
Full House: r3c3=5
Naked Single: r2c4=1
Naked Single: r3c8=8
Naked Single: r3c5=4
Full House: r3c4=9
Full House: r7c4=4
Naked Single: r8c5=7
Full House: r2c5=8
Naked Single: r1c6=5
Full House: r1c9=9
Full House: r2c6=7
Naked Single: r8c9=6
Naked Single: r2c9=5
Full House: r2c7=6
Full House: r7c9=7
Naked Single: r8c1=4
Naked Single: r8c8=1
Naked Single: r4c7=5
Full House: r4c8=6
Naked Single: r9c1=5
Full House: r7c1=6
Naked Single: r8c2=8
Full House: r8c7=9
Naked Single: r9c8=2
Full House: r7c8=5
Naked Single: r7c2=1
Full House: r9c2=7
Naked Single: r7c7=8
Full House: r9c7=4
Naked Single: r9c3=9
Full House: r7c3=2
Full House: r7c6=9
Full House: r9c6=1
|
normal_sudoku_3065 | 9..54....3..18.7.6..13.....4.3.91....18.3....29...8.3.1.98.4....3492..1.82..139.4 | 972546183345182796681379542463291875518437269297658431159864327734925618826713954 | normal_sudoku_3065 | 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 | 9 | 9 . . 5 4 . . . .
3 . . 1 8 . 7 . 6
. . 1 3 . . . . .
4 . 3 . 9 1 . . .
. 1 8 . 3 . . . .
2 9 . . . 8 . 3 .
1 . 9 8 . 4 . . .
. 3 4 9 2 . . 1 .
8 2 . . 1 3 9 . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 972546183345182796681379542463291875518437269297658431159864327734925618826713954 #1 Extreme (11440)
Locked Candidates Type 1 (Pointing): 2 in b2 => r5c6<>2
Hidden Pair: 1,3 in r1c79 => r1c79<>2, r1c79<>8
Finned Swordfish: 5 r249 c238 fr4c7 fr4c9 => r5c8<>5
Forcing Net Verity => r3c2<>5
r7c7=5 (r7c7<>2) r7c7<>3 r7c9=3 r7c9<>2 r7c8=2 r1c8<>2 r1c8=8 (r3c7<>8) (r3c8<>8) r3c9<>8 r3c2=8 r3c2<>5
r7c8=5 (r2c8<>5) r9c8<>5 r9c3=5 r2c3<>5 r2c2=5 r3c2<>5
r7c9=5 (r7c9<>2) r7c9<>3 r7c7=3 r7c7<>2 r7c8=2 r1c8<>2 r1c8=8 (r3c7<>8) (r3c8<>8) r3c9<>8 r3c2=8 r3c2<>5
r8c7=5 (r8c1<>5) r8c6<>5 r5c6=5 r5c1<>5 r3c1=5 r3c2<>5
r8c9=5 (r8c1<>5) r8c6<>5 r5c6=5 r5c1<>5 r3c1=5 r3c2<>5
r9c8=5 r2c8<>5 r2c23=5 r3c2<>5
Forcing Net Verity => r3c2<>6
r3c5=6 r3c2<>6
r6c5=6 (r6c3<>6) (r4c4<>6) (r5c4<>6) r6c4<>6 r9c4=6 r9c3<>6 r1c3=6 r3c2<>6
r7c5=6 (r7c2<>6) (r3c5<>6 r3c5=7 r3c1<>7) (r3c5<>6 r3c5=7 r1c6<>7) (r3c5<>6 r3c5=7 r3c6<>7) r9c4<>6 r9c4=7 r8c6<>7 r5c6=7 r5c1<>7 r8c1=7 r7c2<>7 r7c2=5 (r2c2<>5) r9c3<>5 r9c8=5 r2c8<>5 r2c3=5 r2c3<>2 r1c3=2 r1c8<>2 r1c8=8 (r3c7<>8) (r3c8<>8) r3c9<>8 r3c2=8 r3c2<>6
Forcing Net Verity => r3c2<>7
r3c5=7 r3c2<>7
r6c5=7 (r6c3<>7) (r4c4<>7) (r5c4<>7) r6c4<>7 r9c4=7 r9c3<>7 r1c3=7 r3c2<>7
r7c5=7 (r7c2<>7) (r3c5<>7 r3c5=6 r3c1<>6) (r3c5<>7 r3c5=6 r1c6<>6) (r3c5<>7 r3c5=6 r3c6<>6) r9c4<>7 r9c4=6 r8c6<>6 r5c6=6 r5c1<>6 r8c1=6 (r8c7<>6 r8c7=8 r3c7<>8) r7c2<>6 r7c2=5 (r2c2<>5) r9c3<>5 r9c8=5 r2c8<>5 r2c3=5 r2c3<>2 r1c3=2 r1c8<>2 r1c8=8 (r3c8<>8) r3c9<>8 r3c2=8 r3c2<>7
Forcing Net Verity => r3c7<>8
r1c6=7 (r8c6<>7) (r3c5<>7) r3c6<>7 r3c1=7 r8c1<>7 r8c9=7 r8c9<>8 r8c7=8 r3c7<>8
r3c6=7 (r1c6<>7) r3c5<>7 r3c5=6 r1c6<>6 r1c6=2 r1c8<>2 r1c8=8 r3c7<>8
r5c6=7 (r5c6<>5 r8c6=5 r7c5<>5 r7c5=6 r7c2<>6) (r5c1<>7) (r1c6<>7) r3c6<>7 r3c5=7 r3c1<>7 r8c1=7 r7c2<>7 r7c2=5 r2c2<>5 r2c2=4 r3c2<>4 r3c2=8 r3c7<>8
r8c6=7 (r1c6<>7) (r3c6<>7 r3c5=7 r6c5<>7) r8c6<>5 r5c6=5 r6c5<>5 r6c5=6 (r6c3<>6) r6c4<>6 r9c4=6 (r4c4<>6) (r5c4<>6) r9c3<>6 r1c3=6 r1c6<>6 r1c6=2 r1c8<>2 r1c8=8 r3c7<>8
Forcing Net Contradiction in r1c8 => r3c8<>5
r3c8=5 (r2c8<>5) r9c8<>5 r9c3=5 r2c3<>5 r2c2=5 r2c2<>4 r2c8=4 (r3c7<>4) (r3c7<>4) r3c8<>4 r3c2=4 r3c2<>8 r1c2=8 r1c8<>8 r1c8=2 r3c7<>2 r3c7=5 r3c8<>5
Forcing Net Verity => r3c9<>8
r1c6=6 (r8c6<>6) (r3c5<>6) r3c6<>6 r3c1=6 r8c1<>6 r8c7=6 r8c7<>8 r8c9=8 r3c9<>8
r3c6=6 (r1c6<>6) r3c5<>6 r3c5=7 r1c6<>7 r1c6=2 r1c8<>2 r1c8=8 r3c9<>8
r5c6=6 (r5c6<>5 r8c6=5 r7c5<>5 r7c5=7 r7c2<>7) (r5c1<>6) (r1c6<>6) r3c6<>6 r3c5=6 r3c1<>6 r8c1=6 r7c2<>6 r7c2=5 r2c2<>5 r2c2=4 r3c2<>4 r3c2=8 r3c9<>8
r8c6=6 (r1c6<>6) (r9c4<>6 r9c4=7 r9c3<>7) (r3c6<>6 r3c5=6 r6c5<>6) r8c6<>5 r5c6=5 r6c5<>5 r6c5=7 r6c3<>7 r1c3=7 r1c6<>7 r1c6=2 r1c8<>2 r1c8=8 r3c9<>8
Locked Candidates Type 1 (Pointing): 8 in b3 => r4c8<>8
Forcing Net Verity => r4c8<>5
r7c7=5 (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r2c8<>2) (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r2c6<>2 r2c6=9 r2c8<>9) (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r1c3<>2) (r7c7<>2) r7c7<>3 r7c9=3 r7c9<>2 r7c8=2 r1c8<>2 r1c6=2 r1c8<>2 r1c8=8 r3c8<>8 r3c2=8 r3c2<>4 r2c2=4 r2c8<>4 r2c8=5 r4c8<>5
r7c8=5 r4c8<>5
r7c9=5 (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r2c8<>2) (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r2c6<>2 r2c6=9 r2c8<>9) (r9c8<>5 r9c3=5 r2c3<>5 r2c3=2 r1c3<>2) (r7c9<>2) r7c9<>3 r7c7=3 r7c7<>2 r7c8=2 r1c8<>2 r1c6=2 r1c8<>2 r1c8=8 r3c8<>8 r3c2=8 r3c2<>4 r2c2=4 r2c8<>4 r2c8=5 r4c8<>5
r8c7=5 (r8c6<>5 r5c6=5 r6c5<>5) (r6c7<>5) r9c8<>5 r9c3=5 r6c3<>5 r6c9=5 r4c8<>5
r8c9=5 (r8c6<>5 r5c6=5 r6c5<>5) (r6c9<>5) r9c8<>5 r9c3=5 r6c3<>5 r6c7=5 r4c8<>5
r9c8=5 r4c8<>5
Forcing Net Verity => r5c4<>6
r7c5=6 (r6c5<>6) (r9c4<>6) (r8c6<>6) r9c4<>6 r9c4=7 r8c6<>7 r5c6=7 (r5c1<>7) r3c6<>7 r3c5=7 (r1c6<>7) (r1c6<>7) (r3c6<>7) r3c1<>7 r8c1=7 r8c1<>6 r8c7=6 (r6c7<>6) r9c8<>6 r9c3=6 r6c3<>6 r6c4=6 r5c4<>6
r8c6=6 (r8c1<>6) (r1c6<>6) r3c6<>6 r3c5=6 r3c1<>6 r5c1=6 r5c4<>6
r9c4=6 r5c4<>6
Forcing Net Verity => r5c4<>7
r7c5=7 (r6c5<>7) (r9c4<>7) (r8c6<>7) r9c4<>7 r9c4=6 r8c6<>6 r5c6=6 (r5c1<>6) r3c6<>6 r3c5=6 (r1c6<>6) (r1c6<>6) (r3c6<>6) r3c1<>6 r8c1=6 r8c1<>7 r8c9=7 (r6c9<>7) r9c8<>7 r9c3=7 r6c3<>7 r6c4=7 r5c4<>7
r8c6=7 (r8c1<>7) (r1c6<>7) r3c6<>7 r3c5=7 r3c1<>7 r5c1=7 r5c4<>7
r9c4=7 r5c4<>7
Forcing Net Verity => r5c7<>5
r5c6=5 r5c7<>5
r5c6=6 (r5c6<>5 r8c6=5 r7c5<>5 r6c5=5 r6c3<>5) (r5c6<>5 r8c6=5 r7c5<>5 r7c5=7 r7c2<>7) (r5c1<>6) (r1c6<>6) r3c6<>6 r3c5=6 r3c1<>6 r8c1=6 r7c2<>6 r7c2=5 r4c2<>5 r5c1=5 r5c7<>5
r5c6=7 (r5c6<>5 r8c6=5 r7c5<>5 r6c5=5 r6c3<>5) (r5c6<>5 r8c6=5 r7c5<>5 r7c5=6 r7c2<>6) (r5c1<>7) (r1c6<>7) r3c6<>7 r3c5=7 r3c1<>7 r8c1=7 r7c2<>7 r7c2=5 r4c2<>5 r5c1=5 r5c7<>5
Forcing Chain Verity => r7c9<>5
r5c1=5 r3c1<>5 r2c23=5 r2c8<>5 r79c8=5 r7c9<>5
r5c6=5 r8c6<>5 r7c5=5 r7c9<>5
r5c9=5 r7c9<>5
Forcing Net Verity => r5c9<>5
r5c6=5 r5c9<>5
r5c6=6 (r5c6<>5 r8c6=5 r7c5<>5 r6c5=5 r6c3<>5) (r5c6<>5 r8c6=5 r7c5<>5 r7c5=7 r7c2<>7) (r5c1<>6) (r1c6<>6) r3c6<>6 r3c5=6 r3c1<>6 r8c1=6 r7c2<>6 r7c2=5 r4c2<>5 r5c1=5 r5c9<>5
r5c6=7 (r5c6<>5 r8c6=5 r7c5<>5 r6c5=5 r6c3<>5) (r5c6<>5 r8c6=5 r7c5<>5 r7c5=6 r7c2<>6) (r5c1<>7) (r1c6<>7) r3c6<>7 r3c5=7 r3c1<>7 r8c1=7 r7c2<>7 r7c2=5 r4c2<>5 r5c1=5 r5c9<>5
