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_5490 | ..583.2..43...9..8.891......14..5...9..41.....5397.6...46....25.2....3...9..2.476 | 675834291431259768289167543714685932962413857853972614346798125127546389598321476 | normal_sudoku_5490 | 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 8 3 . 2 . .
4 3 . . . 9 . . 8
. 8 9 1 . . . . .
. 1 4 . . 5 . . .
9 . . 4 1 . . . .
. 5 3 9 7 . 6 . .
. 4 6 . . . . 2 5
. 2 . . . . 3 . .
. 9 . . 2 . 4 7 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 675834291431259768289167543714685932962413857853972614346798125127546389598321476 #1 Extreme (2212)
Naked Pair: 2,8 in r6c16 => r6c8<>8, r6c9<>2
X-Wing: 2 r36 c16 => r4c1,r5c6<>2
Turbot Fish: 1 r1c1 =1= r2c3 -1- r2c7 =1= r7c7 => r7c1<>1
Finned X-Wing: 8 r69 c16 fr9c3 => r78c1<>8
Naked Pair: 3,7 in r7c14 => r7c6<>3, r7c6<>7
Discontinuous Nice Loop: 1 r1c8 -1- r6c8 =1= r6c9 -1- r8c9 -9- r1c9 =9= r1c8 => r1c8<>1
Discontinuous Nice Loop: 5 r2c4 -5- r2c5 -6- r4c5 -8- r6c6 -2- r3c6 =2= r2c4 => r2c4<>5
Locked Candidates Type 1 (Pointing): 5 in b2 => r8c5<>5
Discontinuous Nice Loop: 7 r3c1 -7- r1c2 -6- r5c2 =6= r5c6 =3= r4c4 =2= r2c4 -2- r2c3 =2= r3c1 => r3c1<>7
Almost Locked Set XZ-Rule: A=r4c5 {68}, B=r579c6 {1368}, X=6, Z=8 => r6c6<>8
Naked Single: r6c6=2
Naked Single: r6c1=8
Hidden Single: r3c1=2
Hidden Single: r2c4=2
Hidden Single: r4c9=2
Hidden Single: r5c3=2
Locked Candidates Type 1 (Pointing): 6 in b1 => r1c68<>6
Locked Candidates Type 1 (Pointing): 7 in b2 => r8c6<>7
Swordfish: 7 c269 r135 => r1c1,r35c7<>7
Naked Single: r3c7=5
Naked Single: r5c7=8
Hidden Single: r2c5=5
Hidden Single: r5c8=5
Hidden Single: r4c5=8
Naked Single: r7c5=9
Naked Single: r7c7=1
Naked Single: r2c7=7
Full House: r4c7=9
Naked Single: r7c6=8
Naked Single: r8c9=9
Full House: r8c8=8
Naked Single: r2c3=1
Full House: r2c8=6
Naked Single: r4c8=3
Naked Single: r1c1=6
Full House: r1c2=7
Full House: r5c2=6
Full House: r4c1=7
Full House: r4c4=6
Full House: r5c6=3
Full House: r5c9=7
Naked Single: r8c3=7
Full House: r9c3=8
Naked Single: r3c8=4
Naked Single: r1c6=4
Naked Single: r7c1=3
Full House: r7c4=7
Naked Single: r9c6=1
Naked Single: r8c4=5
Full House: r9c4=3
Full House: r9c1=5
Full House: r8c1=1
Naked Single: r1c8=9
Full House: r1c9=1
Full House: r3c9=3
Full House: r6c8=1
Full House: r6c9=4
Naked Single: r3c5=6
Full House: r3c6=7
Full House: r8c6=6
Full House: r8c5=4
|
normal_sudoku_3766 | ...29...82978..6.58....692.92..6.48.....2.7.971.9....26.9..2..4.32.498.64..6..29. | 563297148297814635841356927925761483386425719714938562679182354132549876458673291 | normal_sudoku_3766 | 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 . . . 8
2 9 7 8 . . 6 . 5
8 . . . . 6 9 2 .
9 2 . . 6 . 4 8 .
. . . . 2 . 7 . 9
7 1 . 9 . . . . 2
6 . 9 . . 2 . . 4
. 3 2 . 4 9 8 . 6
4 . . 6 . . 2 9 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 563297148297814635841356927925761483386425719714938562679182354132549876458673291 #1 Extreme (3968)
Naked Pair: 3,5 in r4c3,r5c1 => r5c23,r6c3<>5, r56c3<>3
Swordfish: 7 r148 c468 => r37c4,r7c8,r9c6<>7
Naked Triple: 1,3,5 in r7c478 => r7c25<>5, r7c5<>1, r7c5<>3
Skyscraper: 1 in r7c7,r8c1 (connected by r1c17) => r8c8<>1
2-String Kite: 4 in r3c4,r6c3 (connected by r5c4,r6c6) => r3c3<>4
Finned Jellyfish: 5 r5678 c1478 fr5c6 fr6c5 fr6c6 => r4c4<>5
Empty Rectangle: 5 in b2 (r4c36) => r3c3<>5
Sue de Coq: r1c123 - {13456} (r1c7 - {13}, r3c2 - {45}) => r1c68<>1, r1c68<>3
Discontinuous Nice Loop: 3 r5c4 -3- r5c1 -5- r4c3 =5= r4c6 =7= r1c6 -7- r1c8 -4- r2c8 =4= r2c6 -4- r3c4 =4= r5c4 => r5c4<>3
Discontinuous Nice Loop: 5 r6c8 -5- r8c8 -7- r1c8 -4- r2c8 =4= r2c6 -4- r6c6 =4= r6c3 =6= r6c8 => r6c8<>5
Grouped Discontinuous Nice Loop: 5 r5c4 -5- r7c4 =5= r7c78 -5- r8c8 -7- r1c8 -4- r2c8 =4= r2c6 -4- r3c4 =4= r5c4 => r5c4<>5
Grouped AIC: 4 4- r6c3 =4= r6c6 -4- r2c6 =4= r2c8 -4- r1c8 -7- r8c8 -5- r5c8 =5= r6c7 -5- r6c5 =5= r456c6 -5- r1c6 =5= r1c123 -5- r3c2 -4- r3c4 =4= r5c4 -4 => r5c23,r6c6<>4
Hidden Single: r6c3=4
Hidden Single: r6c8=6
Locked Candidates Type 1 (Pointing): 8 in b4 => r5c6<>8
Grouped AIC: 4 4- r2c6 =4= r2c8 -4- r1c8 -7- r8c8 -5- r5c8 =5= r6c7 -5- r6c5 =5= r456c6 -5- r1c6 =5= r1c123 -5- r3c2 -4- r3c4 =4= r5c4 -4 => r3c4,r5c6<>4
Hidden Single: r3c2=4
Hidden Single: r5c4=4
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c6<>5
Discontinuous Nice Loop: 3 r5c6 -3- r5c1 =3= r4c3 -3- r4c9 -1- r5c8 =1= r5c6 => r5c6<>3
Grouped AIC: 4/7 7- r1c6 =7= r3c5 =5= r3c4 -5- r7c4 =5= r7c78 -5- r8c8 -7- r1c8 -4 => r1c6<>4, r1c8<>7
Naked Single: r1c6=7
Naked Single: r1c8=4
Hidden Single: r2c6=4
Hidden Single: r8c8=7
Hidden Single: r3c9=7
Hidden Single: r4c4=7
Locked Candidates Type 1 (Pointing): 1 in b5 => r9c6<>1
Locked Candidates Type 1 (Pointing): 5 in b9 => r7c4<>5
2-String Kite: 3 in r2c8,r7c4 (connected by r2c5,r3c4) => r7c8<>3
Skyscraper: 3 in r1c1,r2c8 (connected by r5c18) => r1c7<>3
Naked Single: r1c7=1
Full House: r2c8=3
Full House: r2c5=1
Hidden Single: r8c1=1
Full House: r8c4=5
Naked Single: r3c4=3
Full House: r3c5=5
Full House: r3c3=1
Full House: r7c4=1
Naked Single: r7c8=5
Full House: r5c8=1
Naked Single: r7c7=3
Full House: r6c7=5
Full House: r4c9=3
Full House: r9c9=1
Naked Single: r5c6=5
Naked Single: r4c3=5
Full House: r4c6=1
Naked Single: r5c1=3
Full House: r1c1=5
Naked Single: r9c3=8
Naked Single: r1c2=6
Full House: r1c3=3
Full House: r5c3=6
Full House: r5c2=8
Naked Single: r7c2=7
Full House: r7c5=8
Full House: r9c2=5
Naked Single: r9c6=3
Full House: r6c6=8
Full House: r6c5=3
Full House: r9c5=7
|
normal_sudoku_324 | 4......7...79..1...5..7..62..5.2..4.8.3..6....4.3....69.6..583..3.6...2...4.9..1. | 418562973267934185359871462695127348873456291142389756926715834731648529584293617 | normal_sudoku_324 | 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 .
. . 7 9 . . 1 . .
. 5 . . 7 . . 6 2
. . 5 . 2 . . 4 .
8 . 3 . . 6 . . .
. 4 . 3 . . . . 6
9 . 6 . . 5 8 3 .
. 3 . 6 . . . 2 .
. . 4 . 9 . . 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 418562973267934185359871462695127348873456291142389756926715834731648529584293617 #1 Extreme (2328)
Hidden Single: r9c7=6
Hidden Single: r9c6=3
Locked Candidates Type 1 (Pointing): 2 in b8 => r1c4<>2
Locked Candidates Type 2 (Claiming): 9 in c8 => r4c79,r5c79,r6c7<>9
Hidden Pair: 3,6 in r12c5 => r1c5<>1, r12c5<>5, r12c5<>8, r2c5<>4
Hidden Single: r1c4=5
2-String Kite: 4 in r2c6,r8c7 (connected by r2c9,r3c7) => r8c6<>4
Locked Candidates Type 2 (Claiming): 4 in c6 => r3c4<>4
W-Wing: 1/8 in r3c4,r8c3 connected by 8 in r9c24 => r3c3<>1
XYZ-Wing: 1/4/8 in r78c5,r8c3 => r8c6<>1
Hidden Rectangle: 1/4 in r5c45,r7c45 => r5c4<>1
Sashimi Swordfish: 8 c358 r268 fr1c3 fr3c3 => r2c2<>8
Naked Triple: 2,3,6 in r2c125 => r2c6<>2, r2c9<>3
Hidden Single: r1c6=2
Hidden Single: r6c3=2
Hidden Single: r5c7=2
Locked Candidates Type 1 (Pointing): 1 in b2 => r3c1<>1
Naked Single: r3c1=3
Hidden Single: r2c5=3
Naked Single: r1c5=6
Locked Candidates Type 1 (Pointing): 9 in b4 => r1c2<>9
AIC: 7 7- r8c6 -8- r8c5 =8= r6c5 -8- r6c8 =8= r2c8 =5= r2c9 -5- r9c9 -7 => r8c79,r9c4<>7
Locked Candidates Type 1 (Pointing): 7 in b9 => r45c9<>7
XY-Wing: 5/7/1 in r5c9,r6c17 => r5c2<>1
XY-Wing: 5/9/7 in r5c28,r6c7 => r6c1<>7
Naked Single: r6c1=1
XYZ-Wing: 5/8/9 in r56c8,r6c5 => r6c7<>5
Naked Single: r6c7=7
Naked Single: r4c7=3
Naked Single: r1c7=9
Naked Single: r3c7=4
Full House: r8c7=5
Naked Single: r8c1=7
Naked Single: r9c9=7
Naked Single: r4c1=6
Naked Single: r8c6=8
Naked Single: r7c9=4
Full House: r8c9=9
Naked Single: r2c1=2
Full House: r9c1=5
Naked Single: r2c6=4
Naked Single: r3c6=1
Full House: r3c4=8
Full House: r3c3=9
Naked Single: r6c6=9
Full House: r4c6=7
Naked Single: r8c3=1
Full House: r1c3=8
Full House: r8c5=4
Naked Single: r9c4=2
Full House: r9c2=8
Full House: r7c2=2
Naked Single: r7c5=1
Full House: r7c4=7
Naked Single: r2c2=6
Full House: r1c2=1
Full House: r1c9=3
Naked Single: r4c2=9
Full House: r5c2=7
Naked Single: r4c4=1
Full House: r5c4=4
Full House: r4c9=8
Naked Single: r5c5=5
Full House: r6c5=8
Full House: r6c8=5
Naked Single: r2c9=5
Full House: r5c9=1
Full House: r5c8=9
Full House: r2c8=8
|
normal_sudoku_6693 | ....8.4..51.34...78.4.72.9....95817.9...3..2..5.2179...45793.......6.7.9697821534 | 739186452512349687864572391426958173971634825358217946145793268283465719697821534 | normal_sudoku_6693 | 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 . 4 . .
5 1 . 3 4 . . . 7
8 . 4 . 7 2 . 9 .
. . . 9 5 8 1 7 .
9 . . . 3 . . 2 .
. 5 . 2 1 7 9 . .
. 4 5 7 9 3 . . .
. . . . 6 . 7 . 9
6 9 7 8 2 1 5 3 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 739186452512349687864572391426958173971634825358217946145793268283465719697821534 #1 Easy (226)
Hidden Single: r5c3=1
Hidden Single: r1c1=7
Hidden Single: r5c2=7
Hidden Single: r5c9=5
Hidden Single: r1c8=5
Hidden Single: r3c7=3
Naked Single: r3c2=6
Naked Single: r3c9=1
Full House: r3c4=5
Naked Single: r8c4=4
Full House: r8c6=5
Naked Single: r5c4=6
Full House: r1c4=1
Full House: r5c6=4
Full House: r5c7=8
Hidden Single: r4c1=4
Naked Single: r6c1=3
Naked Single: r4c2=2
Naked Single: r6c9=6
Naked Single: r1c2=3
Full House: r8c2=8
Naked Single: r4c3=6
Full House: r4c9=3
Full House: r6c3=8
Full House: r6c8=4
Naked Single: r1c9=2
Full House: r7c9=8
Naked Single: r8c8=1
Naked Single: r1c3=9
Full House: r1c6=6
Full House: r2c3=2
Full House: r2c6=9
Full House: r8c3=3
Full House: r8c1=2
Full House: r7c1=1
Naked Single: r2c7=6
Full House: r2c8=8
Full House: r7c8=6
Full House: r7c7=2
|
normal_sudoku_2830 | .89.3.7..537....896.47983..9..1.3..7..1.7.9..76..59..1.723.4.9....9.72...9..2..73 | 289536714537241689614798352925183467841672935763459821172364598358917246496825173 | normal_sudoku_2830 | 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 . 3 . 7 . .
5 3 7 . . . . 8 9
6 . 4 7 9 8 3 . .
9 . . 1 . 3 . . 7
. . 1 . 7 . 9 . .
7 6 . . 5 9 . . 1
. 7 2 3 . 4 . 9 .
. . . 9 . 7 2 . .