Grouped Discontinuous Nice Loop: 5 r7c7 -5- r7c5 =5= r6c5 -5- r5c6 =5= r5c1 -5- r3c1 =5= r2c23 -5- r2c8 =5= r79c8 -5- r7c7 => r7c7<>5
Forcing Net Verity => r1c6<>2
r1c6=6 r1c6<>2
r3c6=6 (r8c6<>6) (r3c1<>6) r3c5<>6 r3c5=7 (r3c1<>7) (r6c5<>7) r3c1<>7 r3c1=5 (r2c3<>5) r5c1<>5 r5c6=5 r6c5<>5 r6c5=6 (r6c3<>6) r6c5<>5 r7c5=5 r8c6<>5 r8c6=7 r8c1<>7 r5c1=7 r6c3<>7 r6c3=5 r9c3<>5 r9c8=5 r2c8<>5 r2c2=5 r2c2<>4 r2c8=4 (r3c7<>4) r3c8<>4 r3c2=4 r3c2<>8 r3c8=8 r1c8<>8 r1c8=2 r1c6<>2
r5c6=6 (r3c6<>6 r3c5=6 r3c1<>6) r5c6<>5 r5c1=5 r3c1<>5 r3c1=7 (r1c2<>7) r1c3<>7 r1c6=7 r1c6<>2
r8c6=6 (r8c6<>5 r5c6=5 r6c5<>5 r7c5=5 r7c2<>5) (r8c6<>5 r5c6=5 r6c5<>5 r6c5=7 r6c3<>7) (r8c1<>6) (r1c6<>6) r3c6<>6 r3c5=6 r3c1<>6 r5c1=6 r6c3<>6 r6c3=5 r4c2<>5 r2c2=5 r2c2<>4 r2c8=4 (r3c7<>4) r3c8<>4 r3c2=4 r3c2<>8 r3c8=8 r1c8<>8 r1c8=2 r1c6<>2
Naked Pair: 6,7 in r1c6,r3c5 => r3c6<>6, r3c6<>7
Hidden Pair: 6,7 in r3c15 => r3c1<>5
Locked Candidates Type 1 (Pointing): 5 in b1 => r2c8<>5
Locked Candidates Type 2 (Claiming): 5 in c8 => r8c79<>5
Finned Franken Swordfish: 6 c34b2 r169 fr3c5 fr4c4 => r6c5<>6
W-Wing: 7/6 in r1c6,r9c4 connected by 6 in r37c5 => r8c6<>7
2-String Kite: 7 in r3c1,r5c6 (connected by r1c6,r3c5) => r5c1<>7
Sashimi Swordfish: 7 c346 r169 fr4c4 fr5c6 => r6c5<>7
Naked Single: r6c5=5
Hidden Single: r5c1=5
Hidden Single: r8c6=5
Naked Triple: 2,6,7 in r4c248 => r4c79<>2, r4c7<>6, r4c9<>7
Remote Pair: 6/7 r7c5 -7- r3c5 -6- r3c1 -7- r8c1 => r7c2<>6, r7c2<>7
Naked Single: r7c2=5
Naked Single: r2c2=4
Naked Single: r3c2=8
Hidden Single: r2c3=5
Hidden Single: r9c8=5
Hidden Single: r1c8=8
Hidden Single: r1c3=2
Remote Pair: 6/7 r4c2 -7- r1c2 -6- r1c6 -7- r5c6 => r4c4<>6, r4c4<>7
Naked Single: r4c4=2
Naked Single: r5c4=4
Hidden Single: r3c8=4
Hidden Single: r6c7=4
Hidden Single: r6c9=1
Naked Single: r1c9=3
Naked Single: r1c7=1
Hidden Single: r7c7=3
Remote Pair: 6/7 r4c8 -7- r4c2 -6- r1c2 -7- r1c6 -6- r3c5 -7- r7c5 => r7c8<>6, r7c8<>7
Naked Single: r7c8=2
Naked Single: r2c8=9
Full House: r2c6=2
Naked Single: r7c9=7
Full House: r7c5=6
Full House: r3c5=7
Full House: r9c4=7
Full House: r6c4=6
Full House: r9c3=6
Full House: r5c6=7
Full House: r6c3=7
Full House: r8c1=7
Full House: r3c1=6
Full House: r4c2=6
Full House: r1c2=7
Full House: r1c6=6
Full House: r3c6=9
Naked Single: r8c9=8
Full House: r8c7=6
Naked Single: r5c8=6
Full House: r4c8=7
Naked Single: r4c9=5
Full House: r4c7=8
Naked Single: r5c7=2
Full House: r3c7=5
Full House: r3c9=2
Full House: r5c9=9
|
normal_sudoku_6721 | 9..1..35...7.5...........726...91.8...3.486....16......4..1...53...2..4.1..9.48.. | 962187354417352968538469172674291583253748619891635427746813295389526741125974836 | normal_sudoku_6721 | 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 | 9 | 9 . . 1 . . 3 5 .
. . 7 . 5 . . . .
. . . . . . . 7 2
6 . . . 9 1 . 8 .
. . 3 . 4 8 6 . .
. . 1 6 . . . . .
. 4 . . 1 . . . 5
3 . . . 2 . . 4 .
1 . . 9 . 4 8 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 962187354417352968538469172674291583253748619891635427746813295389526741125974836 #1 Extreme (4138)
Locked Candidates Type 1 (Pointing): 9 in b4 => r8c2<>9
Locked Candidates Type 1 (Pointing): 5 in b8 => r8c23<>5
Locked Candidates Type 1 (Pointing): 8 in b8 => r23c4<>8
Hidden Pair: 1,3 in r23c2 => r2c2<>2, r23c2<>6, r23c2<>8, r3c2<>5
Turbot Fish: 4 r1c9 =4= r1c3 -4- r4c3 =4= r6c1 => r6c9<>4
Grouped Discontinuous Nice Loop: 4 r3c7 -4- r3c4 -3- r4c4 =3= r4c9 =4= r46c7 -4- r3c7 => r3c7<>4
Almost Locked Set XZ-Rule: A=r6c5 {37}, B=r5c89,r6c89 {12379}, X=3, Z=7 => r6c7<>7
Almost Locked Set XY-Wing: A=r679c8 {2369}, B=r4c23,r5c12 {24579}, C=r45689c9 {134679}, X,Y=4,6, Z=9 => r5c8<>9
Forcing Chain Verity => r1c9<>6
r1c2=8 r6c2<>8 r6c1=8 r6c1<>4 r4c3=4 r1c3<>4 r1c9=4 r1c9<>6
r1c3=8 r1c3<>4 r1c9=4 r1c9<>6
r2c1=8 r2c9<>8 r1c9=8 r1c9<>6
r3c1=8 r3c1<>5 r3c3=5 r3c3<>6 r1c23=6 r1c9<>6
r3c3=8 r3c3<>6 r1c23=6 r1c9<>6
Locked Candidates Type 1 (Pointing): 6 in b3 => r2c6<>6
Forcing Chain Contradiction in c1 => r5c8=1
r5c8<>1 r2c8=1 r2c8<>6 r2c9=6 r2c9<>8 r2c1=8 r2c1<>2
r5c8<>1 r5c8=2 r5c1<>2
r5c8<>1 r2c8=1 r2c8<>6 r2c9=6 r2c9<>8 r1c9=8 r1c9<>4 r1c3=4 r4c3<>4 r6c1=4 r6c1<>2
r5c8<>1 r5c8=2 r9c8<>2 r7c78=2 r7c1<>2
Discontinuous Nice Loop: 7 r4c7 -7- r5c9 -9- r5c2 =9= r6c2 =8= r6c1 =4= r6c7 =5= r4c7 => r4c7<>7
Locked Candidates Type 1 (Pointing): 7 in b6 => r89c9<>7
Discontinuous Nice Loop: 6 r9c2 -6- r9c9 -3- r4c9 =3= r4c4 -3- r6c5 -7- r9c5 =7= r9c2 => r9c2<>6
Discontinuous Nice Loop: 6 r9c3 -6- r9c9 -3- r4c9 =3= r4c4 -3- r6c5 -7- r9c5 =7= r9c2 =5= r9c3 => r9c3<>6
Almost Locked Set XZ-Rule: A=r4c23,r5c1 {2457}, B=r456c9,r6c8 {23479}, X=4, Z=2 => r6c12<>2
Almost Locked Set XY-Wing: A=r9c23 {257}, B=r456c9,r6c8 {23479}, C=r4c237 {2457}, X,Y=4,7, Z=2 => r9c8<>2
Locked Pair: 3,6 in r9c89 => r7c8,r9c5<>3, r7c8,r8c9,r9c5<>6
Naked Single: r9c5=7
Naked Single: r6c5=3
Hidden Single: r1c6=7
Hidden Single: r4c9=3
Naked Single: r9c9=6
Naked Single: r9c8=3
Hidden Single: r2c8=6
Locked Pair: 7,9 in r56c9 => r28c9,r6c78<>9
Naked Single: r8c9=1
Naked Single: r6c8=2
Full House: r7c8=9
Naked Single: r6c6=5
Naked Single: r8c7=7
Full House: r7c7=2
Naked Single: r6c7=4
Naked Single: r8c6=6
Naked Single: r4c7=5
Naked Single: r7c6=3
Naked Single: r8c2=8
Naked Single: r3c6=9
Full House: r2c6=2
Naked Single: r7c4=8
Full House: r8c4=5
Full House: r8c3=9
Naked Single: r7c1=7
Full House: r7c3=6
Naked Single: r3c7=1
Full House: r2c7=9
Naked Single: r6c1=8
Naked Single: r3c2=3
Naked Single: r2c1=4
Naked Single: r2c2=1
Naked Single: r3c4=4
Naked Single: r2c4=3
Full House: r2c9=8
Full House: r1c9=4
Naked Single: r3c1=5
Full House: r5c1=2
Naked Single: r3c3=8
Full House: r3c5=6
Full House: r1c5=8
Naked Single: r4c2=7
Naked Single: r4c3=4
Full House: r4c4=2
Full House: r5c4=7
Naked Single: r1c3=2
Full House: r1c2=6
Full House: r9c3=5
Full House: r9c2=2
Naked Single: r6c2=9
Full House: r5c2=5
Full House: r5c9=9
Full House: r6c9=7
|
normal_sudoku_4345 | .3.4.....26..3.14.874..2.35.1..4.5.9...5...1.54.8..32....35....456.8...33....485. | 931475682265938147874162935618243579723596418549817326182359764456781293397624851 | normal_sudoku_4345 | 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 | 9 | . 3 . 4 . . . . .
2 6 . . 3 . 1 4 .
8 7 4 . . 2 . 3 5
. 1 . . 4 . 5 . 9
. . . 5 . . . 1 .
5 4 . 8 . . 3 2 .
. . . 3 5 . . . .
4 5 6 . 8 . . . 3
3 . . . . 4 8 5 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 931475682265938147874162935618243579723596418549817326182359764456781293397624851 #1 Extreme (2434)
Locked Candidates Type 1 (Pointing): 1 in b1 => r1c56<>1
Locked Candidates Type 2 (Claiming): 1 in r8 => r7c6,r9c45<>1
Naked Triple: 6,7,9 in r45c1,r6c3 => r45c3<>7, r5c23<>9
Locked Candidates Type 2 (Claiming): 9 in c2 => r7c13,r9c3<>9
Hidden Pair: 5,8 in r12c6 => r1c6<>6, r12c6<>7, r12c6<>9
2-String Kite: 2 in r4c3,r9c5 (connected by r4c4,r5c5) => r9c3<>2
Naked Pair: 1,7 in r7c1,r9c3 => r7c3<>1, r7c3<>7
XY-Chain: 6 6- r4c1 -7- r6c3 -9- r2c3 -5- r2c6 -8- r2c9 -7- r6c9 -6 => r4c8<>6
XY-Chain: 7 7- r2c9 -8- r2c6 -5- r2c3 -9- r6c3 -7 => r6c9<>7
Naked Single: r6c9=6
Locked Candidates Type 1 (Pointing): 6 in b9 => r7c6<>6
Locked Candidates Type 2 (Claiming): 6 in c6 => r4c4,r5c5<>6
Naked Triple: 1,7,9 in r678c6 => r45c6<>7, r5c6<>9
W-Wing: 9/7 in r6c3,r7c6 connected by 7 in r7c1,r9c3 => r6c6<>9
Locked Candidates Type 1 (Pointing): 9 in b5 => r139c5<>9
Locked Candidates Type 1 (Pointing): 9 in b2 => r89c4<>9
Hidden Single: r9c2=9
Locked Candidates Type 1 (Pointing): 2 in b7 => r7c79<>2
Uniqueness Test 1: 2/8 in r5c23,r7c23 => r5c3<>2, r5c3<>8
Naked Single: r5c3=3
Naked Single: r5c6=6
Naked Single: r4c6=3
Hidden Single: r4c1=6
Skyscraper: 7 in r2c9,r4c8 (connected by r24c4) => r1c8,r5c9<>7
Turbot Fish: 7 r4c8 =7= r5c7 -7- r5c1 =7= r7c1 => r7c8<>7
XY-Wing: 4/8/7 in r25c9,r5c7 => r1c7<>7
Locked Candidates Type 1 (Pointing): 7 in b3 => r79c9<>7
Sashimi X-Wing: 7 c36 r69 fr7c6 fr8c6 => r9c45<>7
Hidden Single: r9c3=7
Naked Single: r6c3=9
Naked Single: r7c1=1
Naked Single: r2c3=5
Naked Single: r5c1=7
Full House: r1c1=9
Full House: r1c3=1
Naked Single: r7c9=4
Naked Single: r2c6=8
Naked Single: r5c7=4
Naked Single: r5c9=8
Full House: r4c8=7
Naked Single: r1c6=5
Naked Single: r2c9=7
Full House: r2c4=9
Naked Single: r5c2=2
Full House: r4c3=8
Full House: r4c4=2
Full House: r5c5=9
Full House: r7c2=8
Full House: r7c3=2
Naked Single: r8c8=9
Naked Single: r1c9=2
Full House: r9c9=1
Naked Single: r9c4=6
Full House: r9c5=2
Naked Single: r7c8=6
Full House: r1c8=8
Naked Single: r1c7=6
Full House: r1c5=7
Full House: r3c7=9
Naked Single: r3c4=1
Full House: r3c5=6
Full House: r6c5=1
Full House: r8c4=7
Full House: r6c6=7
Naked Single: r7c7=7
Full House: r7c6=9
Full House: r8c6=1
Full House: r8c7=2
|
normal_sudoku_4882 | 61......2..82...4.2....79.85..3724......86..9..24....3....5..3...39..8..1..7...9. | 619548372758239641234617958591372486347186529862495713926854137473921865185763294 | normal_sudoku_4882 | 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 | 9 | 6 1 . . . . . . 2
. . 8 2 . . . 4 .
2 . . . . 7 9 . 8
5 . . 3 7 2 4 . .
. . . . 8 6 . . 9
. . 2 4 . . . . 3
. . . . 5 . . 3 .
. . 3 9 . . 8 . .
1 . . 7 . . . 9 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 619548372758239641234617958591372486347186529862495713926854137473921865185763294 #1 Extreme (12762)
Locked Candidates Type 1 (Pointing): 9 in b5 => r6c12<>9
Grouped Discontinuous Nice Loop: 4 r9c2 -4- r78c1 =4= r5c1 =3= r5c2 -3- r3c2 =3= r3c5 -3- r9c5 =3= r9c6 =8= r9c2 => r9c2<>4
Forcing Net Contradiction in c8 => r3c4<>5
r3c4=5 (r3c3<>5 r3c3=4 r1c3<>4) (r3c3<>5 r3c3=4 r7c3<>4) (r3c4<>6 r7c4=6 r7c3<>6) (r3c3<>5 r3c3=4 r5c3<>4) r5c4<>5 r5c4=1 r5c3<>1 r5c3=7 (r1c3<>7) r7c3<>7 r7c3=9 r1c3<>9 r1c3=5 r1c8<>5
r3c4=5 r3c8<>5
r3c4=5 (r3c4<>6 r7c4=6 r8c5<>6) (r3c4<>6 r7c4=6 r7c3<>6) r5c4<>5 r5c4=1 r5c3<>1 r4c3=1 (r4c9<>1 r4c9=6 r8c9<>6) r4c3<>6 r9c3=6 r8c2<>6 r8c8=6 r8c8<>2 r5c8=2 r5c8<>5
r3c4=5 (r1c6<>5) r2c6<>5 r6c6=5 r6c8<>5
r3c4=5 (r3c4<>6 r7c4=6 r8c5<>6) (r3c4<>6 r7c4=6 r7c3<>6) r5c4<>5 r5c4=1 r5c3<>1 r4c3=1 (r4c9<>1 r4c9=6 r8c9<>6) r4c3<>6 r9c3=6 r8c2<>6 r8c8=6 r8c8<>5
Forcing Chain Contradiction in c8 => r5c8<>5
r5c8=5 r5c4<>5 r5c4=1 r3c4<>1 r3c4=6 r3c8<>6
r5c8=5 r5c4<>5 r5c4=1 r5c3<>1 r4c3=1 r4c9<>1 r4c9=6 r4c8<>6
r5c8=5 r5c4<>5 r5c4=1 r5c3<>1 r4c3=1 r4c9<>1 r4c9=6 r6c8<>6
r5c8=5 r5c8<>2 r8c8=2 r8c8<>6
Forcing Chain Contradiction in b6 => r6c7<>1
r6c7=1 r6c56<>1 r5c4=1 r5c4<>5 r5c7=5 r5c7<>7
r6c7=1 r6c56<>1 r5c4=1 r5c4<>5 r5c7=5 r5c7<>2 r5c8=2 r5c8<>7
r6c7=1 r6c7<>7
r6c7=1 r6c56<>1 r5c4=1 r5c4<>5 r1c4=5 r1c8<>5 r1c8=7 r6c8<>7
Forcing Net Contradiction in c3 => r4c8=8
r4c8<>8 r4c2=8 r4c2<>9 r4c3=9 r4c3<>6
r4c8<>8 r4c2=8 r6c1<>8 (r7c1=8 r7c4<>8) r6c1=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r7c4<>1 r7c4=6 r7c3<>6
r4c8<>8 r4c2=8 (r6c1<>8 r6c1=7 r6c2<>7 r6c2=6 r6c7<>6 r6c7=5 r9c7<>5) (r6c1<>8 r7c1=8 r7c1<>9) r4c2<>9 r4c3=9 r7c3<>9 r7c2=9 r7c2<>2 r7c7=2 r9c7<>2 r9c7=6 r9c3<>6
Forcing Net Contradiction in c8 => r6c1=8
r6c1<>8 (r7c1=8 r7c4<>8) r6c1=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r7c4<>1 r7c4=6 r3c4<>6 r3c4=1 r3c8<>1
r6c1<>8 r6c1=7 (r5c3<>7) (r5c2<>7) (r5c1<>7) r8c1<>7 r8c1=4 r5c1<>4 r5c1=3 r5c2<>3 r5c2=4 r5c3<>4 r5c3=1 r5c8<>1
r6c1<>8 (r7c1=8 r7c4<>8) r6c1=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 (r8c5<>1) r7c4<>1 r7c4=6 r3c4<>6 r3c4=1 (r2c5<>1) r3c5<>1 r6c5=1 r6c8<>1