. 9 . . 2 . . 7 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 289536714537241689614798352925183467841672935763459821172364598358917246496825173 #1 Extreme (3730)
Locked Candidates Type 1 (Pointing): 5 in b2 => r1c89<>5
Locked Candidates Type 1 (Pointing): 5 in b8 => r9c37<>5
Locked Candidates Type 1 (Pointing): 5 in b7 => r8c89<>5
Locked Candidates Type 2 (Claiming): 2 in r2 => r1c46<>2
2-String Kite: 2 in r1c1,r4c8 (connected by r4c2,r5c1) => r1c8<>2
Discontinuous Nice Loop: 4 r5c8 -4- r6c7 -8- r6c3 -3- r6c8 =3= r5c8 => r5c8<>4
Discontinuous Nice Loop: 6 r5c8 -6- r5c6 -2- r6c4 =2= r6c8 =3= r5c8 => r5c8<>6
Discontinuous Nice Loop: 4 r8c1 -4- r9c1 =4= r9c7 -4- r6c7 -8- r6c3 -3- r8c3 =3= r8c1 => r8c1<>4
Grouped Discontinuous Nice Loop: 4 r5c9 -4- r5c12 =4= r4c2 =2= r4c8 -2- r6c8 =2= r6c4 =4= r6c78 -4- r5c9 => r5c9<>4
Forcing Chain Contradiction in b6 => r1c1=2
r1c1<>2 r1c1=1 r3c2<>1 r3c8=1 r3c8<>5 r45c8=5 r4c7<>5
r1c1<>2 r5c1=2 r4c2<>2 r4c8=2 r4c8<>5
r1c1<>2 r5c1=2 r5c1<>3 r5c8=3 r5c8<>5
r1c1<>2 r1c9=2 r3c9<>2 r3c9=5 r5c9<>5
Full House: r3c2=1
Discontinuous Nice Loop: 8 r7c7 -8- r6c7 -4- r9c7 =4= r9c1 -4- r8c2 -5- r8c3 =5= r4c3 -5- r4c7 =5= r7c7 => r7c7<>8
Forcing Chain Contradiction in r5c9 => r7c7=5
r7c7<>5 r7c9=5 r3c9<>5 r3c9=2 r5c9<>2
r7c7<>5 r7c9=5 r5c9<>5
r7c7<>5 r4c7=5 r4c3<>5 r4c3=8 r9c3<>8 r9c3=6 r9c46<>6 r78c5=6 r4c5<>6 r4c78=6 r5c9<>6
r7c7<>5 r4c7=5 r4c3<>5 r8c3=5 r8c2<>5 r8c2=4 r9c1<>4 r9c7=4 r9c7<>8 r46c7=8 r5c9<>8
Naked Triple: 4,6,8 in r178c9 => r5c9<>6, r5c9<>8
Locked Candidates Type 1 (Pointing): 6 in b6 => r4c5<>6
Locked Candidates Type 1 (Pointing): 8 in b6 => r9c7<>8
2-String Kite: 1 in r1c6,r9c7 (connected by r1c8,r2c7) => r9c6<>1
Locked Candidates Type 1 (Pointing): 1 in b8 => r2c5<>1
Naked Triple: 5,6,8 in r9c346 => r9c1<>8, r9c7<>6
Skyscraper: 8 in r5c1,r9c3 (connected by r59c4) => r46c3,r78c1<>8
Naked Single: r4c3=5
Naked Single: r6c3=3
Naked Single: r7c1=1
Naked Single: r8c1=3
Naked Single: r9c1=4
Full House: r5c1=8
Naked Single: r8c2=5
Naked Single: r9c7=1
Hidden Single: r5c8=3
Hidden Single: r8c5=1
Hidden Single: r2c6=1
Hidden Single: r1c8=1
Hidden Single: r5c9=5
Naked Single: r3c9=2
Full House: r3c8=5
Hidden Single: r2c4=2
Hidden Single: r5c6=2
Naked Single: r5c2=4
Full House: r4c2=2
Full House: r5c4=6
Hidden Single: r6c8=2
Skyscraper: 4 in r1c9,r6c7 (connected by r16c4) => r2c7<>4
Naked Single: r2c7=6
Full House: r1c9=4
Full House: r2c5=4
Naked Single: r1c4=5
Full House: r1c6=6
Full House: r9c6=5
Naked Single: r4c5=8
Full House: r6c4=4
Full House: r9c4=8
Full House: r7c5=6
Full House: r6c7=8
Full House: r4c7=4
Full House: r9c3=6
Full House: r7c9=8
Full House: r4c8=6
Full House: r8c3=8
Full House: r8c9=6
Full House: r8c8=4
|
normal_sudoku_3464 | 9.3.74...48.9.63...7638...9..746.....9...3.4..34.982.5.4.6.95....9.476.8.6.8...94 | 953274861481956372276381459127465983598123746634798215842619537319547628765832194 | normal_sudoku_3464 | 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 . 7 4 . . .
4 8 . 9 . 6 3 . .
. 7 6 3 8 . . . 9
. . 7 4 6 . . . .
. 9 . . . 3 . 4 .
. 3 4 . 9 8 2 . 5
. 4 . 6 . 9 5 . .
. . 9 . 4 7 6 . 8
. 6 . 8 . . . 9 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 953274861481956372276381459127465983598123746634798215842619537319547628765832194 #1 Extreme (6266)
Hidden Single: r3c7=4
Hidden Single: r4c7=9
Forcing Net Contradiction in r8 => r1c7=8
r1c7<>8 (r1c7=1 r3c8<>1) r1c8=8 r1c8<>6 r6c8=6 (r6c8<>7 r2c8=7 r2c9<>7 r2c9=2 r3c8<>2) r6c1<>6 r6c1=1 r3c1<>1 r3c6=1 r3c6<>2 r3c1=2 r8c1<>2
r1c7<>8 (r1c7=1 r1c2<>1) r1c8=8 r1c8<>6 r6c8=6 r6c1<>6 r6c1=1 r4c2<>1 r8c2=1 r8c2<>2
r1c7<>8 (r1c7=1 r3c8<>1) r1c8=8 (r1c8<>2) r1c8<>6 (r1c9=6 r1c9<>2) r6c8=6 (r6c8<>7 r2c8=7 r2c9<>7 r2c9=2 r3c8<>2) r6c1<>6 r6c1=1 r3c1<>1 r3c6=1 r3c6<>2 r3c1=2 r1c2<>2 r1c4=2 r8c4<>2
r1c7<>8 (r1c7=1 r9c7<>1) (r1c7=1 r2c8<>1) (r1c7=1 r2c9<>1) (r1c7=1 r3c8<>1) r1c8=8 r1c8<>6 r6c8=6 r6c1<>6 r6c1=1 (r9c1<>1) r3c1<>1 r3c6=1 (r9c6<>1) r2c5<>1 r2c3=1 r9c3<>1 r9c5=1 r9c5<>3 r9c1=3 r8c1<>3 r8c8=3 r8c8<>2
Hidden Single: r4c8=8
Hidden Single: r4c9=3
Finned Jellyfish: 1 c3579 r2579 fr1c9 => r2c8<>1
Discontinuous Nice Loop: 7 r5c9 -7- r5c7 =7= r9c7 -7- r9c1 =7= r7c1 =8= r5c1 =6= r5c9 => r5c9<>7
Finned Franken Swordfish: 1 r34b6 c168 fr4c2 fr5c7 fr5c9 => r5c1<>1
Forcing Chain Contradiction in r3 => r1c8<>1
r1c8=1 r1c8<>6 r6c8=6 r6c1<>6 r6c1=1 r3c1<>1
r1c8=1 r1c8<>6 r6c8=6 r6c1<>6 r6c1=1 r4c12<>1 r4c6=1 r3c6<>1
r1c8=1 r3c8<>1
Forcing Net Contradiction in r8 => r1c8<>2
r1c8=2 r8c1=3
r1c8=2 (r8c8<>2) r1c8<>6 r6c8=6 r6c8<>7 r6c4=7 r5c4<>7 r5c7=7 r9c7<>7 r9c7=1 r8c8<>1 r8c8=3
Forcing Net Contradiction in c8 => r5c1<>2
r5c1=2 (r3c1<>2) (r4c1<>2) r4c2<>2 r4c6=2 r3c6<>2 r3c8=2
r5c1=2 r5c1<>8 r5c3=8 r7c3<>8 r7c1=8 (r7c1<>3) r7c1<>7 r9c1=7 (r9c7<>7 r9c7=1 r8c8<>1) r9c1<>3 r8c1=3 r8c8<>3 r8c8=2
Forcing Net Contradiction in c3 => r5c4<>5
r5c4=5 (r5c5<>5) r5c4<>7 r5c7=7 r9c7<>7 r9c1=7 r9c1<>3 r9c5=3 r9c5<>5 r2c5=5 r2c3<>5
r5c4=5 r5c3<>5
r5c4=5 (r4c6<>5) (r5c5<>5) r5c4<>7 r5c7=7 r9c7<>7 r9c1=7 r9c1<>3 r9c5=3 r9c5<>5 r2c5=5 r3c6<>5 r9c6=5 r9c3<>5
Forcing Net Contradiction in r4 => r1c8=6
r1c8<>6 r6c8=6 r6c1<>6 r6c1=1 (r4c1<>1) r4c2<>1 r4c6=1 r4c6<>5 r4c1=5
r1c8<>6 r1c8=5 (r1c2<>5) r1c4<>5 r8c4=5 r8c2<>5 r4c2=5
Hidden Single: r5c9=6
Hidden Single: r6c1=6
Forcing Net Verity => r2c3=1
r2c3=1 r2c3=1
r5c3=1 (r5c7<>1 r5c7=7 r5c4<>7 r5c4=2 r5c5<>2) (r5c7<>1 r5c7=7 r5c4<>7 r5c4=2 r5c5<>2) (r5c4<>1) (r4c2<>1) (r4c1<>1) r4c2<>1 r4c6=1 (r9c6<>1) (r6c4<>1) (r3c6<>1) r6c4<>1 r6c8=1 r3c8<>1 r3c1=1 (r7c1<>1 r7c5=1 r7c5<>2) r1c2<>1 r8c2=1 r8c4<>1 r1c4=1 (r1c4<>5 r1c2=5 r2c3<>5) (r1c4<>5 r1c2=5 r2c3<>5) (r1c9<>1 r1c9=2 r3c8<>2) r6c4<>1 r6c8=1 r3c8<>1 r3c8=5 r2c8<>5 r2c5=5 r5c5<>5 r5c5=1 r5c5<>5 r4c6=5 r9c6<>5 r9c6=2 r9c5<>2 r2c5=2 r2c3<>2 r2c3=1
r7c3=1 (r5c3<>1) (r9c3<>1) (r5c3<>1) r7c3<>8 r7c1=8 (r7c1<>7 r9c1=7 r9c1<>3 r9c5=3 r7c5<>3) r5c1<>8 r5c1=5 (r4c1<>5) r4c2<>5 r4c6=5 (r4c6<>1) r9c6<>5 r9c6=2 r7c5<>2 r7c5=1 (r5c5<>1) r5c5<>1 r5c4=1 r5c7<>1 r9c7=1 (r9c5<>1) (r5c7<>1) (r9c6<>1) r9c6<>1 r3c6=1 r2c5<>1 r7c5=1 (r5c5<>1) r7c3<>1 r2c3=1
r9c3=1 (r8c1<>1) (r8c2<>1) r9c7<>1 r5c7=1 r6c8<>1 (r6c8=7 r2c8<>7 r2c9=7 r2c9<>1) r6c4=1 r8c4<>1 r8c8=1 (r7c9<>1) r9c7<>1 r9c7=7 r7c9<>7 r7c9=2 r7c5<>2 r7c5=1 (r7c5<>3) r2c5<>1 r2c3=1
Locked Candidates Type 1 (Pointing): 1 in b4 => r4c6<>1
Skyscraper: 1 in r1c9,r6c8 (connected by r16c4) => r3c8<>1
Hidden Single: r3c6=1
Hidden Single: r1c9=1
Naked Pair: 2,5 in r9c36 => r9c15<>2, r9c15<>5
Skyscraper: 5 in r4c6,r5c3 (connected by r9c36) => r4c12,r5c5<>5
Hidden Single: r4c6=5
Full House: r9c6=2
Naked Single: r9c3=5
Hidden Single: r2c5=5
Full House: r1c4=2
Full House: r1c2=5
Full House: r3c1=2
Full House: r3c8=5
Naked Single: r4c1=1
Full House: r4c2=2
Full House: r8c2=1
Naked Single: r8c1=3
Naked Single: r5c3=8
Full House: r5c1=5
Full House: r7c3=2
Naked Single: r8c4=5
Full House: r8c8=2
Naked Single: r9c1=7
Full House: r7c1=8
Naked Single: r7c9=7
Full House: r2c9=2
Full House: r2c8=7
Naked Single: r9c7=1
Full House: r5c7=7
Full House: r6c8=1
Full House: r7c8=3
Full House: r9c5=3
Full House: r6c4=7
Full House: r5c4=1
Full House: r7c5=1
Full House: r5c5=2
|
normal_sudoku_1409 | 74..9.3511....3.866.3..1..28....2..3.....781...7....2.5..12..3...1...2.5236..51.. | 742698351159243786683751942864912573925367814317584629598126437471839265236475198 | normal_sudoku_1409 | 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 . . 9 . 3 5 1
1 . . . . 3 . 8 6
6 . 3 . . 1 . . 2
8 . . . . 2 . . 3
. . . . . 7 8 1 .
. . 7 . . . . 2 .
5 . . 1 2 . . 3 .
. . 1 . . . 2 . 5
2 3 6 . . 5 1 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 742698351159243786683751942864912573925367814317584629598126437471839265236475198 #1 Extreme (2408)
Locked Pair: 4,9 in r56c9 => r4c78,r6c7,r79c9<>4, r4c78,r6c7,r79c9<>9
Locked Candidates Type 2 (Claiming): 7 in c9 => r7c7,r89c8<>7
Finned X-Wing: 6 c58 r48 fr5c5 fr6c5 => r4c4<>6
Finned Swordfish: 4 c169 r568 fr7c6 => r8c45<>4
Finned Swordfish: 9 c169 r568 fr7c6 => r8c4<>9
Sue de Coq: r7c23 - {4789} (r7c9 - {78}, r8c1 - {49}) => r8c2<>9, r7c6<>8
Grouped Discontinuous Nice Loop: 6 r4c5 -6- r4c8 =6= r8c8 -6- r7c7 =6= r7c6 -6- r1c6 -8- r1c3 -2- r5c3 =2= r5c2 =6= r5c45 -6- r4c5 => r4c5<>6
Grouped Discontinuous Nice Loop: 5 r6c2 -5- r6c7 -6- r4c78 =6= r4c2 =1= r6c2 => r6c2<>5
Grouped Discontinuous Nice Loop: 9 r7c7 =6= r7c6 -6- r1c6 -8- r1c3 =8= r7c3 =4= r8c1 =9= r7c23 -9- r7c7 => r7c7<>9
Locked Candidates Type 1 (Pointing): 9 in b9 => r3c8<>9
Finned Jellyfish: 9 r2347 c2347 fr7c6 => r9c4<>9
Hidden Single: r9c8=9
Locked Candidates Type 1 (Pointing): 9 in b8 => r6c6<>9
Locked Candidates Type 2 (Claiming): 4 in r9 => r78c6<>4
Hidden Single: r6c6=4
Naked Single: r6c9=9
Naked Single: r5c9=4
Naked Single: r6c1=3
Naked Single: r5c1=9
Full House: r8c1=4
Naked Single: r8c8=6
Naked Single: r4c8=7
Full House: r3c8=4
Naked Single: r7c7=4
Hidden Single: r4c3=4
Hidden Single: r4c4=9
Hidden Single: r8c6=9
Naked Single: r7c6=6
Full House: r1c6=8
Naked Single: r1c3=2
Full House: r1c4=6
Naked Single: r5c3=5
Naked Single: r2c3=9
Full House: r7c3=8
Naked Single: r5c4=3
Naked Single: r2c2=5
Full House: r3c2=8
Naked Single: r2c7=7
Full House: r3c7=9
Naked Single: r7c9=7
Full House: r7c2=9
Full House: r8c2=7
Full House: r9c9=8
Naked Single: r5c5=6
Full House: r5c2=2
Naked Single: r2c5=4
Full House: r2c4=2
Naked Single: r8c4=8
Full House: r8c5=3
Naked Single: r9c5=7
Full House: r9c4=4
Naked Single: r6c4=5
Full House: r3c4=7
Full House: r3c5=5
Naked Single: r4c5=1
Full House: r6c5=8
Naked Single: r6c7=6
Full House: r4c7=5
Full House: r4c2=6
Full House: r6c2=1
|
normal_sudoku_2583 | 128659347...4..98.9..83...5....9..7..793....4...78..39.839..75..9.5.34.85....8.93 | 128659347356417982947832615435291876879365124612784539283946751791523468564178293 | normal_sudoku_2583 | 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 9 3 4 7
. . . 4 . . 9 8 .