r6c1<>8 r6c1=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r8c8<>1
Almost Locked Set XY-Wing: A=r9c379 {2456}, B=r2345678c2 {23456789}, C=r7c134679 {1246789}, X,Y=2,8, Z=5,6 => r9c2<>5, r9c2<>6
Forcing Net Contradiction in r5c4 => r1c3<>5
r1c3=5 (r3c2<>5 r8c2=5 r8c9<>5 r9c9=5 r9c7<>5 r9c7=2 r9c5<>2) (r3c3<>5 r3c3=4 r9c3<>4 r9c3=6 r9c5<>6) (r1c4<>5 r5c4=5 r6c6<>5 r2c6=5 r2c6<>3) (r1c7<>5) r1c8<>5 r1c8=7 r1c7<>7 r1c7=3 r1c6<>3 r9c6=3 r9c5<>3 r9c5=4 r8c6<>4 r8c6=1 r6c6<>1 r6c8=1 r6c56<>1 r5c4=1
r1c3=5 r1c4<>5 r5c4=5
Forcing Net Contradiction in b8 => r1c6<>4
r1c6=4 (r8c6<>4 r8c6=1 r7c4<>1) r1c6<>8 r1c4=8 r7c4<>8 r7c4=6
r1c6=4 (r8c6<>4 r8c6=1 r8c8<>1) (r8c6<>4 r8c6=1 r8c5<>1) (r8c6<>4 r8c6=1 r7c4<>1) r1c6<>8 r1c4=8 r7c4<>8 r7c4=6 r3c4<>6 r3c4=1 (r3c8<>1) (r2c5<>1) r3c5<>1 r6c5=1 r6c8<>1 r5c8=1 (r5c8<>2 r8c8=2 r8c8<>6) r4c9<>1 r4c9=6 (r8c9<>6) (r6c7<>6) r6c8<>6 r6c2=6 r8c2<>6 r8c5=6
Locked Candidates Type 1 (Pointing): 4 in b2 => r89c5<>4
Forcing Net Contradiction in r7c1 => r1c5<>3
r1c5=3 (r9c5<>3 r9c6=3 r9c6<>4) r1c5<>4 r1c3=4 (r3c3<>4 r3c3=5 r9c3<>5) r9c3<>4 r9c9=4 r9c9<>5 r9c7=5 (r1c7<>5) (r6c7<>5) r5c7<>5 r5c4=5 r6c6<>5 r6c8=5 r1c8<>5 r1c8=7 r1c7<>7 r1c7=3 r1c5<>3
Forcing Net Contradiction in c7 => r1c7<>5
r1c7=5 r1c7<>3 r2c7=3 r2c7<>6
r1c7=5 (r5c7<>5 r5c4=5 r6c6<>5 r2c6=5 r2c6<>1) (r5c7<>5 r5c4=5 r6c6<>5 r2c6=5 r2c6<>9) r1c7<>3 (r2c7=3 r2c7<>1) r1c6=3 r1c6<>9 r6c6=9 r6c5<>9 r6c5=1 r2c5<>1 r2c9=1 r4c9<>1 r4c9=6 r6c7<>6
r1c7=5 (r5c7<>5 r5c4=5 r6c6<>5 r2c6=5 r2c6<>1) (r5c7<>5 r5c4=5 r6c6<>5 r2c6=5 r2c6<>9) r1c7<>3 (r2c7=3 r2c7<>1) r1c6=3 r1c6<>9 r6c6=9 r6c5<>9 r6c5=1 (r3c5<>1) r2c5<>1 r2c9=1 r3c8<>1 r3c4=1 r3c4<>6 r7c4=6 r7c7<>6
r1c7=5 (r1c6<>5) r1c7<>3 r1c6=3 (r1c6<>9 r6c6=9 r6c5<>9 r6c5=1 r2c5<>1 r2c9=1 r3c8<>1 r3c4=1 r3c4<>6 r7c4=6 r7c2<>6) (r1c6<>9 r6c6=9 r6c5<>9 r6c5=1 r2c5<>1 r2c9=1 r3c8<>1 r3c4=1 r3c4<>6 r7c4=6 r7c3<>6) (r3c5<>3 r3c2=3 r3c2<>5) r1c6<>8 r1c4=8 r1c4<>5 r5c4=5 r6c6<>5 r2c6=5 r2c2<>5 r8c2=5 r8c2<>6 r9c3=6 r9c7<>6
Forcing Net Contradiction in r9 => r1c7=3
r1c7<>3 (r1c7=7 r1c8<>7 r1c8=5 r6c8<>5) r1c6=3 (r9c6<>3 r9c5=3 r9c5<>6) (r3c5<>3 r3c2=3 r3c2<>5 r3c3=5 r9c3<>5) r1c6<>8 r1c4=8 r1c4<>5 r5c4=5 r6c6<>5 r6c7=5 r9c7<>5 r9c9=5 r9c9<>6 r9c3=6
r1c7<>3 (r2c7=3 r2c7<>6) (r1c7=7 r1c8<>7 r1c8=5 r6c8<>5) r1c6=3 (r9c6<>3 r9c5=3 r9c5<>2 r8c5=2 r8c5<>6 r7c4=6 r7c7<>6) r1c6<>8 r1c4=8 r1c4<>5 r5c4=5 r6c6<>5 r6c7=5 r6c7<>6 r9c7=6
Forcing Net Verity => r2c9<>7
r1c8=7 r2c9<>7
r5c8=7 (r6c8<>7 r6c2=7 r6c2<>6) (r1c8<>7 r1c8=5 r6c8<>5) r5c8<>2 r5c7=2 r5c7<>5 r5c4=5 r6c6<>5 r6c7=5 (r9c7<>5 r9c7=6 r7c9<>6) (r9c7<>5 r9c7=6 r8c9<>6) (r9c7<>5 r9c7=6 r9c9<>6) r6c7<>6 r6c8=6 r4c9<>6 r2c9=6 r2c9<>7
r6c8=7 (r1c8<>7 r1c8=5 r1c4<>5 r1c4=8 r1c6<>8 r1c6=9 r2c5<>9 r2c1=9 r7c1<>9 r7c3=9 r7c3<>6 r9c3=6 r9c3<>5 r9c79=5 r8c9<>5) (r1c8<>7 r1c8=5 r1c4<>5 r1c4=8 r1c6<>8 r1c6=9 r2c5<>9 r2c1=9 r7c1<>9 r7c3=9 r7c3<>6 r9c3=6 r9c7<>6) (r1c8<>7 r1c8=5 r1c4<>5 r1c4=8 r1c6<>8 r1c6=9 r2c5<>9 r2c1=9 r7c1<>9 r7c3=9 r7c3<>6 r9c3=6 r9c5<>6) (r1c8<>7 r1c3=7 r5c3<>7) r6c2<>7 r6c2=6 (r4c3<>6) r4c2<>6 r4c2=9 r4c3<>9 r4c3=1 r5c3<>1 r5c3=4 (r3c3<>4) r1c3<>4 r1c5=4 r3c5<>4 r3c2=4 r3c2<>3 r3c5=3 r9c5<>3 r9c5=2 r9c7<>2 r9c7=5 r9c9<>5 r2c9=5 r2c9<>7
r8c8=7 (r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r6c6<>1) r1c8<>7 r1c8=5 r1c4<>5 r5c4=5 r6c6<>5 r6c6=9 (r1c6<>9) r6c6<>5 r5c4=5 r1c4<>5 r1c4=8 r1c6<>8 r1c6=5 r1c8<>5 r1c8=7 r2c9<>7
Locked Candidates Type 2 (Claiming): 7 in c9 => r7c7,r8c8<>7
Forcing Chain Contradiction in c4 => r7c9<>6
r7c9=6 r7c4<>6 r3c4=6 r3c4<>1
r7c9=6 r4c9<>6 r4c9=1 r4c3<>1 r5c3=1 r5c4<>1
r7c9=6 r7c9<>7 r8c9=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r7c4<>1
Forcing Net Verity => r3c5<>6
r3c8=1 r3c4<>1 r3c4=6 r3c5<>6
r3c8=5 (r8c8<>5) r3c3<>5 (r3c3=4 r7c3<>4) (r3c3=4 r1c3<>4 r1c3=9 r7c3<>9) r9c3=5 r8c2<>5 r8c9=5 r8c9<>7 r7c9=7 r7c3<>7 r7c3=6 r7c4<>6 r3c4=6 r3c5<>6
r3c8=6 r3c5<>6
Forcing Net Verity => r1c8=7
r5c1=7 (r6c2<>7 r6c2=6 r4c2<>6 r4c2=9 r4c3<>9) (r7c1<>7) r8c1<>7 r8c1=4 r7c1<>4 r7c1=9 r7c3<>9 r1c3=9 r1c3<>7 r1c8=7
r5c2=7 (r5c2<>4) r5c2<>3 r5c1=3 r5c1<>4 r5c3=4 (r3c3<>4 r3c3=5 r3c2<>5 r8c2=5 r8c9<>5) (r3c3<>4 r3c3=5 r9c3<>5 r9c3=6 r9c7<>6) (r3c3<>4 r3c3=5 r9c3<>5 r9c3=6 r9c5<>6) (r3c3<>4) r1c3<>4 r1c5=4 r3c5<>4 r3c2=4 r3c2<>3 r3c5=3 r9c5<>3 r9c5=2 r9c7<>2 r9c7=5 r9c9<>5 r2c9=5 r1c8<>5 r1c8=7
r5c3=7 r1c3<>7 r1c8=7
r5c7=7 (r5c8<>7) r6c8<>7 r1c8=7
r5c8=7 (r6c8<>7 r6c2=7 r6c2<>6) (r1c8<>7 r1c8=5 r6c8<>5) r5c8<>2 r5c7=2 (r5c7<>1) r5c7<>5 r5c4=5 r6c6<>5 r6c7=5 r6c7<>6 r6c8=6 (r3c8<>6 r3c4=6 r3c4<>1) r4c9<>6 r4c9=1 r4c3<>1 r5c3=1 r5c4<>1 r7c4=1 r7c7<>1 r2c7=1 r2c7<>7 r1c8=7
Locked Candidates Type 2 (Claiming): 5 in r1 => r2c6<>5
Naked Pair: 4,9 in r1c35 => r1c6<>9
Discontinuous Nice Loop: 9 r7c2 -9- r7c1 =9= r2c1 =7= r2c2 -7- r6c2 -6- r4c2 -9- r7c2 => r7c2<>9
Discontinuous Nice Loop: 6 r8c9 -6- r4c9 -1- r4c3 =1= r5c3 =7= r7c3 -7- r7c9 =7= r8c9 => r8c9<>6
Forcing Chain Contradiction in c4 => r2c9<>6
r2c9=6 r2c5<>6 r3c4=6 r3c4<>1
r2c9=6 r4c9<>6 r4c9=1 r4c3<>1 r5c3=1 r5c4<>1
r2c9=6 r4c9<>6 r4c9=1 r4c3<>1 r5c3=1 r5c3<>7 r7c3=7 r8c1<>7 r8c1=4 r8c6<>4 r8c6=1 r7c4<>1
2-String Kite: 6 in r2c7,r7c4 (connected by r2c5,r3c4) => r7c7<>6