9 . . 8 3 . . . 5
. . . . 9 . . 7 .
. 7 9 3 . . . . 4
. . . 7 8 . . 3 9
. 8 3 9 . . 7 5 .
. 9 . 5 . 3 4 . 8
5 . . . . 8 . 9 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 128659347356417982947832615435291876879365124612784539283946751791523468564178293 #1 Extreme (2124)
Locked Candidates Type 1 (Pointing): 4 in b5 => r7c6<>4
Locked Candidates Type 1 (Pointing): 7 in b8 => r2c5<>7
Empty Rectangle: 1 in b7 (r49c4) => r4c3<>1
Finned Swordfish: 1 r257 c569 fr5c7 fr5c8 => r4c9<>1
Empty Rectangle: 1 in b2 (r27c9) => r7c6<>1
W-Wing: 6/2 in r4c9,r7c6 connected by 2 in r49c4 => r4c6,r7c9<>6
Grouped AIC: 6 6- r4c9 -2- r4c4 =2= r9c4 -2- r7c6 -6- r789c5 =6= r5c5 -6 => r5c78<>6
Grouped Discontinuous Nice Loop: 1 r2c9 -1- r7c9 =1= r7c5 =4= r9c5 =7= r9c3 -7- r3c3 =7= r3c6 =1= r2c56 -1- r2c9 => r2c9<>1
Hidden Single: r7c9=1
Locked Candidates Type 1 (Pointing): 1 in b3 => r3c6<>1
Empty Rectangle: 2 in b2 (r24c9) => r4c6<>2
W-Wing: 1/2 in r2c5,r4c4 connected by 2 in r24c9 => r5c5<>1
W-Wing: 2/6 in r2c9,r9c7 connected by 6 in r38c8 => r3c7<>2
W-Wing: 6/2 in r4c9,r9c7 connected by 2 in r49c4 => r46c7<>6
Hidden Single: r4c9=6
Full House: r2c9=2
Naked Single: r2c5=1
Naked Single: r2c6=7
Full House: r3c6=2
Naked Single: r7c6=6
Hidden Single: r8c3=1
Hidden Single: r9c4=1
Full House: r4c4=2
Naked Single: r5c5=6
Hidden Single: r8c1=7
Naked Single: r8c5=2
Full House: r8c8=6
Full House: r9c7=2
Naked Single: r7c5=4
Full House: r7c1=2
Full House: r9c5=7
Naked Single: r3c8=1
Full House: r3c7=6
Full House: r5c8=2
Naked Single: r5c1=8
Naked Single: r3c2=4
Full House: r3c3=7
Naked Single: r9c2=6
Full House: r9c3=4
Naked Single: r4c3=5
Naked Single: r2c3=6
Full House: r6c3=2
Naked Single: r6c2=1
Naked Single: r2c1=3
Full House: r2c2=5
Full House: r4c2=3
Naked Single: r6c7=5
Naked Single: r4c1=4
Full House: r6c1=6
Full House: r6c6=4
Naked Single: r5c7=1
Full House: r4c7=8
Full House: r4c6=1
Full House: r5c6=5
|
normal_sudoku_3381 | 7....498...4.7...2.8....74..5..4682..621..43.4...2...7...419356..56..174641.5.298 | 726534981314978562589261743157346829862197435493825617278419356935682174641753298 | normal_sudoku_3381 | 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 9 8 .
. . 4 . 7 . . . 2
. 8 . . . . 7 4 .
. 5 . . 4 6 8 2 .
. 6 2 1 . . 4 3 .
4 . . . 2 . . . 7
. . . 4 1 9 3 5 6
. . 5 6 . . 1 7 4
6 4 1 . 5 . 2 9 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 726534981314978562589261743157346829862197435493825617278419356935682174641753298 #1 Easy (180)
Hidden Single: r5c6=7
Naked Single: r9c6=3
Full House: r9c4=7
Naked Single: r8c5=8
Full House: r8c6=2
Naked Single: r5c5=9
Naked Single: r4c4=3
Naked Single: r5c1=8
Full House: r5c9=5
Naked Single: r7c1=2
Naked Single: r6c7=6
Full House: r2c7=5
Naked Single: r7c2=7
Full House: r7c3=8
Naked Single: r6c8=1
Full House: r2c8=6
Full House: r4c9=9
Naked Single: r4c1=1
Full House: r4c3=7
Hidden Single: r1c4=5
Naked Single: r3c6=1
Naked Single: r6c4=8
Full House: r6c6=5
Full House: r2c6=8
Naked Single: r3c9=3
Full House: r1c9=1
Naked Single: r2c4=9
Full House: r3c4=2
Naked Single: r3c5=6
Full House: r1c5=3
Naked Single: r2c1=3
Full House: r2c2=1
Naked Single: r3c3=9
Full House: r3c1=5
Full House: r8c1=9
Full House: r8c2=3
Naked Single: r1c2=2
Full House: r1c3=6
Full House: r6c3=3
Full House: r6c2=9
|
normal_sudoku_2431 | 1.26.397.9.6...3.237..92.6121.37.69..63.2..177.9...2.3.2..3.....9.28..3..3.1.4.29 | 142653978986741352375892461218375694463928517759416283821539746694287135537164829 | normal_sudoku_2431 | 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 6 . 3 9 7 .
9 . 6 . . . 3 . 2
3 7 . . 9 2 . 6 1
2 1 . 3 7 . 6 9 .
. 6 3 . 2 . . 1 7
7 . 9 . . . 2 . 3
. 2 . . 3 . . . .
. 9 . 2 8 . . 3 .
. 3 . 1 . 4 . 2 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 142653978986741352375892461218375694463928517759416283821539746694287135537164829 #1 Extreme (2476)
Naked Triple: 4,5,8 in r6c248 => r6c5<>4, r6c56<>5, r6c6<>8
Locked Candidates Type 1 (Pointing): 4 in b5 => r23c4<>4
Skyscraper: 4 in r3c7,r4c9 (connected by r34c3) => r1c9,r5c7<>4
Finned Swordfish: 4 r348 c379 fr8c1 => r7c3<>4
Finned Franken Swordfish: 8 r16b2 c248 fr1c9 fr2c6 => r2c8<>8
Discontinuous Nice Loop: 8 r4c9 -8- r1c9 -5- r2c8 -4- r6c8 =4= r4c9 => r4c9<>8
Sashimi Jellyfish: 8 r3459 c1347 fr4c6 fr5c6 => r6c4<>8
Grouped AIC: 5 5- r3c4 -8- r3c3 =8= r12c2 -8- r6c2 =8= r6c8 -8- r5c7 -5 => r3c7,r5c4<>5
XY-Wing: 4/8/5 in r2c8,r3c47 => r2c456<>5
2-String Kite: 5 in r3c3,r9c5 (connected by r1c5,r3c4) => r9c3<>5
XY-Wing: 4/8/5 in r2c8,r35c7 => r6c8<>5
Skyscraper: 5 in r3c3,r6c2 (connected by r36c4) => r12c2,r4c3<>5
Hidden Single: r2c8=5
Naked Single: r1c9=8
Full House: r3c7=4
Naked Single: r1c2=4
Full House: r1c5=5
Naked Single: r2c2=8
Full House: r3c3=5
Full House: r3c4=8
Full House: r6c2=5
Naked Single: r9c5=6
Naked Single: r2c4=7
Naked Single: r6c4=4
Naked Single: r6c5=1
Full House: r2c5=4
Full House: r2c6=1
Naked Single: r5c4=9
Full House: r7c4=5
Naked Single: r6c8=8
Full House: r6c6=6
Full House: r7c8=4
Naked Single: r8c6=7
Full House: r7c6=9
Naked Single: r5c7=5
Full House: r4c9=4
Naked Single: r7c9=6
Full House: r8c9=5
Naked Single: r5c6=8
Full House: r4c6=5
Full House: r4c3=8
Full House: r5c1=4
Naked Single: r8c7=1
Naked Single: r7c1=8
Naked Single: r9c3=7
Naked Single: r8c1=6
Full House: r8c3=4
Full House: r9c1=5
Full House: r7c3=1
Full House: r7c7=7
Full House: r9c7=8
|
normal_sudoku_3684 | 8...56..7..23..86.67...2513..9.23......6......6..49.3...62...4..2..61..81...3.... | 893156427512374869674982513489523176235617984761849235356298741927461358148735692 | normal_sudoku_3684 | 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 6 . . 7
. . 2 3 . . 8 6 .
6 7 . . . 2 5 1 3
. . 9 . 2 3 . . .
. . . 6 . . . . .
. 6 . . 4 9 . 3 .
. . 6 2 . . . 4 .
. 2 . . 6 1 . . 8
1 . . . 3 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 893156427512374869674982513489523176235617984761849235356298741927461358148735692 #1 Extreme (11420)
Naked Single: r3c3=4
Locked Candidates Type 2 (Claiming): 9 in r3 => r1c4,r2c5<>9
Discontinuous Nice Loop: 5 r8c1 -5- r2c1 -9- r2c9 -4- r2c6 =4= r9c6 -4- r9c2 =4= r8c1 => r8c1<>5
Forcing Chain Contradiction in r4 => r4c9<>4
r4c9=4 r2c9<>4 r2c6=4 r2c6<>7 r2c5=7 r2c5<>1 r2c2=1 r4c2<>1
r4c9=4 r2c9<>4 r2c6=4 r1c4<>4 r1c4=1 r4c4<>1
r4c9=4 r4c9<>6 r4c7=6 r4c7<>1
r4c9=4 r4c9<>1
Finned Swordfish: 4 r148 c147 fr4c2 => r5c1<>4
Forcing Net Contradiction in b7 => r7c9<>9
r7c9=9 r7c1<>9
r7c9=9 r7c2<>9
r7c9=9 r2c9<>9 r2c9=4 r1c7<>4 r1c4=4 r8c4<>4 r8c1=4 r8c1<>9
r7c9=9 (r2c9<>9 r2c9=4 r2c6<>4 r9c6=4 r9c6<>8) r7c5<>9 r3c5=9 r3c4<>9 r3c4=8 (r9c4<>8) r6c4<>8 r6c3=8 r9c3<>8 r9c2=8 r9c2<>9
Forcing Net Contradiction in c8 => r5c9<>1
r5c9=1 (r7c9<>1 r7c7=1 r7c7<>3 r8c7=3 r8c7<>9) (r5c9<>4 r2c9=4 r2c9<>9 r9c9=9 r8c8<>9) r5c5<>1 r2c5=1 r1c4<>1 r1c4=4 r8c4<>4 r8c1=4 r8c1<>9 r8c4=9 r3c4<>9 r3c4=8 (r4c4<>8) r6c4<>8 r6c3=8 r4c2<>8 r4c8=8 r4c8<>5
r5c9=1 (r7c9<>1 r7c9=5 r7c6<>5) r5c9<>4 r2c9=4 r2c6<>4 r9c6=4 r9c6<>5 r5c6=5 r5c8<>5
r5c9=1 r7c9<>1 r7c9=5 r8c8<>5
r5c9=1 r7c9<>1 r7c9=5 r9c8<>5
Forcing Net Contradiction in r5c8 => r5c9<>5
r5c9=5 (r6c9<>5) r7c9<>5 r7c9=1 r6c9<>1 r6c9=2 r5c8<>2
r5c9=5 r5c8<>5
r5c9=5 (r5c6<>5) r5c9<>4 r2c9=4 r2c6<>4 r2c6=7 (r2c5<>7 r2c5=1 r5c5<>1) r5c6<>7 r5c6=8 r5c5<>8 r5c5=7 r5c8<>7
r5c9=5 (r5c6<>5) r5c9<>4 r2c9=4 r2c6<>4 r2c6=7 r5c6<>7 r5c6=8 r5c8<>8
r5c9=5 (r7c9<>5 r7c9=1 r6c9<>1 r6c9=2 r9c9<>2) (r5c9<>9) r5c9<>4 r2c9=4 r2c9<>9 r9c9=9 r9c9<>6 r9c7=6 r9c7<>2 r9c8=2 r1c8<>2 r1c8=9 r5c8<>9
Forcing Net Contradiction in r3 => r8c1<>3
r8c1=3 r8c1<>4 r8c4=4 r1c4<>4 r1c4=1 (r1c3<>1) r2c5<>1 r5c5=1 r5c3<>1 r6c3=1 r6c3<>8 r6c4=8 r3c4<>8 r3c4=9
r8c1=3 (r8c1<>9) r8c1<>4 r8c4=4 r1c4<>4 r1c7=4 r2c9<>4 r2c9=9 r2c1<>9 r7c1=9 r7c5<>9 r3c5=9
Forcing Net Contradiction in c6 => r7c1<>5
r7c1=5 (r4c1<>5) (r2c1<>5 r2c2=5 r4c2<>5) (r7c9<>5 r7c9=1 r6c9<>1) r7c1<>3 r5c1=3 r5c1<>2 r6c1=2 r6c9<>2 r6c9=5 (r4c8<>5) r4c9<>5 r4c4=5 r5c6<>5
r7c1=5 r7c6<>5
r7c1=5 r2c1<>5 r2c1=9 r2c9<>9 r2c9=4 r2c6<>4 r9c6=4 r9c6<>5
Forcing Net Contradiction in r7c7 => r6c3<>5
r6c3=5 (r6c1<>5 r2c1=5 r2c1<>9) r6c3<>8 r6c4=8 r3c4<>8 r3c4=9 r3c5<>9 r7c5=9 r7c1<>9 r8c1=9 r8c1<>4 r8c4=4 r1c4<>4 r1c4=1 (r1c3<>1) r2c5<>1 r5c5=1 r5c3<>1 r6c3=1 r6c3<>5
Forcing Net Contradiction in r7c7 => r7c6<>7
r7c6=7 r2c6<>7 (r2c6=4 r2c9<>4 r2c9=9 r2c1<>9 r2c1=5 r6c1<>5) (r2c6=4 r1c4<>4 r1c4=1 r1c3<>1) r2c5=7 r2c5<>1 r5c5=1 r5c3<>1 r6c3=1 r6c3<>8 r6c4=8 r6c4<>5 r6c9=5 r7c9<>5 r7c9=1 r7c7<>1
r7c6=7 r2c6<>7 r2c6=4 r1c4<>4 r1c4=1 r1c3<>1 r1c3=3 r8c3<>3 r8c7=3 r7c7<>3
r7c6=7 r7c7<>7
r7c6=7 r2c6<>7 (r2c6=4 r1c4<>4 r1c4=1 r1c3<>1) r2c5=7 r2c5<>1 r5c5=1 r5c3<>1 r6c3=1 r6c3<>8 r6c4=8 r3c4<>8 r3c4=9 r3c5<>9 r7c5=9 r7c7<>9
Forcing Net Contradiction in r6c3 => r8c1<>7
r8c1=7 r8c1<>4 r8c4=4 r1c4<>4 r1c4=1 (r1c3<>1) r2c5<>1 r5c5=1 r5c3<>1 r6c3=1
r8c1=7 (r8c1<>9) r8c1<>4 r8c4=4 r1c4<>4 r1c7=4 r2c9<>4 r2c9=9 r2c1<>9 r7c1=9 r7c5<>9 r3c5=9 r3c4<>9 r3c4=8 r6c4<>8 r6c3=8
Forcing Net Contradiction in r7c7 => r5c3<>7
r5c3=7 (r5c5<>7) (r4c1<>7) (r5c1<>7) r6c1<>7 r7c1=7 (r7c1<>3 r5c1=3 r5c1<>2 r6c1=2 r6c1<>5) r7c5<>7 r2c5=7 r2c5<>1 (r2c2=1 r1c3<>1) r5c5=1 r5c3<>1 r6c3=1 r6c3<>8 r6c4=8 r6c4<>5 r6c9=5 r7c9<>5 r7c9=1 r7c7<>1
r5c3=7 (r5c5<>7) (r4c1<>7) (r5c1<>7) r6c1<>7 r7c1=7 r7c5<>7 r2c5=7 r2c5<>1 r2c2=1 r1c3<>1 r1c3=3 r8c3<>3 r8c7=3 r7c7<>3
r5c3=7 (r4c1<>7) (r5c1<>7) r6c1<>7 r7c1=7 r7c7<>7
r5c3=7 (r5c3<>1) (r5c5<>7) (r4c1<>7) (r5c1<>7) r6c1<>7 r7c1=7 r7c5<>7 r2c5=7 r2c5<>1 r2c2=1 r1c3<>1 r6c3=1 r6c3<>8 r6c4=8 r3c4<>8 r3c4=9 r3c5<>9 r7c5=9 r7c7<>9
Forcing Net Contradiction in r7c2 => r8c4<>5
r8c4=5 (r6c4<>5) (r7c6<>5) (r8c3<>5) (r7c6<>5) r9c6<>5 r5c6=5 r5c3<>5 r9c3=5 r7c2<>5 r7c9=5 r6c9<>5 r6c1=5 r6c1<>2 r5c1=2 r5c1<>3 r7c1=3 r7c2<>3
r8c4=5 (r8c3<>5) (r7c6<>5) r9c6<>5 r5c6=5 r5c3<>5 r9c3=5 r7c2<>5
r8c4=5 r7c6<>5 r7c6=8 r7c2<>8
r8c4=5 (r7c6<>5 r7c6=8 r9c4<>8) (r7c6<>5 r7c6=8 r9c6<>8) (r8c3<>5) (r7c6<>5) r9c6<>5 r5c6=5 r5c3<>5 r9c3=5 (r9c8<>5 r4c8=5 r4c8<>8) r9c3<>8 r9c2=8 r4c2<>8 r4c4=8 r3c4<>8 r3c4=9 r3c5<>9 r7c5=9 r7c2<>9
Forcing Net Contradiction in r7c7 => r5c5<>8
r5c5=8 (r5c6<>8) r5c5<>1 r2c5=1 r2c5<>7 r2c6=7 r5c6<>7 r5c6=5 (r5c8<>5) (r5c3<>5) (r4c4<>5) r6c4<>5 r9c4=5 (r9c8<>5) r9c3<>5 r8c3=5 r8c8<>5 r4c8=5 r4c8<>8 r5c8=8 r5c5<>8
Naked Pair: 1,7 in r25c5 => r7c5<>7
Empty Rectangle: 7 in b4 (r7c17) => r6c7<>7
XYZ-Wing: 1/2/5 in r6c79,r7c9 => r4c9<>1
AIC: 1 1- r6c7 -2- r6c1 =2= r5c1 =3= r7c1 =7= r7c7 =1= r7c9 -1 => r6c9,r7c7<>1
Hidden Single: r7c9=1
Discontinuous Nice Loop: 7 r9c7 -7- r7c7 =7= r7c1 =3= r5c1 =2= r6c1 -2- r6c9 -5- r4c9 -6- r4c7 =6= r9c7 => r9c7<>7
Grouped Discontinuous Nice Loop: 5 r5c6 -5- r5c3 =5= r89c3 -5- r7c2 =5= r7c6 -5- r5c6 => r5c6<>5
Locked Candidates Type 1 (Pointing): 5 in b5 => r9c4<>5
Grouped AIC: 3/7 7- r7c7 =7= r7c1 -7- r456c1 =7= r6c3 =8= r6c4 -8- r5c6 -7- r5c5 -1- r2c5 =1= r2c2 -1- r1c3 -3- r8c3 =3= r8c7 -3 => r7c7<>3, r8c7<>7
Hidden Single: r8c7=3
Grouped Discontinuous Nice Loop: 7 r5c7 -7- r5c6 -8- r6c4 =8= r6c3 =7= r456c1 -7- r7c1 =7= r7c7 -7- r5c7 => r5c7<>7
Grouped Discontinuous Nice Loop: 7 r6c3 -7- r456c1 =7= r7c1 -7- r7c7 -9- r7c5 -8- r3c5 =8= r3c4 -8- r6c4 =8= r6c3 => r6c3<>7
Locked Candidates Type 1 (Pointing): 7 in b4 => r7c1<>7
Hidden Single: r7c7=7
Naked Triple: 2,5,9 in r189c8 => r45c8<>5, r5c8<>2, r5c8<>9
Locked Candidates Type 1 (Pointing): 5 in b6 => r9c9<>5
Locked Candidates Type 2 (Claiming): 5 in r5 => r4c12,r6c1<>5
Naked Pair: 7,8 in r5c68 => r5c15<>7, r5c23<>8
Naked Single: r5c5=1
Naked Single: r2c5=7
Naked Single: r2c6=4
Naked Single: r1c4=1
Naked Single: r2c9=9
Naked Single: r1c3=3
Naked Single: r1c8=2
Full House: r1c7=4
Full House: r1c2=9
Naked Single: r2c1=5
Full House: r2c2=1
Naked Single: r5c3=5
Naked Single: r8c3=7
Naked Single: r9c3=8
Full House: r6c3=1
Naked Single: r6c7=2
Naked Single: r5c7=9
Naked Single: r5c9=4
Naked Single: r6c1=7
Naked Single: r6c9=5
Full House: r6c4=8
Naked Single: r9c7=6
Full House: r4c7=1
Naked Single: r5c2=3
Naked Single: r4c1=4
Naked Single: r4c9=6
Full House: r9c9=2
Naked Single: r3c4=9
Full House: r3c5=8
Full House: r7c5=9
Naked Single: r5c6=7
Full House: r4c4=5
Naked Single: r5c1=2
Full House: r4c2=8
Full House: r5c8=8
Full House: r4c8=7
Naked Single: r7c2=5
Full House: r9c2=4
Naked Single: r8c1=9
Full House: r7c1=3
Full House: r7c6=8
Full House: r9c6=5
Naked Single: r8c4=4
Full House: r9c4=7
Full House: r8c8=5
Full House: r9c8=9
|
normal_sudoku_285 | 465..938.7283549..913..84.51879.654.2.9.758.6......7..3..5..19.....8.6....1..32.. | 465719382728354961913268475187926543239475816654831729376542198592187634841693257 | normal_sudoku_285 | 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 5 . . 9 3 8 .
7 2 8 3 5 4 9 . .
9 1 3 . . 8 4 . 5
1 8 7 9 . 6 5 4 .
2 . 9 . 7 5 8 . 6
. . . . . . 7 . .
3 . . 5 . . 1 9 .
. . . . 8 . 6 . .
. . 1 . . 3 2 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 465719382728354961913268475187926543239475816654831729376542198592187634841693257 #1 Easy (226)
Naked Single: r2c9=1
Full House: r2c8=6
Naked Single: r8c1=5
Naked Single: r6c1=6
Full House: r9c1=8
Naked Single: r6c3=4
Naked Single: r5c2=3
Full House: r6c2=5
Naked Single: r8c3=2
Full House: r7c3=6
Naked Single: r5c8=1
Full House: r5c4=4
Hidden Single: r6c9=9
Hidden Single: r6c4=8
Hidden Single: r7c9=8
Hidden Single: r8c2=9
Hidden Single: r9c5=9
Hidden Single: r9c8=5
Hidden Single: r8c9=4
Naked Single: r9c9=7
Full House: r8c8=3
Naked Single: r1c9=2
Full House: r3c8=7
Full House: r6c8=2
Full House: r4c9=3
Full House: r4c5=2
Naked Single: r9c2=4
Full House: r9c4=6
Full House: r7c2=7
Naked Single: r1c5=1
Full House: r1c4=7
Naked Single: r6c6=1
Full House: r6c5=3
Naked Single: r3c5=6
Full House: r7c5=4
Full House: r3c4=2
Full House: r7c6=2
Full House: r8c4=1
Full House: r8c6=7
|
normal_sudoku_6844 | ..14..6233.....495.9....781968.2.147.7....8595.4...3621..67.2.8...2.591...2.185.. | 781459623326781495495362781968523147273146859514897362159674238847235916632918574 | normal_sudoku_6844 | 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 2 3
3 . . . . . 4 9 5
. 9 . . . . 7 8 1
9 6 8 . 2 . 1 4 7
. 7 . . . . 8 5 9
5 . 4 . . . 3 6 2
1 . . 6 7 . 2 . 8
. . . 2 . 5 9 1 .
. . 2 . 1 8 5 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 781459623326781495495362781968523147273146859514897362159674238847235916632918574 #1 Easy (156)
Naked Single: r6c2=1
Naked Single: r5c1=2
Full House: r5c3=3
Naked Single: r7c8=3
Full House: r9c8=7
Naked Single: r4c6=3
Full House: r4c4=5
Naked Single: r5c4=1
Naked Single: r3c4=3
Naked Single: r9c4=9
Naked Single: r7c6=4
Full House: r8c5=3
Naked Single: r5c6=6
Full House: r5c5=4
Naked Single: r7c2=5
Full House: r7c3=9
Naked Single: r3c6=2
Naked Single: r1c2=8
Naked Single: r1c1=7
Naked Single: r2c2=2
Naked Single: r8c2=4
Full House: r9c2=3
Naked Single: r1c6=9
Full House: r1c5=5
Naked Single: r2c3=6
Naked Single: r8c9=6
Full House: r9c9=4
Full House: r9c1=6
Naked Single: r6c6=7
Full House: r2c6=1
Naked Single: r3c5=6
Naked Single: r2c5=8
Full House: r2c4=7
Full House: r6c4=8
Full House: r6c5=9
Naked Single: r3c1=4
Full House: r3c3=5
Full House: r8c3=7
Full House: r8c1=8
|
normal_sudoku_345 | 2974.631..5.97...2.681....773..49.81.297....381..6.97.94.6..73.57...41.6.8...7... | 297486315154973862368125497736549281429718653815362974942651738573894126681237549 | normal_sudoku_345 | 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 7 4 . 6 3 1 .
. 5 . 9 7 . . . 2
. 6 8 1 . . . . 7
7 3 . . 4 9 . 8 1
. 2 9 7 . . . . 3
8 1 . . 6 . 9 7 .
9 4 . 6 . . 7 3 .
5 7 . . . 4 1 . 6
. 8 . . . 7 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 297486315154973862368125497736549281429718653815362974942651738573894126681237549 #1 Easy (176)
Hidden Single: r3c8=9
Naked Single: r8c8=2
Naked Single: r8c3=3
Naked Single: r8c4=8
Full House: r8c5=9
Hidden Single: r4c7=2
Naked Single: r4c4=5
Full House: r4c3=6
Naked Single: r5c1=4
Full House: r6c3=5
Naked Single: r3c1=3
Naked Single: r6c9=4
Naked Single: r2c1=1
Full House: r2c3=4
Full House: r9c1=6
Naked Single: r2c8=6
Naked Single: r2c7=8
Full House: r2c6=3
Naked Single: r5c8=5
Full House: r5c7=6
Full House: r9c8=4
Naked Single: r1c9=5
Full House: r1c5=8
Full House: r3c7=4
Full House: r9c7=5
Naked Single: r6c6=2
Full House: r6c4=3
Full House: r9c4=2
Naked Single: r7c9=8
Full House: r9c9=9
Naked Single: r5c5=1
Full House: r5c6=8
Naked Single: r3c6=5
Full House: r3c5=2
Full House: r7c6=1
Naked Single: r9c3=1
Full House: r9c5=3
Full House: r7c5=5
Full House: r7c3=2
|
normal_sudoku_1549 | .5.4..813.......979378..25..2...6748...7.256.57....32....2...3..486..972.6.9..185 | 652479813814325697937861254321596748489732561576184329795218436148653972263947185 | normal_sudoku_1549 | 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 . . 8 1 3
. . . . . . . 9 7
9 3 7 8 . . 2 5 .
. 2 . . . 6 7 4 8
. . . 7 . 2 5 6 .
5 7 . . . . 3 2 .
. . . 2 . . . 3 .
. 4 8 6 . . 9 7 2
. 6 . 9 . . 1 8 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 652479813814325697937861254321596748489732561576184329795218436148653972263947185 #1 Easy (178)
Naked Single: r3c6=1
Naked Single: r6c4=1
Naked Single: r3c5=6
Full House: r3c9=4
Full House: r2c7=6
Full House: r7c7=4
Full House: r7c9=6
Naked Single: r6c9=9
Full House: r5c9=1
Hidden Single: r6c3=6
Naked Single: r1c3=2
Naked Single: r1c1=6
Naked Single: r9c3=3
Naked Single: r8c1=1
Naked Single: r4c1=3
Naked Single: r7c1=7
Naked Single: r7c2=9
Naked Single: r4c4=5
Full House: r2c4=3
Naked Single: r9c1=2
Full House: r7c3=5
Naked Single: r5c2=8
Full House: r2c2=1
Naked Single: r4c5=9
Full House: r4c3=1
Naked Single: r2c6=5
Naked Single: r7c6=8
Full House: r7c5=1
Naked Single: r5c1=4
Full House: r2c1=8
Full House: r2c3=4
Full House: r2c5=2
Full House: r5c3=9
Full House: r5c5=3
Naked Single: r1c5=7
Full House: r1c6=9
Naked Single: r8c6=3
Full House: r8c5=5
Naked Single: r6c6=4
Full House: r6c5=8
Full House: r9c5=4
Full House: r9c6=7
|
normal_sudoku_3574 | ..7.36....6..1....31..7586..2.641.7.546.8.1..7.159.6.46...59.4119..28..62..16.9.. | 857936412469812735312475869923641578546287193781593624678359241194728356235164987 | normal_sudoku_3574 | 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 . . 1 . . . .
3 1 . . 7 5 8 6 .
. 2 . 6 4 1 . 7 .
5 4 6 . 8 . 1 . .
7 . 1 5 9 . 6 . 4
6 . . . 5 9 . 4 1
1 9 . . 2 8 . . 6
2 . . 1 6 . 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 857936412469812735312475869923641578546287193781593624678359241194728356235164987 #1 Medium (290)
Hidden Single: r1c8=1
Hidden Single: r7c7=2
Locked Candidates Type 1 (Pointing): 9 in b4 => r4c9<>9
Locked Candidates Type 1 (Pointing): 4 in b7 => r23c3<>4
Hidden Single: r3c4=4
Naked Single: r2c6=2
Naked Single: r6c6=3
Naked Single: r5c6=7
Full House: r5c4=2
Full House: r9c6=4
Naked Single: r6c2=8
Full House: r6c8=2
Naked Single: r1c2=5
Naked Single: r4c1=9
Full House: r4c3=3
Naked Single: r1c7=4
Naked Single: r4c7=5
Full House: r4c9=8
Naked Single: r7c3=8
Naked Single: r1c1=8
Full House: r2c1=4
Naked Single: r2c3=9
Full House: r3c3=2
Full House: r3c9=9
Naked Single: r9c3=5
Full House: r8c3=4
Naked Single: r1c4=9
Full House: r2c4=8
Full House: r1c9=2
Naked Single: r5c9=3
Full House: r5c8=9
Naked Single: r9c9=7
Full House: r2c9=5
Naked Single: r8c7=3
Full House: r2c7=7
Full House: r2c8=3
Naked Single: r9c2=3
Full House: r9c8=8
Full House: r8c8=5
Full House: r8c4=7
Full House: r7c2=7
Full House: r7c4=3
|
normal_sudoku_746 | .943...1.1....4938....19.4.96.1..4.2.15.4..934....35617415..3.9.394.1.5....93.1.4 | 694385217157624938328719645963157482815246793472893561741568329239471856586932174 | normal_sudoku_746 | 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 4 3 . . . 1 .
1 . . . . 4 9 3 8
. . . . 1 9 . 4 .