Grouped Discontinuous Nice Loop: 6 r9c3 -6- r7c23 =6= r7c4 -6- r3c4 =6= r3c8 -6- r8c8 =6= r9c79 -6- r9c3 => r9c3<>6
Naked Pair: 4,5 in r39c3 => r157c3<>4
Naked Single: r1c3=9
Naked Single: r1c5=4
Hidden Single: r7c1=9
Hidden Single: r4c2=9
Naked Triple: 1,6,7 in r45c3,r6c2 => r5c12<>7
Hidden Rectangle: 1/9 in r2c56,r6c56 => r2c6<>1
XY-Wing: 1/3/9 in r2c6,r36c5 => r2c5,r6c6<>9
Hidden Single: r2c6=9
Hidden Single: r6c5=9
Hidden Single: r9c6=3
Hidden Single: r9c2=8
Multi Colors 1: 6 (r2c5,r3c8,r7c4) / (r2c7,r3c4), (r4c3,r9c9) / (r4c9,r6c2,r7c3) => r9c7<>6
XY-Chain: 6 6- r4c9 -1- r4c3 -6- r7c3 -7- r8c1 -4- r8c6 -1- r6c6 -5- r5c4 -1- r5c3 -7- r6c2 -6 => r4c3,r6c78<>6
Naked Single: r4c3=1
Full House: r4c9=6
Naked Single: r5c3=7
Naked Single: r6c2=6
Naked Single: r7c3=6
Hidden Single: r2c7=6
Hidden Single: r9c5=6
Hidden Single: r8c8=6
Hidden Single: r6c7=7
Hidden Single: r3c4=6
Hidden Single: r9c7=2
Naked Single: r7c7=1
Full House: r5c7=5
Naked Single: r7c4=8
Naked Single: r5c4=1
Full House: r1c4=5
Full House: r6c6=5
Full House: r6c8=1
Full House: r5c8=2
Full House: r1c6=8
Full House: r3c8=5
Full House: r2c9=1
Naked Single: r7c6=4
Full House: r8c6=1
Full House: r8c5=2
Naked Single: r3c3=4
Full House: r9c3=5
Full House: r9c9=4
Naked Single: r2c5=3
Full House: r3c5=1
Full House: r3c2=3
Naked Single: r7c9=7
Full House: r7c2=2
Full House: r8c9=5
Naked Single: r2c1=7
Full House: r2c2=5
Naked Single: r5c2=4
Full House: r5c1=3
Full House: r8c1=4
Full House: r8c2=7
|
normal_sudoku_3253 | ...67..34.74..38.636.28417.......48.83.46..17..7.186.3.5.....68.....63.1.9.8...4. | 981675234274193856365284179516739482839462517427518693152347968748956321693821745 | normal_sudoku_3253 | 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 | 9 | . . . 6 7 . . 3 4
. 7 4 . . 3 8 . 6
3 6 . 2 8 4 1 7 .
. . . . . . 4 8 .
8 3 . 4 6 . . 1 7
. . 7 . 1 8 6 . 3
. 5 . . . . . 6 8
. . . . . 6 3 . 1
. 9 . 8 . . . 4 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 981675234274193856365284179516739482839462517427518693152347968748956321693821745 #1 Extreme (5860)
Empty Rectangle: 2 in b5 (r49c9) => r9c6<>2
Hidden Rectangle: 2/8 in r1c23,r8c23 => r1c2<>2
Finned X-Wing: 2 r26 c18 fr6c2 => r4c1<>2
Almost Locked Set XZ-Rule: A=r4c123569 {1235679}, B=r9c579 {2357}, X=3, Z=7 => r9c6<>7
Almost Locked Set XZ-Rule: A=r12c1,r3c3 {1259}, B=r78c1,r8c23 {12478}, X=1, Z=2 => r9c1<>2
Forcing Chain Contradiction in r8 => r2c4<>5
r2c4=5 r6c4<>5 r6c4=9 r8c4<>9
r2c4=5 r2c5<>5 r2c5=9 r8c5<>9
r2c4=5 r2c4<>1 r7c4=1 r9c6<>1 r9c6=5 r8c45<>5 r8c8=5 r8c8<>9
Forcing Chain Contradiction in r5 => r2c8<>9
r2c8=9 r3c9<>9 r3c3=9 r5c3<>9
r2c8=9 r2c45<>9 r1c6=9 r5c6<>9
r2c8=9 r8c8<>9 r7c7=9 r5c7<>9
Forcing Chain Contradiction in r1c6 => r1c1<>5
r1c1=5 r3c3<>5 r3c3=9 r3c9<>9 r4c9=9 r6c8<>9 r8c8=9 r8c8<>5 r8c45=5 r9c6<>5 r9c6=1 r1c6<>1
r1c1=5 r1c6<>5
r1c1=5 r3c3<>5 r3c3=9 r3c9<>9 r1c7=9 r1c6<>9
Forcing Chain Contradiction in r5c3 => r1c3<>5
r1c3=5 r1c6<>5 r2c5=5 r2c8<>5 r2c8=2 r6c8<>2 r6c12=2 r5c3<>2
r1c3=5 r5c3<>5
r1c3=5 r3c3<>5 r3c3=9 r5c3<>9
Forcing Chain Contradiction in r5 => r2c4=1
r2c4<>1 r2c1=1 r2c1<>5 r3c3=5 r5c3<>5
r2c4<>1 r2c4=9 r6c4<>9 r6c4=5 r5c6<>5
r2c4<>1 r1c6=1 r1c6<>5 r1c7=5 r5c7<>5
Forcing Chain Contradiction in r5 => r9c6=1
r9c6<>1 r9c6=5 r1c6<>5 r1c7=5 r3c9<>5 r3c3=5 r5c3<>5
r9c6<>1 r9c6=5 r5c6<>5
r9c6<>1 r9c6=5 r1c6<>5 r1c7=5 r5c7<>5
Grouped Discontinuous Nice Loop: 9 r4c5 -9- r2c5 -5- r1c6 =5= r45c6 -5- r6c4 -9- r4c5 => r4c5<>9
Grouped Discontinuous Nice Loop: 9 r8c5 -9- r8c8 =9= r6c8 -9- r6c4 -5- r8c4 =5= r89c5 -5- r2c5 -9- r8c5 => r8c5<>9
Forcing Chain Verity => r1c6=5
r4c1=9 r2c1<>9 r2c5=9 r2c5<>5 r1c6=5
r4c3=9 r4c3<>6 r4c1=6 r9c1<>6 r9c1=7 r8c1<>7 r8c4=7 r8c4<>5 r46c4=5 r45c6<>5 r1c6=5
r4c4=9 r6c4<>9 r6c4=5 r45c6<>5 r1c6=5
r4c6=9 r1c6<>9 r1c6=5
r4c9=9 r3c9<>9 r3c9=5 r1c7<>5 r1c6=5
Full House: r2c5=9
Skyscraper: 5 in r3c9,r5c7 (connected by r35c3) => r4c9<>5
XY-Wing: 5/9/2 in r1c7,r39c9 => r79c7<>2
XY-Wing: 5/9/2 in r2c8,r34c9 => r6c8<>2
Locked Candidates Type 2 (Claiming): 2 in r6 => r4c23,r5c3<>2
Naked Single: r4c2=1
Naked Single: r1c2=8
Hidden Single: r8c3=8
Naked Pair: 5,9 in r6c48 => r6c1<>5, r6c1<>9
Naked Pair: 5,9 in r35c3 => r14c3<>9, r4c3<>5
Naked Single: r4c3=6
Hidden Single: r9c1=6
Hidden Single: r9c7=7
Naked Single: r7c7=9
Naked Single: r1c7=2
Full House: r5c7=5
Naked Single: r1c3=1
Full House: r1c1=9
Naked Single: r2c8=5
Full House: r2c1=2
Full House: r3c3=5
Full House: r3c9=9
Naked Single: r5c3=9
Full House: r5c6=2
Naked Single: r6c8=9
Full House: r8c8=2
Full House: r4c9=2
Full House: r9c9=5
Naked Single: r4c1=5
Naked Single: r6c1=4
Full House: r6c2=2
Full House: r6c4=5
Full House: r8c2=4
Naked Single: r7c6=7
Full House: r4c6=9
Naked Single: r4c5=3
Full House: r4c4=7
Naked Single: r8c1=7
Full House: r7c1=1
Naked Single: r8c5=5
Full House: r8c4=9
Full House: r7c4=3
Naked Single: r9c5=2
Full House: r7c5=4
Full House: r7c3=2
Full House: r9c3=3
|
normal_sudoku_5732 | 31.8...95.8.1..23..25.931.883..1952..9.53..81.51...3.9.4.....1.17..4.9..563971842 | 317862495489157236625493178836719524294536781751284369948325617172648953563971842 | normal_sudoku_5732 | 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 | 9 | 3 1 . 8 . . . 9 5
. 8 . 1 . . 2 3 .