9 6 . 1 . . 4 . 2
. 1 5 . 4 . . 9 3
4 . . . . 3 5 6 1
7 4 1 5 . . 3 . 9
. 3 9 4 . 1 . 5 .
. . . 9 3 . 1 . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 694385217157624938328719645963157482815246793472893561741568329239471856586932174 #1 Medium (566)
Hidden Single: r4c3=3
Hidden Single: r3c1=3
Hidden Single: r6c5=9
Locked Candidates Type 1 (Pointing): 2 in b3 => r8c7<>2
Locked Candidates Type 1 (Pointing): 7 in b4 => r6c4<>7
Locked Candidates Type 1 (Pointing): 6 in b9 => r8c15<>6
Locked Candidates Type 1 (Pointing): 6 in b7 => r9c6<>6
Naked Pair: 2,8 in r58c1 => r19c1<>2, r19c1<>8
Locked Candidates Type 1 (Pointing): 8 in b1 => r3c4<>8
Locked Candidates Type 2 (Claiming): 8 in c4 => r4c56,r5c6<>8
Hidden Single: r4c8=8
Full House: r5c7=7
Naked Single: r7c8=2
Full House: r9c8=7
Naked Single: r8c9=6
Full House: r8c7=8
Naked Single: r8c1=2
Full House: r8c5=7
Naked Single: r5c1=8
Naked Single: r4c5=5
Full House: r4c6=7
Hidden Single: r9c6=2
Naked Single: r5c6=6
Full House: r5c4=2
Full House: r6c4=8
Naked Single: r7c6=8
Full House: r1c6=5
Full House: r7c5=6
Naked Single: r1c1=6
Full House: r9c1=5
Naked Single: r1c9=7
Full House: r3c9=5
Naked Single: r2c5=2
Full House: r1c5=8
Full House: r1c7=2
Full House: r3c7=6
Naked Single: r9c2=8
Full House: r9c3=6
Naked Single: r2c3=7
Naked Single: r3c4=7
Full House: r2c4=6
Full House: r2c2=5
Naked Single: r3c2=2
Full House: r3c3=8
Full House: r6c3=2
Full House: r6c2=7
|
normal_sudoku_2524 | ..3.......6.......9...5.32....51.24..1582.9732....9815..7.9.1..........48..1..59. | 153482769762931458948756321389517246615824973274369815437695182591278634826143597 | normal_sudoku_2524 | 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 . . . . . . .
9 . . . 5 . 3 2 .
. . . 5 1 . 2 4 .
. 1 5 8 2 . 9 7 3
2 . . . . 9 8 1 5
. . 7 . 9 . 1 . .
. . . . . . . . 4
8 . . 1 . . 5 9 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 153482769762931458948756321389517246615824973274369815437695182591278634826143597 #1 Extreme (2130)
Full House: r4c9=6
Locked Candidates Type 1 (Pointing): 6 in b3 => r1c456<>6
Naked Pair: 4,6 in r5c1,r6c3 => r6c2<>4
Naked Pair: 3,7 in r4c1,r6c2 => r4c2<>3, r4c2<>7
Almost Locked Set XZ-Rule: A=r69c3 {246}, B=r8c7,r9c9 {267}, X=2, Z=6 => r8c3<>6
2-String Kite: 6 in r5c6,r9c3 (connected by r5c1,r6c3) => r9c6<>6
Forcing Net Contradiction in r3 => r4c1=3
r4c1<>3 r4c1=7 (r4c6<>7 r4c6=3 r9c6<>3) r6c2<>7 r6c2=3 r9c2<>3 r9c5=3 (r9c5<>4) r9c5<>6 r9c3=6 (r9c3<>4) (r7c1<>6) r8c1<>6 r5c1=6 r5c6<>6 r5c6=4 r9c6<>4 r9c2=4 r3c2<>4
r4c1<>3 r4c1=7 (r4c6<>7 r4c6=3 r9c6<>3) r6c2<>7 r6c2=3 r9c2<>3 r9c5=3 r9c5<>6 r9c3=6 r6c3<>6 r6c3=4 r3c3<>4
r4c1<>3 r4c1=7 (r4c6<>7 r4c6=3 r9c6<>3) r6c2<>7 r6c2=3 r9c2<>3 r9c5=3 (r9c5<>4) r9c5<>6 r9c3=6 (r9c3<>4) (r7c1<>6) r8c1<>6 r5c1=6 r5c6<>6 r5c6=4 (r7c6<>4) r9c6<>4 r9c2=4 (r7c1<>4) r7c2<>4 r7c4=4 r3c4<>4
r4c1<>3 r4c1=7 (r4c6<>7 r4c6=3 r9c6<>3) r6c2<>7 r6c2=3 r9c2<>3 r9c5=3 r9c5<>6 r9c3=6 (r7c1<>6) r8c1<>6 r5c1=6 r5c6<>6 r5c6=4 r3c6<>4
Naked Single: r4c6=7
Naked Single: r6c2=7
Skyscraper: 7 in r3c4,r9c5 (connected by r39c9) => r12c5,r8c4<>7
AIC: 4 4- r5c6 -6- r3c6 =6= r3c4 =7= r3c9 -7- r9c9 =7= r9c5 =6= r9c3 -6- r6c3 -4 => r5c1,r6c45<>4
Naked Single: r5c1=6
Full House: r5c6=4
Naked Single: r6c3=4
Hidden Single: r9c3=6
Skyscraper: 4 in r3c4,r9c5 (connected by r39c2) => r12c5,r7c4<>4
Naked Single: r1c5=8
Naked Single: r2c5=3
Naked Single: r6c5=6
Full House: r6c4=3
Naked Single: r8c5=7
Full House: r9c5=4
Naked Single: r8c7=6
Naked Single: r8c4=2
Naked Single: r7c4=6
Naked Single: r9c6=3
Naked Single: r9c2=2
Full House: r9c9=7
Hidden Single: r1c8=6
Hidden Single: r2c3=2
Naked Single: r2c6=1
Naked Single: r1c6=2
Naked Single: r3c6=6
Hidden Single: r7c9=2
Hidden Single: r3c4=7
Hidden Single: r2c8=5
Hidden Single: r3c2=4
Naked Single: r1c2=5
Naked Single: r2c1=7
Naked Single: r7c2=3
Naked Single: r1c1=1
Full House: r3c3=8
Full House: r3c9=1
Naked Single: r2c7=4
Full House: r1c7=7
Naked Single: r7c8=8
Full House: r8c8=3
Naked Single: r8c2=9
Full House: r4c2=8
Full House: r4c3=9
Full House: r8c3=1
Naked Single: r1c9=9
Full House: r1c4=4
Full House: r2c4=9
Full House: r2c9=8
Naked Single: r8c1=5
Full House: r7c1=4
Full House: r7c6=5
Full House: r8c6=8
|
normal_sudoku_6535 | .624....88.4.5....3....8.4.2869..4..1..684329..3..5.86.....78...285...6..3.8....4 | 762491538894352671351768942286973415175684329943125786619247853428539167537816294 | normal_sudoku_6535 | 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 4 . . . . 8
8 . 4 . 5 . . . .
3 . . . . 8 . 4 .
2 8 6 9 . . 4 . .
1 . . 6 8 4 3 2 9
. . 3 . . 5 . 8 6
. . . . . 7 8 . .
. 2 8 5 . . . 6 .
. 3 . 8 . . . . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 762491538894352671351768942286973415175684329943125786619247853428539167537816294 #1 Extreme (5310)
Locked Candidates Type 2 (Claiming): 7 in r5 => r6c12<>7
Naked Triple: 1,3,9 in r148c6 => r29c6<>1, r2c6<>3, r29c6<>9
Turbot Fish: 2 r2c6 =2= r9c6 -2- r9c7 =2= r7c9 => r2c9<>2
Empty Rectangle: 3 in b3 (r27c4) => r7c8<>3
Locked Candidates Type 1 (Pointing): 3 in b9 => r2c9<>3
Almost Locked Set XY-Wing: A=r2c24689 {123679}, B=r1689c7 {12579}, C=r9c6 {26}, X,Y=2,6, Z=1,7,9 => r2c7<>1, r2c7<>7, r2c7<>9
Naked Pair: 2,6 in r2c67 => r2c4<>2
Forcing Chain Contradiction in r3c4 => r3c7<>7
r3c7=7 r2c9<>7 r2c9=1 r2c2<>1 r3c23=1 r3c4<>1
r3c7=7 r3c7<>6 r3c5=6 r2c6<>6 r2c6=2 r3c4<>2
r3c7=7 r3c4<>7
Forcing Chain Verity => r7c1<>9
r7c4=3 r2c4<>3 r2c8=3 r2c8<>9 r2c2=9 r6c2<>9 r6c1=9 r7c1<>9
r7c5=3 r7c5<>6 r7c1=6 r7c1<>9
r7c9=3 r7c9<>2 r9c7=2 r9c6<>2 r9c6=6 r9c1<>6 r7c1=6 r7c1<>9
Forcing Net Contradiction in r6 => r1c1<>9
r1c1=9 (r1c6<>9 r8c6=9 r8c7<>9) (r8c1<>9) r6c1<>9 r6c1=4 r8c1<>4 r8c1=7 r8c7<>7 r8c7=1 r6c7<>1 r6c7=7 r6c5<>7 r6c4=7
r1c1=9 (r1c6<>9 r8c6=9 r8c7<>9) (r8c1<>9) r6c1<>9 r6c1=4 r8c1<>4 r8c1=7 r8c7<>7 r8c7=1 r6c7<>1 r6c7=7
Grouped Discontinuous Nice Loop: 5 r3c3 -5- r5c3 -7- r5c2 =7= r23c2 -7- r1c1 -5- r3c3 => r3c3<>5
Forcing Net Contradiction in c5 => r6c1=9
r6c1<>9 r6c1=4 r6c2<>4 r6c2=9 (r7c2<>9) (r2c2<>9 r2c8=9 r7c8<>9) (r2c2<>9) r3c2<>9 r3c3=9 r7c3<>9 r7c5=9
r6c1<>9 r6c1=4 (r8c1<>4 r8c5=4 r8c5<>3) r6c2<>4 r6c2=9 (r2c2<>9 r2c8=9 r2c8<>3 r2c4=3 r1c6<>3) (r2c2<>9 r2c8=9 r2c8<>3 r2c4=3 r7c4<>3) (r7c2<>9) (r2c2<>9 r2c8=9 r7c8<>9) (r2c2<>9) r3c2<>9 r3c3=9 r7c3<>9 r7c5=9 (r1c5<>9 r1c6=9 r1c6<>1) r7c5<>3 r7c9=3 (r7c9<>2 r7c4=2 r9c5<>2) (r7c9<>2 r7c4=2 r9c6<>2 r9c6=6 r9c5<>6) r8c9<>3 r8c6=3 r4c6<>3 (r4c6=1 r6c5<>1 r6c7=1 r1c7<>1) r4c5=3 r1c5<>3 r1c8=3 r1c8<>1 r1c5=1 r9c5<>1 r9c5=9
Naked Single: r6c2=4
Naked Triple: 1,5,9 in r7c238 => r7c19<>5, r7c459<>1, r7c5<>9
Naked Pair: 2,3 in r7c49 => r7c5<>2, r7c5<>3
Empty Rectangle: 5 in b9 (r19c1) => r1c8<>5
Grouped AIC: 7 7- r2c9 -1- r1c78 =1= r1c56 -1- r23c4 =1= r6c4 -1- r6c7 -7 => r1c7,r4c9<>7
Sashimi Swordfish: 7 r148 c158 fr8c7 fr8c9 => r9c8<>7
Grouped AIC: 1 1- r2c9 -7- r8c9 =7= r89c7 -7- r6c7 -1 => r13c7,r4c9<>1
Naked Single: r4c9=5
Locked Candidates Type 1 (Pointing): 5 in b3 => r9c7<>5
Finned Swordfish: 1 r148 c568 fr8c7 fr8c9 => r79c8<>1
Locked Pair: 5,9 in r79c8 => r12c8,r89c7<>9
Hidden Single: r2c2=9
Locked Candidates Type 1 (Pointing): 1 in b1 => r3c459<>1
Locked Candidates Type 2 (Claiming): 1 in r7 => r9c3<>1
Locked Candidates Type 2 (Claiming): 9 in r8 => r9c5<>9
Naked Pair: 2,7 in r3c49 => r3c235<>7, r3c57<>2
Naked Single: r3c3=1
Naked Single: r3c2=5
Full House: r1c1=7
Naked Single: r5c2=7
Full House: r7c2=1
Full House: r5c3=5
Naked Single: r8c1=4
Naked Single: r7c3=9
Full House: r9c3=7
Naked Single: r7c1=6
Full House: r9c1=5
Naked Single: r7c8=5
Naked Single: r7c5=4
Naked Single: r9c8=9
Hidden Single: r1c7=5
Hidden Single: r3c7=9
Naked Single: r3c5=6
Naked Single: r2c6=2
Naked Single: r2c7=6
Naked Single: r3c4=7
Full House: r3c9=2
Naked Single: r9c6=6
Naked Single: r7c9=3
Full House: r7c4=2
Naked Single: r6c4=1
Full House: r2c4=3
Naked Single: r9c5=1
Full House: r9c7=2
Naked Single: r4c6=3
Naked Single: r6c7=7
Full House: r4c8=1
Full House: r4c5=7
Full House: r6c5=2
Full House: r8c7=1
Full House: r8c9=7
Full House: r2c9=1
Full House: r2c8=7
Full House: r1c8=3
Naked Single: r1c5=9
Full House: r1c6=1
Full House: r8c6=9
Full House: r8c5=3
|
normal_sudoku_1507 | ..46.35.2..2.5.....5.4....32........745.6.3.11.8.........7.92...2..4.7.64.7..6.1. | 974613582382957164651482973293174658745268391168395427816739245529841736437526819 | normal_sudoku_1507 | 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 . 3 5 . 2
. . 2 . 5 . . . .
. 5 . 4 . . . . 3
2 . . . . . . . .
7 4 5 . 6 . 3 . 1
1 . 8 . . . . . .
. . . 7 . 9 2 . .