. 2 5 . 9 3 1 . 8
8 3 . . 1 9 5 2 .
. 9 . 5 3 . . 8 1
. 5 1 . . . 3 . 9
. 4 . . . . . 1 .
1 7 . . 4 . 9 . .
5 6 3 9 7 1 8 4 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 317862495489157236625493178836719524294536781751284369948325617172648953563971842 #1 Extreme (3324)
Hidden Single: r8c8=5
Empty Rectangle: 7 in b2 (r36c8) => r6c6<>7
Hidden Rectangle: 5/6 in r2c56,r7c56 => r7c6<>6
Hidden Rectangle: 3/6 in r7c49,r8c49 => r7c4<>6
Finned X-Wing: 4 r36 c14 fr6c6 => r4c4<>4
2-String Kite: 4 in r1c7,r4c3 (connected by r4c9,r5c7) => r1c3<>4
Forcing Chain Contradiction in r3c4 => r4c9<>6
r4c9=6 r4c9<>4 r2c9=4 r1c7<>4 r1c6=4 r3c4<>4
r4c9=6 r6c8<>6 r3c8=6 r3c4<>6
r4c9=6 r4c4<>6 r4c4=7 r3c4<>7
W-Wing: 7/6 in r3c8,r7c7 connected by 6 in r5c7,r6c8 => r1c7<>7
Finned Franken Swordfish: 6 r34b6 c148 fr4c3 fr5c7 => r5c1<>6
Grouped AIC: 7 7- r1c3 -6- r23c1 =6= r6c1 -6- r6c8 -7- r3c8 =7= r2c9 -7 => r2c13<>7
Finned Swordfish: 7 r124 c369 fr4c4 => r5c6<>7
Locked Candidates Type 1 (Pointing): 7 in b5 => r3c4<>7
Finned Swordfish: 7 c148 r346 fr5c1 => r4c3<>7
W-Wing: 6/4 in r1c7,r4c3 connected by 4 in r24c9 => r1c3<>6
Naked Single: r1c3=7
Hidden Single: r2c6=7
Hidden Single: r3c8=7
Full House: r6c8=6
Hidden Single: r2c5=5
Hidden Single: r7c6=5
Locked Candidates Type 1 (Pointing): 6 in b4 => r2c3<>6
X-Wing: 6 c57 r17 => r1c6,r7c9<>6
XYZ-Wing: 2/4/8 in r16c6,r6c5 => r5c6<>2
Locked Candidates Type 1 (Pointing): 2 in b5 => r6c1<>2
W-Wing: 6/4 in r4c3,r5c6 connected by 4 in r4c9,r5c7 => r4c4,r5c3<>6
Naked Single: r4c4=7
Naked Single: r4c9=4
Full House: r4c3=6
Full House: r5c7=7
Naked Single: r2c9=6
Full House: r1c7=4
Full House: r7c7=6
Naked Single: r8c9=3
Full House: r7c9=7
Naked Single: r1c6=2
Full House: r1c5=6
Full House: r3c4=4
Full House: r3c1=6
Naked Single: r6c4=2
Naked Single: r6c5=8
Full House: r7c5=2
Naked Single: r7c4=3
Full House: r8c4=6
Full House: r8c6=8
Full House: r8c3=2
Naked Single: r6c6=4
Full House: r5c6=6
Full House: r6c1=7
Naked Single: r7c1=9
Full House: r7c3=8
Naked Single: r5c3=4
Full House: r2c3=9
Full House: r2c1=4
Full House: r5c1=2
|
normal_sudoku_6992 | 7.....58.4.1...63.56...31.981...6.9.9..2...16..6.1.......4...6.1.7......65...89.. | 739162584481579632562843179814356297975284316326917458298431765147695823653728941 | normal_sudoku_6992 | 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 | 9 | 7 . . . . . 5 8 .
4 . 1 . . . 6 3 .
5 6 . . . 3 1 . 9
8 1 . . . 6 . 9 .
9 . . 2 . . . 1 6
. . 6 . 1 . . . .
. . . 4 . . . 6 .
1 . 7 . . . . . .
6 5 . . . 8 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 739162584481579632562843179814356297975284316326917458298431765147695823653728941 #1 Extreme (12246)
Grouped Discontinuous Nice Loop: 5 r8c4 =6= r1c4 =1= r1c6 -1- r7c6 =1= r7c9 =5= r7c56 -5- r8c4 => r8c4<>5
Forcing Chain Contradiction in r4 => r6c8<>4
r6c8=4 r456c7<>4 r8c7=4 r8c2<>4 r9c3=4 r4c3<>4
r6c8=4 r3c8<>4 r3c5=4 r4c5<>4
r6c8=4 r4c7<>4
r6c8=4 r4c9<>4
Forcing Chain Contradiction in c6 => r6c8<>7
r6c8=7 r3c8<>7 r2c9=7 r2c6<>7
r6c8=7 r6c2<>7 r5c2=7 r5c6<>7
r6c8=7 r6c6<>7
r6c8=7 r456c7<>7 r7c7=7 r7c6<>7
Forcing Chain Contradiction in c4 => r6c6<>5
r6c6=5 r46c4<>5 r2c4=5 r2c4<>8
r6c6=5 r6c8<>5 r6c8=2 r4c79<>2 r4c3=2 r3c3<>2 r3c3=8 r3c4<>8
r6c6=5 r6c6<>9 r6c4=9 r6c4<>8
Forcing Net Contradiction in r6c8 => r6c8=5
r6c8<>5 r6c8=2 (r6c1<>2 r7c1=2 r7c7<>2 r8c7=2 r9c9<>2) (r3c8<>2) (r4c7<>2) r4c9<>2 r4c3=2 r3c3<>2 r3c5=2 (r9c5<>2) r3c5<>4 r3c8=4 r3c8<>7 r9c8=7 r9c8<>2 r9c3=2 r7c1<>2 r6c1=2 r6c8<>2 r6c8=5
Almost Locked Set XZ-Rule: A=r7c1237 {23789}, B=r89c8 {247}, X=7, Z=2 => r7c9<>2
Forcing Chain Contradiction in r7c7 => r9c3<>2
r9c3=2 r9c3<>4 r8c2=4 r8c8<>4 r8c8=2 r7c7<>2
r9c3=2 r7c1<>2 r7c1=3 r7c7<>3
r9c3=2 r3c3<>2 r3c3=8 r3c4<>8 r3c4=7 r3c8<>7 r9c8=7 r7c7<>7
r9c3=2 r9c3<>4 r8c2=4 r8c2<>8 r7c23=8 r7c7<>8
Grouped Discontinuous Nice Loop: 2 r3c5 -2- r9c5 =2= r9c89 -2- r8c8 -4- r3c8 =4= r3c5 => r3c5<>2
Almost Locked Set XY-Wing: A=r6c1 {23}, B=r1278c2 {23489}, C=r7c1,r9c3 {234}, X,Y=2,4, Z=3 => r56c2<>3
Forcing Chain Contradiction in c6 => r5c5<>4
r5c5=4 r5c5<>8 r6c4=8 r3c4<>8 r3c4=7 r2c6<>7
r5c5=4 r5c2<>4 r5c2=7 r5c6<>7
r5c5=4 r5c5<>8 r6c4=8 r6c4<>9 r6c6=9 r6c6<>7
r5c5=4 r13c5<>4 r1c6=4 r1c6<>1 r7c6=1 r7c6<>7
Forcing Net Verity => r9c5=2
r9c5=2 r9c5=2
r9c8=2 (r8c8<>2 r8c8=4 r9c9<>4) (r8c8<>2 r8c8=4 r3c8<>4 r3c5=4 r4c5<>4) (r8c8<>2 r8c8=4 r3c8<>4 r3c5=4 r1c6<>4 r1c9=4 r4c9<>4) r9c8<>7 r3c8=7 (r2c9<>7 r2c9=2 r4c9<>2) r3c8<>2 r3c3=2 r4c3<>2 r4c7=2 r4c7<>4 r4c3=4 r9c3<>4 r9c8=4 (r9c8<>2) r8c8<>4 r8c8=2 r9c9<>2 r9c5=2
r9c9=2 (r4c9<>2) (r1c9<>2 r1c9=4 r4c9<>4) (r4c9<>2) (r1c9<>2 r1c9=4 r3c8<>4 r3c5=4 r4c5<>4) (r1c9<>2 r1c9=4 r4c9<>4) (r9c9<>4) r8c8<>2 r8c8=4 r9c8<>4 r9c3=4 r4c3<>4 r4c7=4 r4c7<>2 r4c3=2 r3c3<>2 r3c8=2 r2c9<>2 r2c9=7 r4c9<>7 r4c9=3 (r6c9<>3 r6c9=8 r6c7<>8) r5c7<>3 r5c5=3 (r9c5<>3) r5c5<>8 r5c7=8 r6c9<>8 r6c4=8 r3c4<>8 r3c4=7 (r4c4<>7 r4c4=5 r5c6<>5 r5c3=5 r5c3<>3) r3c8<>7 r9c8=7 r9c5<>7 r9c5=2
Discontinuous Nice Loop: 9 r1c4 -9- r6c4 =9= r6c6 -9- r8c6 -5- r8c9 =5= r7c9 =1= r7c6 -1- r1c6 =1= r1c4 => r1c4<>9
Discontinuous Nice Loop: 9 r7c6 -9- r8c6 -5- r8c9 =5= r7c9 =1= r7c6 => r7c6<>9
Discontinuous Nice Loop: 9 r8c4 -9- r8c6 -5- r8c9 =5= r7c9 =1= r7c6 -1- r1c6 =1= r1c4 =6= r8c4 => r8c4<>9
Discontinuous Nice Loop: 5 r5c5 -5- r4c4 =5= r2c4 =9= r6c4 =8= r5c5 => r5c5<>5
Discontinuous Nice Loop: 7 r9c9 -7- r2c9 -2- r2c6 =2= r1c6 =1= r1c4 -1- r9c4 =1= r9c9 => r9c9<>7
Turbot Fish: 7 r2c9 =7= r3c8 -7- r9c8 =7= r9c4 => r2c4<>7
Almost Locked Set XY-Wing: A=r5c26 {457}, B=r123478c5 {3456789}, C=r13489c4 {135678}, X,Y=5,8, Z=7 => r5c5<>7
Almost Locked Set XY-Wing: A=r7c1237 {23789}, B=r8c456789 {2345689}, C=r9c8 {47}, X,Y=4,7, Z=8,9 => r7c9<>8, r7c5,r8c2<>9
Almost Locked Set Chain: 3- r6c1 {23} -2- r7c1 {23} -3- r9c3 {34} -4- r9c8 {47} -7- r189c4 {1367} -3 => r6c4<>3
Almost Locked Set XZ-Rule: A=r1246c9 {23478}, B=r4c45,r56c6,r6c4 {345789}, X=8, Z=3 => r4c7<>3
Forcing Chain Contradiction in r2 => r2c5<>8
r2c5=8 r5c5<>8 r6c4=8 r6c4<>9 r2c4=9 r2c4<>5
r2c5=8 r2c5<>5
r2c5=8 r5c5<>8 r6c4=8 r6c4<>9 r6c6=9 r8c6<>9 r8c6=5 r2c6<>5
Forcing Chain Contradiction in r4c3 => r1c3<>2
r1c3=2 r4c3<>2
r1c3=2 r3c3<>2 r3c3=8 r3c5<>8 r5c5=8 r5c5<>3 r4c45=3 r4c3<>3
r1c3=2 r3c3<>2 r3c8=2 r8c8<>2 r8c8=4 r8c2<>4 r9c3=4 r4c3<>4
r1c3=2 r3c3<>2 r3c3=8 r2c2<>8 r2c4=8 r2c4<>5 r4c4=5 r4c3<>5
Empty Rectangle: 2 in b1 (r38c8) => r8c2<>2
Locked Candidates Type 1 (Pointing): 2 in b7 => r7c7<>2
Grouped Discontinuous Nice Loop: 2 r7c2 -2- r12c2 =2= r3c3 =8= r7c3 =9= r7c2 => r7c2<>2
Discontinuous Nice Loop: 3 r5c3 -3- r6c1 -2- r7c1 =2= r7c3 =8= r3c3 -8- r2c2 =8= r2c4 =5= r4c4 -5- r4c3 =5= r5c3 => r5c3<>3
Naked Triple: 4,5,7 in r5c236 => r5c7<>4, r5c7<>7
Sue de Coq: r78c7 - {23478} (r5c7 - {38}, r89c8 - {247}) => r7c9<>7, r8c9<>2, r89c9<>4, r6c7<>3, r6c7<>8
Finned Swordfish: 2 r348 c378 fr4c9 => r6c7<>2
AIC: 2/3 3- r6c1 =3= r6c9 =8= r6c4 -8- r2c4 =8= r2c2 -8- r3c3 -2- r7c3 =2= r7c1 -2 => r6c1<>2, r7c1<>3
Naked Single: r6c1=3
Full House: r7c1=2
Swordfish: 2 r126 c269 => r4c9<>2
AIC: 9 9- r1c3 =9= r7c3 =8= r3c3 =2= r4c3 -2- r4c7 =2= r6c9 =8= r6c4 =9= r2c4 -9 => r1c56,r2c2<>9
Naked Pair: 2,8 in r2c2,r3c3 => r1c2<>2
Uniqueness Test 2: 3/9 in r1c23,r7c23 => r7c7,r8c2<>8
Naked Pair: 3,4 in r8c2,r9c3 => r7c23<>3
XY-Wing: 4/7/3 in r7c7,r9c38 => r9c9<>3
Naked Single: r9c9=1
Hidden Single: r7c6=1
Hidden Single: r1c4=1
Hidden Single: r1c5=6
Hidden Single: r8c4=6
2-String Kite: 4 in r1c9,r4c5 (connected by r1c6,r3c5) => r4c9<>4
2-String Kite: 7 in r3c8,r7c5 (connected by r7c7,r9c8) => r3c5<>7
X-Wing: 7 r39 c48 => r46c4<>7
Finned X-Wing: 3 r57 c57 fr7c9 => r8c7<>3
Finned X-Wing: 7 r47 c57 fr4c9 => r6c7<>7
Naked Single: r6c7=4
Hidden Single: r1c9=4
Naked Single: r1c6=2
Hidden Single: r5c6=4
Naked Single: r5c2=7
Naked Single: r5c3=5
Naked Single: r6c2=2
Full House: r4c3=4
Naked Single: r2c2=8
Naked Single: r9c3=3
Naked Single: r3c3=2
Naked Single: r7c2=9
Naked Single: r1c3=9
Full House: r1c2=3
Full House: r8c2=4
Full House: r7c3=8
Naked Single: r9c4=7
Full House: r9c8=4
Naked Single: r3c8=7
Full House: r8c8=2
Full House: r2c9=2
Naked Single: r3c4=8
Full House: r3c5=4
Naked Single: r8c7=8
Naked Single: r6c4=9
Naked Single: r5c7=3
Full House: r5c5=8
Naked Single: r2c4=5
Full House: r4c4=3
Naked Single: r6c6=7
Full House: r4c5=5
Full House: r6c9=8
Naked Single: r4c9=7
Full House: r4c7=2
Full House: r7c7=7
Naked Single: r2c6=9
Full House: r2c5=7
Full House: r8c6=5
Naked Single: r7c5=3
Full House: r7c9=5
Full House: r8c9=3
Full House: r8c5=9
|
normal_sudoku_1013 | .1..392..7..2..1.8.42.71.6..2.4.78..1.7.58...4.8.23.....17854..28..9.751.7...2.86 | 816539247735246198942871563329467815167958324458123679691785432283694751574312986 | normal_sudoku_1013 | 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 | 9 | . 1 . . 3 9 2 . .
7 . . 2 . . 1 . 8
. 4 2 . 7 1 . 6 .
. 2 . 4 . 7 8 . .
1 . 7 . 5 8 . . .
4 . 8 . 2 3 . . .
. . 1 7 8 5 4 . .
2 8 . . 9 . 7 5 1
. 7 . . . 2 . 8 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 816539247735246198942871563329467815167958324458123679691785432283694751574312986 #1 Unfair (1704)
Locked Pair: 4,6 in r2c56 => r1c4,r2c23<>6, r2c8<>4
Locked Candidates Type 1 (Pointing): 6 in b8 => r8c3<>6
Locked Candidates Type 2 (Claiming): 5 in r2 => r1c13,r3c1<>5
Naked Single: r1c3=6
Naked Single: r1c1=8
Naked Single: r1c4=5
Naked Single: r3c4=8
Naked Triple: 3,6,9 in r5c247 => r5c89<>3, r5c89<>9
Empty Rectangle: 3 in b9 (r5c27) => r7c2<>3
XYZ-Wing: 3/6/9 in r37c1,r7c2 => r9c1<>9
Discontinuous Nice Loop: 5 r4c1 -5- r9c1 -3- r9c4 -1- r9c5 =1= r4c5 =6= r4c1 => r4c1<>5
Hidden Single: r9c1=5
Finned Swordfish: 3 c189 r347 fr2c8 => r3c7<>3
Sashimi Swordfish: 3 r589 c347 fr5c2 => r4c3<>3
Swordfish: 3 r347 c189 => r2c8<>3
Naked Single: r2c8=9
Naked Single: r3c7=5
Naked Single: r3c9=3
Full House: r3c1=9
Skyscraper: 9 in r4c3,r7c2 (connected by r47c9) => r56c2,r9c3<>9
Hidden Single: r7c2=9
Naked Single: r7c9=2
Naked Single: r5c9=4
Naked Single: r7c8=3
Full House: r7c1=6
Full House: r9c7=9
Full House: r4c1=3
Naked Single: r1c9=7
Full House: r1c8=4
Naked Single: r5c8=2
Naked Single: r4c8=1
Full House: r6c8=7
Naked Single: r6c7=6
Full House: r5c7=3
Naked Single: r5c2=6
Full House: r5c4=9
Naked Single: r4c5=6
Full House: r6c4=1
Naked Single: r6c2=5
Full House: r2c2=3
Full House: r4c3=9
Full House: r6c9=9
Full House: r2c3=5
Full House: r4c9=5
Naked Single: r2c5=4
Full House: r2c6=6
Full House: r9c5=1
Full House: r8c6=4
Naked Single: r9c4=3
Full House: r8c4=6
Full House: r8c3=3
Full House: r9c3=4
|
normal_sudoku_839 | .6......1..3..25..8..7...3..3.617.844.6528....87349.56.5..9......82..4.53....5.9. | 762953841193482567845761932539617284416528379287349156651894723978236415324175698 | normal_sudoku_839 | 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 | 9 | . 6 . . . . . . 1
. . 3 . . 2 5 . .
8 . . 7 . . . 3 .
. 3 . 6 1 7 . 8 4
4 . 6 5 2 8 . . .
. 8 7 3 4 9 . 5 6
. 5 . . 9 . . . .
. . 8 2 . . 4 . 5
3 . . . . 5 . 9 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 762953841193482567845761932539617284416528379287349156651894723978236415324175698 #1 Hard (414)
Locked Candidates Type 1 (Pointing): 2 in b6 => r1379c7<>2
Locked Candidates Type 1 (Pointing): 3 in b9 => r7c6<>3
Skyscraper: 6 in r2c8,r9c7 (connected by r29c5) => r3c7,r78c8<>6
Naked Single: r3c7=9
Naked Single: r3c9=2
Naked Single: r4c7=2
Naked Single: r6c7=1
Full House: r6c1=2
Naked Single: r5c8=7
Naked Single: r1c8=4
Naked Single: r5c7=3
Full House: r5c9=9
Full House: r5c2=1
Naked Single: r8c8=1
Naked Single: r1c6=3
Naked Single: r2c8=6
Full House: r7c8=2
Naked Single: r3c2=4
Naked Single: r8c6=6
Naked Single: r2c5=8
Naked Single: r3c6=1
Full House: r7c6=4
Naked Single: r1c4=9
Naked Single: r1c5=5
Naked Single: r2c9=7
Full House: r1c7=8
Naked Single: r9c5=7
Naked Single: r3c3=5
Full House: r3c5=6
Full House: r2c4=4
Full House: r8c5=3
Naked Single: r7c3=1
Naked Single: r1c1=7
Full House: r1c3=2
Naked Single: r2c2=9
Full House: r2c1=1
Naked Single: r9c9=8
Full House: r7c9=3
Naked Single: r9c2=2
Full House: r8c2=7
Full House: r8c1=9
Naked Single: r9c7=6
Full House: r7c7=7
Naked Single: r4c3=9
Full House: r9c3=4
Full House: r7c1=6
Full House: r7c4=8
Full House: r9c4=1
Full House: r4c1=5
|
normal_sudoku_822 | 9.5463.82.8....5....285...953...92.88..32..5.127685394.5....82...85..4.7.41..89.5 | 975463182486192573312857649534719268869324751127685394753941826298536417641278935 | normal_sudoku_822 | 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 | 9 | 9 . 5 4 6 3 . 8 2
. 8 . . . . 5 . .