. 2 . . 4 . 7 . 6
4 . 7 . . 6 . 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 974613582382957164651482973293174658745268391168395427816739245529841736437526819 #1 Extreme (7864)
Almost Locked Set XZ-Rule: A=r7c23589 {134568}, B=r9c279 {3589}, X=5, Z=3 => r7c1<>3
Forcing Chain Contradiction in r9 => r2c2<>6
r2c2=6 r46c2<>6 r4c3=6 r4c3<>3 r46c2=3 r9c2<>3
r2c2=6 r23c1<>6 r7c1=6 r7c1<>5 r8c1=5 r8c46<>5 r9c4=5 r9c4<>3
r2c2=6 r23c1<>6 r7c1=6 r7c1<>5 r8c1=5 r8c46<>5 r9c4=5 r9c4<>2 r9c5=2 r9c5<>3
Forcing Chain Contradiction in r2c6 => r3c5<>1
r3c5=1 r2c6<>1
r3c5=1 r1c5<>1 r1c2=1 r1c2<>7 r2c2=7 r2c6<>7
r3c5=1 r3c5<>2 r3c6=2 r5c6<>2 r5c6=8 r2c6<>8
Forcing Chain Contradiction in r2c6 => r6c8<>7
r6c8=7 r123c8<>7 r2c9=7 r2c2<>7 r1c2=7 r1c2<>1 r1c5=1 r2c6<>1
r6c8=7 r3c8<>7 r3c56=7 r2c6<>7
r6c8=7 r6c8<>2 r5c8=2 r5c6<>2 r5c6=8 r2c6<>8
Forcing Net Contradiction in r9c4 => r1c2<>8
r1c2=8 (r1c2<>1 r1c5=1 r2c6<>1) r1c2<>7 r2c2=7 r2c6<>7 r2c6=8 r5c6<>8 r5c6=2 r3c6<>2 r3c5=2 r9c5<>2 r9c4=2
r1c2=8 (r1c2<>1 r1c5=1 r2c4<>1) (r1c2<>1 r1c5=1 r2c6<>1) r1c2<>7 r2c2=7 r2c6<>7 r2c6=8 r2c4<>8 r2c4=9 (r2c9<>9) r5c4<>9 r5c8=9 (r4c9<>9) r6c9<>9 r9c9=9 r9c9<>5 r9c4=5
Forcing Net Contradiction in r7c8 => r1c2<>9
r1c2=9 (r3c1<>9 r8c1=9 r8c3<>9) (r1c2<>1) r1c2<>7 r2c2=7 r2c2<>1 r7c2=1 r8c3<>1 r8c3=3 r8c8<>3 r7c8=3
r1c2=9 (r1c2<>1 r1c5=1 r2c4<>1) (r1c2<>1 r1c5=1 r2c6<>1) r1c2<>7 r2c2=7 (r2c9<>7) r2c6<>7 r2c6=8 (r2c9<>8) r2c4<>8 r2c4=9 r2c9<>9 r2c9=4 r7c9<>4 r7c8=4
Forcing Net Contradiction in r8c8 => r1c5<>8
r1c5=8 (r1c1<>8 r1c1=9 r1c8<>9 r1c8=7 r3c8<>7) (r1c1<>8 r1c1=9 r3c1<>9) (r1c1<>8 r1c1=9 r3c3<>9) r1c5<>1 r1c2=1 r3c3<>1 r3c3=6 (r3c8<>6) r3c1<>6 r3c1=8 r3c8<>8 r3c8=9 (r3c5<>9) r5c8<>9 r5c4=9 (r4c5<>9) r6c5<>9 r1c5=9 r1c5<>8
Forcing Net Contradiction in r8c8 => r2c1<>8
r2c1=8 (r8c1<>8) r2c1<>3 (r8c1=3 r8c8<>3 r7c8=3 r7c5<>3) r2c2=3 r2c2<>7 r1c2=7 r1c2<>1 r1c5=1 r7c5<>1 r7c5=8 (r8c4<>8) r8c6<>8 r8c8=8 r1c8<>8 r1c1=8 r2c1<>8
Forcing Net Contradiction in b3 => r2c1<>9
r2c1=9 r2c1<>3 r2c2=3 (r2c2<>1) r2c2<>7 r1c2=7 r1c2<>1 r1c5=1 (r2c4<>1) r2c6<>1 r2c7=1 r2c7<>6
r2c1=9 r2c1<>3 (r8c1=3 r8c8<>3 r7c8=3 r7c8<>4 r7c9=4 r2c9<>4) r2c2=3 (r2c2<>1) r2c2<>7 r1c2=7 r1c2<>1 r1c5=1 (r2c4<>1) r2c6<>1 r2c7=1 r2c7<>4 r2c8=4 r2c8<>6
r2c1=9 (r3c1<>9) r1c1<>9 r1c1=8 r3c1<>8 r3c1=6 r3c7<>6
r2c1=9 (r3c1<>9) r1c1<>9 r1c1=8 r3c1<>8 r3c1=6 r3c8<>6
Forcing Net Contradiction in r2c9 => r1c8<>9
r1c8=9 (r2c7<>9) (r2c8<>9) (r2c9<>9) r5c8<>9 r5c4=9 r2c4<>9 r2c2=9 (r3c1<>9 r8c1=9 r8c3<>9) (r2c2<>1) r2c2<>7 r1c2=7 r1c2<>1 r7c2=1 r8c3<>1 r8c3=3 r8c8<>3 r7c8=3 r7c8<>4 r7c9=4 r2c9<>4
r1c8=9 (r3c7<>9) (r3c8<>9) (r2c7<>9) (r2c8<>9) (r2c9<>9) r5c8<>9 r5c4=9 r2c4<>9 r2c2=9 (r3c1<>9) r3c3<>9 r3c5=9 (r3c5<>7) r3c5<>2 r3c6=2 r3c6<>7 r3c8=7 r2c9<>7
r1c8=9 (r2c7<>9) (r2c8<>9) (r2c9<>9) r5c8<>9 r5c4=9 (r2c4<>9) r2c4<>9 r2c2=9 r2c2<>7 r1c2=7 r1c2<>1 r1c5=1 r2c4<>1 r2c4=8 r2c9<>8
r1c8=9 r2c9<>9
Discontinuous Nice Loop: 9 r2c2 -9- r1c1 -8- r1c8 -7- r1c2 =7= r2c2 => r2c2<>9
Finned X-Wing: 9 r25 c48 fr2c7 fr2c9 => r3c8<>9
Almost Locked Set XY-Wing: A=r13c8 {678}, B=r1c5,r2c46 {1789}, C=r3c13567 {126789}, X,Y=6,7, Z=8 => r2c789<>8
Finned Jellyfish: 8 r1258 c1468 fr2c2 => r3c1<>8
Sue de Coq: r1c12 - {1789} (r1c8 - {78}, r23c1,r3c3 - {1369}) => r2c2<>1, r2c2<>3, r1c5<>7
Hidden Single: r2c1=3
Locked Candidates Type 1 (Pointing): 6 in b1 => r3c78<>6
Locked Pair: 7,8 in r13c8 => r2c89,r4c8<>7, r3c7,r4578c8<>8
Locked Candidates Type 1 (Pointing): 8 in b6 => r4c456<>8
Naked Triple: 1,6,9 in r3c137 => r3c5<>9, r3c6<>1
Finned Swordfish: 8 r258 c146 fr2c2 => r1c1<>8
Naked Single: r1c1=9
Naked Single: r1c5=1
Naked Single: r3c1=6
Naked Single: r1c2=7
Full House: r1c8=8
Naked Single: r3c3=1
Full House: r2c2=8
Naked Single: r3c8=7
Naked Single: r3c7=9
Naked Single: r2c4=9
Naked Single: r2c6=7
Naked Single: r2c9=4
Naked Single: r9c7=8
Naked Single: r2c8=6
Full House: r2c7=1
Naked Single: r7c9=5
Naked Single: r7c1=8
Full House: r8c1=5
Naked Single: r9c9=9
Naked Single: r7c5=3
Naked Single: r6c9=7
Full House: r4c9=8
Naked Single: r8c8=3
Full House: r7c8=4
Naked Single: r9c2=3
Naked Single: r7c3=6
Full House: r7c2=1
Full House: r8c3=9
Full House: r4c3=3
Naked Single: r9c5=2
Full House: r9c4=5
Naked Single: r3c5=8
Full House: r3c6=2
Naked Single: r6c5=9
Full House: r4c5=7
Naked Single: r4c4=1
Naked Single: r5c6=8
Naked Single: r6c2=6
Full House: r4c2=9
Naked Single: r8c4=8
Full House: r8c6=1
Naked Single: r5c4=2
Full House: r5c8=9
Full House: r6c4=3
Naked Single: r6c7=4
Full House: r4c7=6
Naked Single: r4c8=5
Full House: r4c6=4
Full House: r6c6=5
Full House: r6c8=2
|
normal_sudoku_3844 | ......9....9.5..87...8.94......2.7..2.31..85...75.8..2.1.6....3..531..78..2.8..1. | 486271935329456187571839426854923761293167854167548392718695243945312678632784519 | normal_sudoku_3844 | 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 . .
. . 9 . 5 . . 8 7
. . . 8 . 9 4 . .
. . . . 2 . 7 . .
2 . 3 1 . . 8 5 .
. . 7 5 . 8 . . 2
. 1 . 6 . . . . 3
. . 5 3 1 . . 7 8
. . 2 . 8 . . 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 486271935329456187571839426854923761293167854167548392718695243945312678632784519 #1 Extreme (2854)
Locked Triple: 2,5,6 in r789c7 => r2c7,r7c8<>2, r26c7,r9c9<>6, r9c9<>5
Locked Candidates Type 1 (Pointing): 2 in b8 => r12c6<>2
Locked Candidates Type 2 (Claiming): 9 in r8 => r79c1,r9c2<>9
Naked Triple: 4,6,9 in r568c2 => r1249c2<>4, r12349c2<>6, r4c2<>9
Hidden Pair: 2,5 in r7c67 => r7c6<>4, r7c6<>7
2-String Kite: 3 in r2c7,r4c6 (connected by r4c8,r6c7) => r2c6<>3
2-String Kite: 7 in r1c4,r7c1 (connected by r7c5,r9c4) => r1c1<>7
2-String Kite: 9 in r4c4,r7c8 (connected by r7c5,r9c4) => r4c8<>9
W-Wing: 4/9 in r4c4,r7c8 connected by 9 in r9c49 => r4c8<>4
Naked Triple: 2,3,6 in r134c8 => r6c8<>3, r6c8<>6
Finned Swordfish: 6 c358 r134 fr5c5 fr6c5 => r4c6<>6
Finned Jellyfish: 6 r2689 c1267 fr6c5 => r5c6<>6
Locked Candidates Type 1 (Pointing): 6 in b5 => r13c5<>6
Hidden Pair: 1,6 in r12c6 => r1c6<>3, r12c6<>4, r1c6<>7
Hidden Single: r4c6=3
Naked Single: r4c8=6
Hidden Single: r6c7=3
Naked Single: r2c7=1
Naked Single: r2c6=6
Naked Single: r1c6=1
Hidden Single: r6c1=1
Hidden Single: r4c9=1
Hidden Single: r3c3=1
Hidden Single: r1c3=6
Naked Single: r1c9=5
Naked Single: r3c9=6
Locked Candidates Type 1 (Pointing): 4 in b1 => r4789c1<>4
Locked Candidates Type 1 (Pointing): 6 in b4 => r8c2<>6
Locked Candidates Type 2 (Claiming): 3 in r2 => r1c12,r3c12<>3
Skyscraper: 4 in r4c3,r6c8 (connected by r7c38) => r6c2<>4
Swordfish: 4 c269 r589 => r5c5,r9c4<>4
Skyscraper: 9 in r4c4,r5c9 (connected by r9c49) => r5c5<>9
X-Wing: 9 c58 r67 => r6c2<>9
Naked Single: r6c2=6
Hidden Single: r5c5=6
Hidden Single: r5c6=7
Locked Candidates Type 2 (Claiming): 4 in c6 => r7c5<>4
XY-Chain: 4 4- r1c1 -8- r7c1 -7- r9c2 -3- r2c2 -2- r2c4 -4 => r1c45,r2c1<>4
Naked Single: r2c1=3
Naked Single: r2c2=2
Full House: r2c4=4
Naked Single: r4c4=9
Full House: r6c5=4
Full House: r6c8=9
Full House: r5c9=4
Full House: r5c2=9
Full House: r9c9=9
Naked Single: r9c4=7
Full House: r1c4=2
Naked Single: r7c8=4
Naked Single: r8c2=4
Naked Single: r7c5=9
Naked Single: r9c1=6
Naked Single: r9c2=3
Naked Single: r1c8=3
Full House: r3c8=2
Naked Single: r7c3=8
Full House: r4c3=4
Naked Single: r8c6=2
Naked Single: r8c1=9
Full House: r7c1=7
Full House: r8c7=6
Naked Single: r9c7=5
Full House: r7c7=2
Full House: r7c6=5
Full House: r9c6=4
Naked Single: r1c5=7
Full House: r3c5=3
Naked Single: r3c1=5
Full House: r3c2=7
Naked Single: r1c2=8
Full House: r1c1=4
Full House: r4c1=8
Full House: r4c2=5
|
normal_sudoku_5468 | ..37..9.28....9.34.9.4..6..9........5.8..4.93.3.95..2.2.419...8..9.4.2...8...2.49 | 413786952826519734795423681942371865578264193631958427264195378359847216187632549 | normal_sudoku_5468 | 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 . 2
8 . . . . 9 . 3 4
. 9 . 4 . . 6 . .
9 . . . . . . . .
5 . 8 . . 4 . 9 3
. 3 . 9 5 . . 2 .
2 . 4 1 9 . . . 8
. . 9 . 4 . 2 . .
. 8 . . . 2 . 4 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 413786952826519734795423681942371865578264193631958427264195378359847216187632549 #1 Extreme (6462)
Locked Candidates Type 1 (Pointing): 8 in b3 => r4c8<>8
Hidden Pair: 4,8 in r46c7 => r46c7<>1, r4c7<>5, r46c7<>7
Grouped Discontinuous Nice Loop: 1 r8c1 -1- r3c1 -7- r2c23 =7= r2c7 -7- r5c7 -1- r9c7 =1= r8c89 -1- r8c1 => r8c1<>1
Forcing Net Contradiction in r3c8 => r2c2<>5
r2c2=5 (r2c7<>5) (r2c3<>5) r3c3<>5 r9c3=5 (r9c4<>5) r9c7<>5 r7c7=5 r7c7<>3 r7c6=3 r9c4<>3 r9c4=6 (r2c4<>6) r5c4<>6 r5c4=2 r2c4<>2 r2c4=5 r2c2<>5
Forcing Net Contradiction in r9 => r7c7<>7
r7c7=7 (r5c7<>7 r5c7=1 r2c7<>1 r2c7=5 r2c3<>5) r7c7<>3 r7c6=3 r3c6<>3 r3c5=3 r3c5<>2 r3c3=2 r3c3<>5 r9c3=5
r7c7=7 r7c7<>3 r9c7=3 r9c7<>5 r9c4=5
Forcing Net Contradiction in r8c1 => r8c2<>1
r8c2=1 (r9c3<>1) (r2c2<>1) (r5c2<>1) (r9c1<>1) r9c3<>1 r9c7=1 (r2c7<>1) r5c7<>1 r5c5=1 r2c5<>1 r2c3=1 (r2c3<>7) r3c1<>1 r3c1=7 r2c2<>7 r2c7=7 r5c7<>7 r5c7=1 r9c7<>1 r9c1=1 r8c2<>1
Locked Candidates Type 1 (Pointing): 1 in b7 => r9c7<>1
Forcing Chain Contradiction in b3 => r8c9<>5
r8c9=5 r8c9<>1 r8c8=1 r1c8<>1
r8c9=5 r79c7<>5 r2c7=5 r2c7<>1
r8c9=5 r8c9<>1 r8c8=1 r3c8<>1
r8c9=5 r79c7<>5 r2c7=5 r2c7<>7 r2c23=7 r3c1<>7 r3c1=1 r3c9<>1
Forcing Net Contradiction in c3 => r1c1<>1
r1c1=1 r3c1<>1 r3c1=7 r2c3<>7
r1c1=1 r3c1<>1 r3c1=7 r3c3<>7
r1c1=1 (r9c1<>1 r9c3=1 r9c3<>7) r3c1<>1 r3c1=7 (r9c1<>7) (r2c2<>7) r2c3<>7 r2c7=7 (r5c7<>7) r9c7<>7 r9c5=7 r5c5<>7 r5c2=7 r4c3<>7
r1c1=1 (r9c1<>1 r9c3=1 r9c3<>7) r3c1<>1 r3c1=7 (r9c1<>7) (r2c2<>7) r2c3<>7 r2c7=7 (r5c7<>7) r9c7<>7 r9c5=7 r5c5<>7 r5c2=7 r6c3<>7
r1c1=1 r9c1<>1 r9c3=1 r9c3<>7
Forcing Net Contradiction in r4 => r1c2<>5
r1c2=5 r1c2<>4 r4c2=4 r4c2<>2
r1c2=5 (r2c3<>5) r3c3<>5 r9c3=5 (r9c7<>5) r9c3<>1 r9c1=1 r3c1<>1 r3c1=7 (r2c2<>7) r2c3<>7 r2c7=7 r9c7<>7 r9c7=3 r7c7<>3 r7c6=3 r3c6<>3 r3c5=3 r3c5<>2 r3c3=2 r4c3<>2
r1c2=5 (r2c3<>5) r3c3<>5 r9c3=5 (r9c7<>5) r9c3<>1 r9c1=1 r3c1<>1 r3c1=7 (r2c2<>7) r2c3<>7 r2c7=7 r9c7<>7 r9c7=3 r7c7<>3 r7c6=3 (r4c6<>3) r3c6<>3 r3c5=3 r4c5<>3 r4c4=3 r4c4<>2
r1c2=5 (r2c3<>5) (r2c3<>5) r3c3<>5 r9c3=5 r9c3<>1 r9c1=1 r3c1<>1 r3c1=7 (r2c2<>7) r2c3<>7 r2c7=7 r2c7<>5 r2c4=5 r2c4<>2 r45c4=2 r4c5<>2
Locked Candidates Type 1 (Pointing): 5 in b1 => r9c3<>5
Forcing Net Contradiction in c4 => r1c5<>6
r1c5=6 (r1c6<>6) r1c1<>6 r1c1=4 (r1c2<>4 r1c2=1 r1c6<>1) r6c1<>4 r6c7=4 r6c7<>8 r6c6=8 r1c6<>8 r1c6=5 r2c4<>5
r1c5=6 r1c1<>6 r1c1=4 r6c1<>4 r6c7=4 r6c7<>8 r6c6=8 r8c6<>8 r8c4=8 r8c4<>5
r1c5=6 (r1c5<>8) r1c1<>6 r1c1=4 r1c2<>4 (r1c2=1 r3c1<>1 r3c1=7 r2c3<>7 r2c7=7 r2c7<>5) r4c2=4 r4c7<>4 r4c7=8 r4c5<>8 r3c5=8 r3c5<>3 r3c6=3 r7c6<>3 r7c7=3 r7c7<>5 r9c7=5 r9c4<>5
Forcing Net Contradiction in r2c5 => r2c3<>7
r2c3=7 (r2c3<>5 r3c3=5 r3c9<>5 r3c9=7 r6c9<>7) (r6c3<>7) r3c1<>7 r3c1=1 r9c1<>1 r9c3=1 r6c3<>1 r6c3=6 r6c9<>6 r6c9=1 r5c7<>1 r2c7=1 r2c5<>1
r2c3=7 r2c3<>5 r3c3=5 r3c3<>2 r3c5=2 r2c5<>2
r2c3=7 (r3c1<>7 r3c1=1 r9c1<>1 r9c3=1 r6c3<>1 r6c3=6 r5c2<>6) (r2c3<>2) r2c3<>5 r3c3=5 r3c3<>2 (r3c5=2 r5c5<>2) r4c3=2 r5c2<>2 r5c4=2 r5c4<>6 r5c5=6 r2c5<>6
Finned Swordfish: 7 r259 c257 fr9c1 fr9c3 => r78c2<>7
Locked Pair: 5,6 in r78c2 => r1245c2,r89c1,r9c3<>6
Locked Candidates Type 2 (Claiming): 6 in r5 => r4c456,r6c6<>6
Locked Candidates Type 2 (Claiming): 6 in r9 => r78c6,r8c4<>6
Hidden Single: r1c6=6
Naked Single: r1c1=4
Naked Single: r1c2=1
Naked Single: r1c5=8
Full House: r1c8=5
Naked Single: r3c1=7
Naked Single: r2c2=2
Naked Single: r3c9=1
Naked Single: r8c1=3
Naked Single: r2c4=5
Naked Single: r2c5=1
Naked Single: r3c3=5
Full House: r2c3=6
Full House: r2c7=7
Full House: r3c8=8
Naked Single: r5c2=7
Naked Single: r9c1=1
Full House: r6c1=6
Naked Single: r3c6=3
Full House: r3c5=2
Naked Single: r8c4=8
Naked Single: r5c7=1
Naked Single: r4c2=4
Naked Single: r6c3=1
Full House: r4c3=2
Full House: r9c3=7
Naked Single: r6c9=7
Naked Single: r5c5=6
Full House: r5c4=2
Naked Single: r4c7=8
Naked Single: r4c4=3
Full House: r9c4=6
Naked Single: r4c8=6
Naked Single: r6c6=8
Full House: r6c7=4
Full House: r4c9=5
Full House: r8c9=6
Naked Single: r9c5=3
Full House: r4c5=7
Full House: r9c7=5
Full House: r4c6=1
Full House: r7c7=3
Naked Single: r7c8=7
Full House: r8c8=1
Naked Single: r8c2=5
Full House: r7c2=6
Full House: r7c6=5
Full House: r8c6=7
|
normal_sudoku_6997 | ..5.4.71..7...5.8.18.67...57319245682.....947.9...8132...2.78....74.6..1....3.6.. | 625849713479315286183672495731924568268153947594768132316297854957486321842531679 | normal_sudoku_6997 | 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 . 7 1 .
. 7 . . . 5 . 8 .
1 8 . 6 7 . . . 5
7 3 1 9 2 4 5 6 8
2 . . . . . 9 4 7
. 9 . . . 8 1 3 2
. . . 2 . 7 8 . .
. . 7 4 . 6 . . 1
. . . . 3 . 6 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 625849713479315286183672495731924568268153947594768132316297854957486321842531679 #1 Medium (308)
Hidden Single: r1c4=8
Hidden Single: r5c3=8
Hidden Single: r6c4=7
Hidden Single: r9c8=7
Hidden Single: r8c5=8
Hidden Single: r9c1=8
Locked Candidates Type 1 (Pointing): 2 in b9 => r8c2<>2
Naked Single: r8c2=5
Naked Single: r5c2=6
Naked Single: r1c2=2
Naked Single: r6c3=4
Full House: r6c1=5
Full House: r6c5=6
Hidden Single: r7c8=5
Hidden Single: r9c4=5
Hidden Single: r3c6=2
Naked Single: r3c8=9
Full House: r8c8=2
Naked Single: r3c3=3
Full House: r3c7=4
Naked Single: r8c7=3
Full House: r2c7=2
Full House: r8c1=9
Naked Single: r1c1=6
Naked Single: r7c3=6
Naked Single: r9c3=2
Full House: r2c3=9
Full House: r2c1=4
Full House: r7c1=3
Naked Single: r1c9=3
Full House: r1c6=9
Full House: r2c9=6
Naked Single: r2c5=1
Full House: r2c4=3
Full House: r5c4=1
Naked Single: r9c6=1
Full House: r7c5=9
Full House: r5c5=5
Full House: r5c6=3
Naked Single: r9c2=4
Full House: r7c2=1
Full House: r7c9=4
Full House: r9c9=9
|
normal_sudoku_1313 | .7.9.....1....7..5..2.6....8...135...4..86.1....2.9.387....8.5..6......1..4.9.7.. | 678952143139847625452361879827413596943586217516279438791628354265734981384195762 | normal_sudoku_1313 | 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 . . . . .
1 . . . . 7 . . 5
. . 2 . 6 . . . .
8 . . . 1 3 5 . .
. 4 . . 8 6 . 1 .
. . . 2 . 9 . 3 8
7 . . . . 8 . 5 .
. 6 . . . . . . 1
. . 4 . 9 . 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 678952143139847625452361879827413596943586217516279438791628354265734981384195762 #1 Extreme (9292)
Discontinuous Nice Loop: 4 r3c4 -4- r3c1 =4= r1c1 =6= r6c1 -6- r6c7 -4- r6c5 =4= r4c4 -4- r3c4 => r3c4<>4
Discontinuous Nice Loop: 4 r3c7 -4- r3c1 =4= r1c1 =6= r6c1 -6- r6c7 -4- r3c7 => r3c7<>4
Forcing Chain Contradiction in c8 => r3c9<>4
r3c9=4 r1c8<>4
r3c9=4 r2c8<>4
r3c9=4 r3c8<>4
r3c9=4 r3c1<>4 r1c1=4 r1c1<>6 r6c1=6 r6c7<>6 r6c7=4 r4c8<>4
r3c9=4 r2c78<>4 r2c45=4 r13c6<>4 r8c6=4 r8c8<>4
Forcing Chain Verity => r7c5<>4
r1c9=4 r2c78<>4 r2c45=4 r13c6<>4 r8c6=4 r7c5<>4
r4c9=4 r4c4<>4 r6c5=4 r7c5<>4
r7c9=4 r7c5<>4
Forcing Chain Contradiction in r8c4 => r1c7<>4
r1c7=4 r1c7<>1 r1c6=1 r1c6<>2 r12c5=2 r7c5<>2 r7c5=3 r8c4<>3
r1c7=4 r2c78<>4 r2c45=4 r13c6<>4 r8c6=4 r8c4<>4
r1c7=4 r6c7<>4 r6c5=4 r6c5<>5 r5c4=5 r8c4<>5
r1c7=4 r6c7<>4 r6c5=4 r6c5<>7 r8c5=7 r8c4<>7
Forcing Net Contradiction in c6 => r3c4<>5
r3c4=5 r1c6<>5
r3c4=5 r3c6<>5
r3c4=5 r5c4<>5 r5c4=7 (r4c4<>7 r4c4=4 r7c4<>4) (r4c4<>7 r4c4=4 r8c4<>4) r8c4<>7 r8c5=7 r8c5<>4 r8c6=4 r8c6<>5
r3c4=5 (r3c2<>5) r5c4<>5 r6c5=5 r6c2<>5 r9c2=5 r9c6<>5
Forcing Net Contradiction in r3 => r7c4<>4
r7c4=4 r4c4<>4 r4c4=7 r4c8<>7 r3c8=7 r3c8<>4 r3c1=4
r7c4=4 (r7c4<>6 r9c4=6 r9c4<>1 r3c4=1 r3c6<>1) r4c4<>4 (r6c5=4 r6c5<>5) r4c4=7 r8c4<>7 r8c5=7 r8c5<>5 r1c5=5 r3c6<>5 r3c6=4
Locked Candidates Type 1 (Pointing): 4 in b8 => r8c78<>4
Forcing Net Contradiction in c1 => r7c7<>2
r7c7=2 (r5c7<>2 r5c7=9 r4c9<>9) (r5c7<>2 r5c7=9 r5c9<>9) r7c7<>4 r7c9=4 r7c9<>9 r3c9=9 r3c1<>9
r7c7=2 r5c7<>2 r5c7=9 r5c1<>9
r7c7=2 (r5c7<>2 r5c7=9 r4c8<>9) (r5c7<>2 r5c7=9 r4c9<>9) (r5c7<>2 r5c7=9 r5c9<>9) r7c7<>4 r7c9=4 r7c9<>9 r3c9=9 (r2c8<>9) r3c8<>9 r8c8=9 r8c1<>9
Forcing Net Verity => r1c7<>6
r7c7=3 r7c5<>3 r7c5=2 (r8c6<>2) r9c6<>2 r1c6=2 r1c6<>1 r1c7=1 r1c7<>6
r7c7=4 r6c7<>4 r6c7=6 r1c7<>6
r7c7=6 r1c7<>6
r7c7=9 (r7c7<>4 r7c9=4 r7c9<>2) r5c7<>9 r5c7=2 (r4c8<>2) r4c9<>2 r4c2=2 r7c2<>2 r7c5=2 (r8c6<>2) r9c6<>2 r1c6=2 r1c6<>1 r1c7=1 r1c7<>6
Forcing Net Contradiction in r7c7 => r2c7<>4
r2c7=4 (r2c7<>2) (r2c7<>6) r6c7<>4 r6c7=6 (r4c8<>6) r4c9<>6 r4c3=6 r2c3<>6 r2c8=6 r2c8<>2 r2c5=2 r7c5<>2 r7c5=3 r7c7<>3
r2c7=4 r7c7<>4
r2c7=4 r6c7<>4 r6c7=6 r7c7<>6
r2c7=4 (r3c8<>4 r4c8=4 r4c8<>7 r3c8=7 r3c8<>9) (r3c8<>4 r4c8=4 r4c8<>9) (r2c7<>6) r6c7<>4 r6c7=6 (r4c8<>6) r4c9<>6 r4c3=6 r2c3<>6 r2c8=6 r2c8<>9 r8c8=9 r7c7<>9
Forcing Chain Contradiction in r2 => r8c4<>4
r8c4=4 r4c4<>4 r6c5=4 r6c7<>4 r6c7=6 r6c1<>6 r1c1=6 r2c3<>6
r8c4=4 r4c4<>4 r6c5=4 r6c7<>4 r6c7=6 r2c7<>6
r8c4=4 r8c6<>4 r13c6=4 r2c45<>4 r2c8=4 r2c8<>6
Forcing Chain Contradiction in r8c4 => r7c9<>2
r7c9=2 r7c5<>2 r7c5=3 r8c4<>3
r7c9=2 r7c9<>4 r7c7=4 r6c7<>4 r6c5=4 r6c5<>5 r5c4=5 r8c4<>5
r7c9=2 r7c9<>4 r7c7=4 r6c7<>4 r6c5=4 r6c5<>7 r8c5=7 r8c4<>7
Forcing Chain Contradiction in c4 => r7c9<>6
r7c9=6 r7c9<>4 r7c7=4 r6c7<>4 r6c5=4 r4c4<>4 r2c4=4 r2c4<>8 r3c4=8 r3c4<>1
r7c9=6 r7c9<>4 r7c7=4 r6c7<>4 r6c5=4 r6c5<>7 r6c3=7 r6c3<>1 r7c3=1 r7c4<>1
r7c9=6 r7c4<>6 r9c4=6 r9c4<>1
Forcing Chain Contradiction in r1 => r9c2<>2
r9c2=2 r9c2<>8 r8c3=8 r1c3<>8
r9c2=2 r7c2<>2 r7c5=2 r12c5<>2 r1c6=2 r1c6<>1 r1c7=1 r1c7<>8
r9c2=2 r9c2<>8 r9c8=8 r1c8<>8
Forcing Net Contradiction in r4 => r4c4=4
r4c4<>4 r4c4=7 (r8c4<>7) r5c4<>7 r5c4=5 r8c4<>5 r8c4=3 r7c5<>3 r7c5=2 r7c2<>2 r4c2=2
r4c4<>4 (r4c4=7 r8c4<>7) r6c5=4 r6c5<>5 r5c4=5 r8c4<>5 r8c4=3 r7c5<>3 r7c5=2 r7c2<>2 r4c2=2 r4c8<>2 r4c9=2
Hidden Single: r6c7=4
Hidden Single: r7c9=4
Locked Candidates Type 1 (Pointing): 6 in b6 => r4c3<>6
Finned Franken Swordfish: 9 c19b9 r358 fr4c9 fr7c7 => r5c7<>9
Naked Single: r5c7=2
Hidden Single: r4c2=2
Hidden Single: r7c5=2
Hidden Single: r2c8=2
Hidden Single: r1c6=2
Hidden Single: r9c9=2
Hidden Single: r8c1=2
Hidden Single: r2c5=4
Hidden Single: r1c7=1
Hidden Single: r8c6=4
Locked Candidates Type 1 (Pointing): 3 in b9 => r23c7<>3
Skyscraper: 8 in r1c3,r9c2 (connected by r19c8) => r23c2,r8c3<>8
Hidden Single: r9c2=8
Naked Single: r9c8=6
Hidden Single: r4c9=6
Naked Single: r1c9=3
Naked Single: r1c5=5
Naked Single: r3c6=1
Full House: r9c6=5
Naked Single: r6c5=7
Full House: r5c4=5
Full House: r8c5=3
Naked Single: r9c1=3
Full House: r9c4=1
Naked Single: r8c4=7
Full House: r7c4=6
Naked Single: r5c1=9
Naked Single: r4c3=7
Full House: r4c8=9
Full House: r5c9=7
Full House: r5c3=3
Full House: r3c9=9
Naked Single: r8c8=8
Naked Single: r3c7=8
Naked Single: r1c8=4
Full House: r3c8=7
Full House: r2c7=6
Naked Single: r8c7=9
Full House: r7c7=3
Full House: r8c3=5
Naked Single: r3c4=3
Full House: r2c4=8
Naked Single: r1c1=6
Full House: r1c3=8
Naked Single: r3c2=5
Full House: r3c1=4
Full House: r6c1=5
Naked Single: r2c3=9
Full House: r2c2=3
Naked Single: r6c2=1
Full House: r6c3=6
Full House: r7c3=1
Full House: r7c2=9
|
normal_sudoku_3062 | .2.9.3..131..76..2....1..7.5..1..8...6.83952428.......6..3....9.3..9.24......4... | 427983651318576492956412378594127863761839524283645917642351789135798246879264135 | normal_sudoku_3062 | 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 . . 1
3 1 . . 7 6 . . 2
. . . . 1 . . 7 .