. . 2 8 5 . . . 9
5 3 . . . 9 2 . 8
8 . . 3 2 . . 5 .
1 2 7 6 8 5 3 9 4
. 5 . . . . 8 2 .
. . 8 5 . . 4 . 7
. 4 1 . . 8 9 . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 975463182486192573312857649534719268869324751127685394753941826298536417641278935 #1 Extreme (2112)
Locked Candidates Type 1 (Pointing): 4 in b4 => r2c3<>4
Locked Candidates Type 1 (Pointing): 7 in b7 => r23c1<>7
Naked Pair: 6,9 in r58c2 => r3c2<>6
Naked Pair: 1,7 in r3c26 => r3c78<>1, r3c78<>7
Naked Single: r3c7=6
X-Wing: 3 c39 r27 => r2c18,r7c15<>3
Swordfish: 6 r249 c138 => r57c3,r78c1,r8c8<>6
Naked Single: r7c1=7
Swordfish: 7 r135 c267 => r2c6<>7
XYZ-Wing: 1/3/9 in r7c4,r8c58 => r8c6<>1
Sue de Coq: r8c12 - {2369} (r8c6 - {26}, r7c3 - {39}) => r9c1<>3
XY-Wing: 2/6/3 in r89c1,r9c8 => r8c8<>3
Naked Single: r8c8=1
Locked Candidates Type 1 (Pointing): 1 in b6 => r5c6<>1
XY-Wing: 3/6/7 in r49c8,r9c5 => r4c5<>7
XY-Wing: 4/7/1 in r35c6,r4c5 => r2c5<>1
Naked Triple: 3,7,9 in r289c5 => r7c5<>9
XY-Chain: 7 7- r2c8 -4- r2c1 -6- r2c3 -3- r7c3 -9- r8c2 -6- r8c6 -2- r2c6 -1- r3c6 -7 => r2c45<>7
Naked Single: r2c5=9
Naked Single: r8c5=3
Naked Single: r8c1=2
Naked Single: r9c5=7
Naked Single: r8c6=6
Full House: r8c2=9
Naked Single: r9c1=6
Full House: r7c3=3
Naked Single: r9c4=2
Full House: r9c8=3
Full House: r7c9=6
Naked Single: r5c2=6
Naked Single: r2c1=4
Full House: r3c1=3
Naked Single: r2c3=6
Naked Single: r2c4=1
Naked Single: r3c8=4
Naked Single: r5c9=1
Full House: r2c9=3
Naked Single: r4c3=4
Full House: r5c3=9
Naked Single: r2c8=7
Full House: r2c6=2
Full House: r3c6=7
Full House: r1c7=1
Full House: r5c7=7
Full House: r4c8=6
Full House: r3c2=1
Full House: r5c6=4
Full House: r1c2=7
Full House: r7c6=1
Naked Single: r4c4=7
Full House: r7c4=9
Full House: r4c5=1
Full House: r7c5=4
|
normal_sudoku_3621 | 98.5..3413.5...7.9.4..3..58.58.12.....9.4.18..3........94.58.378.3...59.57....814 | 987526341365481729241937658458712963729643185136895472694158237813274596572369814 | normal_sudoku_3621 | 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 | 9 | 9 8 . 5 . . 3 4 1
3 . 5 . . . 7 . 9
. 4 . . 3 . . 5 8
. 5 8 . 1 2 . . .
. . 9 . 4 . 1 8 .
. 3 . . . . . . .
. 9 4 . 5 8 . 3 7
8 . 3 . . . 5 9 .
5 7 . . . . 8 1 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 987526341365481729241937658458712963729643185136895472694158237813274596572369814 #1 Extreme (5388)
Naked Pair: 2,6 in r37c7 => r46c7<>6, r6c7<>2
2-String Kite: 1 in r2c2,r7c4 (connected by r7c1,r8c2) => r2c4<>1
Finned X-Wing: 2 r19 c35 fr9c4 => r8c5<>2
Almost Locked Set XY-Wing: A=r8c259 {1267}, B=r123569c6 {1345679}, C=r2c2458 {12468}, X,Y=1,4, Z=6,7 => r8c6<>6, r8c6<>7
Forcing Chain Contradiction in b2 => r1c5<>7
r1c5=7 r1c5<>2
r1c5=7 r8c5<>7 r8c4=7 r8c4<>4 r2c4=4 r2c4<>2
r1c5=7 r8c5<>7 r8c4=7 r8c4<>4 r2c4=4 r2c4<>8 r2c5=8 r2c5<>2
r1c5=7 r8c5<>7 r8c5=6 r8c9<>6 r8c9=2 r7c7<>2 r3c7=2 r3c4<>2
Forcing Chain Contradiction in c3 => r8c5=7
r8c5<>7 r8c5=6 r1c5<>6 r1c5=2 r1c3<>2
r8c5<>7 r8c5=6 r8c9<>6 r8c9=2 r7c7<>2 r3c7=2 r3c3<>2
r8c5<>7 r8c5=6 r8c9<>6 r8c9=2 r5c9<>2 r5c12=2 r6c3<>2
r8c5<>7 r8c5=6 r9c456<>6 r9c3=6 r9c3<>2
Forcing Chain Contradiction in r7c4 => r2c4<>2
r2c4=2 r2c4<>4 r2c6=4 r8c6<>4 r8c6=1 r7c4<>1
r2c4=2 r7c4<>2
r2c4=2 r2c8<>2 r2c8=6 r3c7<>6 r7c7=6 r7c4<>6
Forcing Chain Contradiction in r7c4 => r2c4<>6
r2c4=6 r2c4<>4 r2c6=4 r8c6<>4 r8c6=1 r7c4<>1
r2c4=6 r2c8<>6 r2c8=2 r3c7<>2 r7c7=2 r7c4<>2
r2c4=6 r7c4<>6
Forcing Chain Verity => r2c5<>2
r8c2=6 r9c3<>6 r9c3=2 r1c3<>2 r1c5=2 r2c5<>2
r8c4=6 r8c4<>4 r2c4=4 r2c4<>8 r2c5=8 r2c5<>2
r8c9=6 r8c9<>2 r7c7=2 r3c7<>2 r2c8=2 r2c5<>2
Hidden Rectangle: 6/8 in r2c45,r6c45 => r6c4<>6
AIC: 6 6- r5c2 -2- r2c2 =2= r2c8 =6= r3c7 -6- r7c7 =6= r8c9 -6 => r5c9,r8c2<>6
2-String Kite: 6 in r3c7,r8c4 (connected by r7c7,r8c9) => r3c4<>6
Turbot Fish: 6 r3c7 =6= r7c7 -6- r7c1 =6= r9c3 => r3c3<>6
Discontinuous Nice Loop: 2 r7c4 -2- r7c7 =2= r8c9 -2- r8c2 -1- r7c1 =1= r7c4 => r7c4<>2
Grouped AIC: 1/4 4- r8c6 =4= r8c4 -4- r2c4 -8- r2c5 -6- r1c56 =6= r1c3 -6- r9c3 -2- r8c2 -1- r2c2 =1= r2c6 -1 => r8c6<>1, r2c6<>4
Naked Single: r8c6=4
Hidden Single: r2c4=4
Hidden Single: r2c5=8
Hidden Single: r6c4=8
Locked Candidates Type 1 (Pointing): 1 in b8 => r3c4<>1
Grouped AIC: 1/6 6- r7c1 =6= r9c3 -6- r1c3 =6= r1c56 -6- r2c6 -1- r2c2 =1= r8c2 -1- r8c4 =1= r7c4 -1 => r7c1<>1, r7c4<>6
Naked Single: r7c4=1
Hidden Single: r8c2=1
Hidden Single: r2c6=1
Remote Pair: 2/6 r5c2 -6- r2c2 -2- r2c8 -6- r3c7 -2- r7c7 -6- r7c1 => r56c1<>2, r456c1<>6
Naked Single: r5c1=7
Naked Single: r4c1=4
Naked Single: r4c7=9
Naked Single: r6c1=1
Naked Single: r6c7=4
Hidden Single: r3c3=1
Hidden Single: r1c3=7
Naked Single: r1c6=6
Full House: r1c5=2
X-Wing: 6 c35 r69 => r6c89,r9c4<>6
Locked Candidates Type 1 (Pointing): 6 in b6 => r4c4<>6
Remote Pair: 2/6 r5c2 -6- r6c3 -2- r9c3 -6- r7c1 -2- r3c1 -6- r2c2 -2- r2c8 -6- r3c7 -2- r7c7 -6- r8c9 => r5c9,r6c8<>2
Naked Single: r6c8=7
Naked Single: r4c8=6
Full House: r2c8=2
Full House: r2c2=6
Full House: r3c7=6
Full House: r3c1=2
Full House: r5c2=2
Full House: r7c7=2
Full House: r7c1=6
Full House: r6c3=6
Full House: r8c9=6
Full House: r9c3=2
Full House: r8c4=2
Naked Single: r4c9=3
Full House: r4c4=7
Naked Single: r6c5=9
Full House: r9c5=6
Naked Single: r5c9=5
Full House: r6c9=2
Full House: r6c6=5
Naked Single: r3c4=9
Full House: r3c6=7
Naked Single: r5c6=3
Full House: r5c4=6
Full House: r9c4=3
Full House: r9c6=9
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.