5 . . 1 . . 8 . .
. 6 . 8 3 9 5 2 4
2 8 . . . . . . .
6 . . 3 . . . . 9
. 3 . . 9 . 2 4 .
. . . . . 4 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 427983651318576492956412378594127863761839524283645917642351789135798246879264135 #1 Extreme (4350)
Locked Candidates Type 1 (Pointing): 1 in b6 => r6c3<>1
Locked Candidates Type 2 (Claiming): 7 in r5 => r4c23,r6c3<>7
Locked Candidates Type 2 (Claiming): 4 in c1 => r123c3,r3c2<>4
Locked Candidates Type 2 (Claiming): 7 in c2 => r789c3,r89c1<>7
Finned X-Wing: 7 r48 c69 fr8c4 => r7c6<>7
Discontinuous Nice Loop: 5 r3c4 -5- r3c2 -9- r4c2 -4- r7c2 =4= r7c3 =2= r9c3 -2- r9c4 =2= r3c4 => r3c4<>5
Forcing Chain Contradiction in r7c8 => r6c7<>3
r6c7=3 r6c7<>1 r6c8=1 r7c8<>1
r6c7=3 r3c7<>3 r3c9=3 r3c9<>5 r12c8=5 r7c8<>5
r6c7=3 r3c7<>3 r3c9=3 r3c9<>8 r12c8=8 r7c8<>8
Forcing Chain Contradiction in r7c8 => r7c3<>8
r7c3=8 r8c1<>8 r8c1=1 r8c6<>1 r7c6=1 r7c8<>1
r7c3=8 r7c3<>4 r7c2=4 r4c2<>4 r4c2=9 r3c2<>9 r3c2=5 r3c9<>5 r12c8=5 r7c8<>5
r7c3=8 r7c8<>8
Grouped Discontinuous Nice Loop: 8 r9c5 -8- r1c5 =8= r3c6 -8- r3c9 =8= r12c8 -8- r7c8 =8= r7c56 -8- r9c5 => r9c5<>8
Forcing Chain Contradiction in c6 => r3c1<>8
r3c1=8 r3c6<>8
r3c1=8 r8c1<>8 r8c1=1 r8c6<>1 r7c6=1 r7c6<>8
r3c1=8 r3c9<>8 r12c8=8 r7c8<>8 r7c56=8 r8c6<>8
Forcing Chain Contradiction in r7c8 => r7c3<>1
r7c3=1 r7c8<>1
r7c3=1 r7c3<>4 r7c2=4 r4c2<>4 r4c2=9 r3c2<>9 r3c2=5 r3c9<>5 r12c8=5 r7c8<>5
r7c3=1 r7c6<>1 r8c6=1 r8c6<>8 r7c56=8 r7c8<>8
Forcing Chain Contradiction in r8c3 => r9c2<>5
r9c2=5 r9c2<>7 r7c2=7 r7c7<>7 r7c7=1 r7c6<>1 r8c6=1 r8c3<>1
r9c2=5 r8c3<>5
r9c2=5 r9c2<>7 r7c2=7 r7c7<>7 r7c7=1 r7c6<>1 r8c6=1 r8c1<>1 r8c1=8 r8c3<>8
Empty Rectangle: 5 in b3 (r37c2) => r7c8<>5
W-Wing: 8/1 in r7c8,r8c1 connected by 1 in r78c6 => r8c9<>8
2-String Kite: 8 in r2c3,r9c9 (connected by r2c8,r3c9) => r9c3<>8
Sue de Coq: r7c56 - {1258} (r7c78 - {178}, r89c4,r9c5 - {2567}) => r8c6<>5, r7c2,r8c6<>7
Hidden Single: r7c7=7
Hidden Single: r9c2=7
Hidden Single: r8c4=7
Hidden Single: r8c9=6
Hidden Single: r8c3=5
Naked Single: r7c2=4
Naked Single: r4c2=9
Full House: r3c2=5
Naked Single: r7c3=2
Hidden Single: r9c9=5
Hidden Single: r3c9=8
Naked Single: r3c6=2
Naked Single: r3c4=4
Naked Single: r4c6=7
Naked Single: r2c4=5
Full House: r1c5=8
Naked Single: r3c1=9
Naked Single: r4c9=3
Full House: r6c9=7
Naked Single: r6c6=5
Naked Single: r2c8=9
Naked Single: r6c4=6
Full House: r9c4=2
Naked Single: r7c5=5
Naked Single: r2c3=8
Full House: r2c7=4
Naked Single: r3c3=6
Full House: r3c7=3
Naked Single: r4c3=4
Naked Single: r4c8=6
Full House: r4c5=2
Full House: r6c5=4
Full House: r9c5=6
Naked Single: r6c8=1
Full House: r6c7=9
Full House: r6c3=3
Naked Single: r1c7=6
Full House: r9c7=1
Full House: r1c8=5
Naked Single: r1c3=7
Full House: r1c1=4
Naked Single: r7c8=8
Full House: r7c6=1
Full House: r9c8=3
Full House: r8c6=8
Full House: r8c1=1
Naked Single: r9c1=8
Full House: r9c3=9
Full House: r5c3=1
Full House: r5c1=7
|
normal_sudoku_5100 | 45..36.8.8...52..6..684.5......95...6..217.5...5.83..12..5...385..3...6...4...7.5 | 451736982837952416926841573182695347643217859795483621279564138518379264364128795 | normal_sudoku_5100 | 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 . . 3 6 . 8 .
8 . . . 5 2 . . 6
. . 6 8 4 . 5 . .
. . . . 9 5 . . .
6 . . 2 1 7 . 5 .
. . 5 . 8 3 . . 1
2 . . 5 . . . 3 8
5 . . 3 . . . 6 .
. . 4 . . . 7 . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 451736982837952416926841573182695347643217859795483621279564138518379264364128795 #1 Extreme (3274)
Locked Candidates Type 1 (Pointing): 6 in b5 => r9c4<>6
Uniqueness Test 4: 4/6 in r4c47,r6c47 => r46c7<>4
Almost Locked Set XY-Wing: A=r2c2348 {13479}, B=r6c4 {46}, C=r12678c7 {123469}, X,Y=3,6, Z=4 => r6c8<>4
Forcing Chain Contradiction in r1 => r3c2<>9
r3c2=9 r3c2<>2 r1c3=2 r1c3<>1
r3c2=9 r3c6<>9 r3c6=1 r1c4<>1
r3c2=9 r3c6<>9 r3c6=1 r12c4<>1 r9c4=1 r9c8<>1 r78c7=1 r1c7<>1
Forcing Chain Contradiction in c8 => r3c9<>9
r3c9=9 r3c9<>3 r2c7=3 r2c7<>4 r2c8=4 r2c8<>1
r3c9=9 r3c6<>9 r3c6=1 r3c8<>1
r3c9=9 r3c6<>9 r3c6=1 r12c4<>1 r9c4=1 r9c8<>1
Forcing Chain Contradiction in c8 => r7c6<>9
r7c6=9 r7c6<>4 r7c7=4 r2c7<>4 r2c8=4 r2c8<>1
r7c6=9 r3c6<>9 r3c6=1 r3c8<>1
r7c6=9 r9c4<>9 r9c4=1 r9c8<>1
Forcing Net Verity => r2c7=4
r3c6=1 (r3c8<>1) (r1c4<>1) r2c4<>1 r9c4=1 r9c8<>1 r2c8=1 r2c8<>4 r2c7=4
r3c6=9 (r3c8<>9) (r3c1<>9) (r1c4<>9) r2c4<>9 r9c4=9 (r9c8<>9) r9c1<>9 r6c1=9 r6c8<>9 r2c8=9 r2c8<>4 r2c7=4
Hidden Single: r4c8=4
Naked Single: r4c4=6
Full House: r6c4=4
Hidden Single: r7c6=4
Hidden Single: r8c9=4
Hidden Single: r3c9=3
Naked Single: r5c9=9
Hidden Single: r5c2=4
Hidden Single: r6c7=6
Naked Pair: 2,7 in r4c9,r6c8 => r4c7<>2
X-Wing: 2 r36 c28 => r4c2,r9c8<>2
Hidden Single: r9c5=2
Naked Single: r8c5=7
Full House: r7c5=6
Hidden Single: r8c7=2
Hidden Single: r9c2=6
Hidden Single: r9c1=3
Hidden Single: r9c6=8
Remote Pair: 1/9 r1c7 -9- r7c7 -1- r9c8 -9- r9c4 -1- r8c6 -9- r3c6 => r1c4,r3c8<>1, r1c4,r3c8<>9
Naked Single: r1c4=7
Naked Single: r1c9=2
Full House: r4c9=7
Naked Single: r3c8=7
Naked Single: r4c1=1
Naked Single: r6c8=2
Naked Single: r3c1=9
Full House: r6c1=7
Full House: r6c2=9
Naked Single: r1c3=1
Full House: r1c7=9
Full House: r2c8=1
Full House: r9c8=9
Full House: r7c7=1
Full House: r9c4=1
Full House: r2c4=9
Full House: r3c6=1
Full House: r3c2=2
Full House: r8c6=9
Naked Single: r7c2=7
Full House: r7c3=9
Naked Single: r8c3=8
Full House: r8c2=1
Naked Single: r2c2=3
Full House: r2c3=7
Full House: r4c2=8
Naked Single: r5c3=3
Full House: r4c3=2
Full House: r4c7=3
Full House: r5c7=8
|
normal_sudoku_3785 | ..56.497379..356.....27951...2.4...6...3.28...1.856.9.8..5.......4..3..5.5.42.7.. | 125684973798135624346279518982741356567392841413856297839517462274963185651428739 | normal_sudoku_3785 | 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 . 4 9 7 3
7 9 . . 3 5 6 . .
. . . 2 7 9 5 1 .
. . 2 . 4 . . . 6
. . . 3 . 2 8 . .
. 1 . 8 5 6 . 9 .
8 . . 5 . . . . .
. . 4 . . 3 . . 5
. 5 . 4 2 . 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 125684973798135624346279518982741356567392841413856297839517462274963185651428739 #1 Easy (230)
Naked Single: r2c4=1
Full House: r1c5=8
Naked Single: r2c3=8
Naked Single: r1c2=2
Full House: r1c1=1
Hidden Single: r4c2=8
Hidden Single: r9c6=8
Hidden Single: r8c8=8
Hidden Single: r3c9=8
Hidden Single: r8c1=2
Naked Single: r8c7=1
Naked Single: r4c7=3
Naked Single: r9c9=9
Naked Single: r4c8=5
Naked Single: r4c1=9
Naked Single: r5c8=4
Naked Single: r4c4=7
Full House: r4c6=1
Full House: r8c4=9
Full House: r5c5=9
Full House: r7c6=7
Naked Single: r2c8=2
Full House: r2c9=4
Naked Single: r6c7=2
Full House: r7c7=4
Naked Single: r8c5=6
Full House: r7c5=1
Full House: r8c2=7
Naked Single: r7c9=2
Naked Single: r6c9=7
Full House: r5c9=1
Naked Single: r5c2=6
Naked Single: r6c3=3
Full House: r6c1=4
Naked Single: r5c1=5
Full House: r5c3=7
Naked Single: r7c2=3
Full House: r3c2=4
Naked Single: r3c3=6
Full House: r3c1=3
Full House: r9c1=6
Naked Single: r7c8=6
Full House: r7c3=9
Full House: r9c3=1
Full House: r9c8=3
|
normal_sudoku_6040 | ..2..7.4.73..5..2..4.2...7..271.6.8....52.31751..78692....8276...67.523127.61..58 | 182367549739854126645291873927136485468529317513478692351982764896745231274613958 | normal_sudoku_6040 | 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 . 4 .
7 3 . . 5 . . 2 .
. 4 . 2 . . . 7 .
. 2 7 1 . 6 . 8 .
. . . 5 2 . 3 1 7
5 1 . . 7 8 6 9 2
. . . . 8 2 7 6 .
. . 6 7 . 5 2 3 1
2 7 . 6 1 . . 5 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 182367549739854126645291873927136485468529317513478692351982764896745231274613958 #1 Hard (452)
Hidden Single: r2c9=6
Locked Candidates Type 1 (Pointing): 4 in b6 => r4c15<>4
Hidden Single: r8c5=4
Locked Candidates Type 2 (Claiming): 9 in r8 => r7c123,r9c3<>9
Naked Single: r7c2=5
Hidden Single: r3c3=5
Naked Pair: 3,4 in r69c3 => r57c3<>4, r7c3<>3
Naked Single: r7c3=1
Remote Pair: 3/4 r6c4 -4- r6c3 -3- r9c3 -4- r7c1 => r7c4<>3
Naked Single: r7c4=9
Full House: r9c6=3
Naked Single: r7c9=4
Full House: r7c1=3
Full House: r9c7=9
Full House: r9c3=4
Naked Single: r4c9=5
Full House: r4c7=4
Naked Single: r4c1=9
Full House: r4c5=3
Naked Single: r6c3=3
Full House: r6c4=4
Full House: r5c6=9
Naked Single: r5c3=8
Full House: r2c3=9
Naked Single: r8c1=8
Full House: r8c2=9
Naked Single: r2c4=8
Full House: r1c4=3
Naked Single: r3c6=1
Full House: r2c6=4
Full House: r2c7=1
Naked Single: r5c2=6
Full House: r1c2=8
Full House: r5c1=4
Naked Single: r1c9=9
Full House: r3c9=3
Naked Single: r3c1=6
Full House: r1c1=1
Naked Single: r3c7=8
Full House: r1c7=5
Full House: r1c5=6
Full House: r3c5=9
|
normal_sudoku_2716 | ....96..39.7.5816...4.12...1.9534..8586127...4.3869.1...824......5.83.416..97.... | 251796483937458162864312759179534628586127394423869517318245976795683241642971835 | normal_sudoku_2716 | 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 6 . . 3
9 . 7 . 5 8 1 6 .
. . 4 . 1 2 . . .
1 . 9 5 3 4 . . 8
5 8 6 1 2 7 . . .
4 . 3 8 6 9 . 1 .
. . 8 2 4 . . . .
. . 5 . 8 3 . 4 1
6 . . 9 7 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 251796483937458162864312759179534628586127394423869517318245976795683241642971835 #1 Easy (220)
Naked Single: r8c4=6
Hidden Single: r4c7=6
Hidden Single: r9c2=4
Hidden Single: r3c2=6
Hidden Single: r7c9=6
Hidden Single: r1c2=5
Hidden Single: r1c3=1
Full House: r9c3=2
Naked Single: r8c1=7
Naked Single: r9c9=5
Naked Single: r7c1=3
Naked Single: r8c2=9
Full House: r7c2=1
Full House: r8c7=2
Naked Single: r9c6=1
Full House: r7c6=5
Naked Single: r3c1=8
Full House: r1c1=2
Full House: r2c2=3
Naked Single: r2c4=4
Full House: r2c9=2
Naked Single: r1c4=7
Full House: r3c4=3
Naked Single: r6c9=7
Naked Single: r1c8=8
Full House: r1c7=4
Naked Single: r3c9=9
Full House: r5c9=4
Naked Single: r4c8=2
Full House: r4c2=7
Full House: r6c2=2
Full House: r6c7=5
Naked Single: r9c8=3
Full House: r9c7=8
Naked Single: r3c7=7
Full House: r3c8=5
Naked Single: r5c8=9
Full House: r5c7=3
Full House: r7c7=9
Full House: r7c8=7
|
normal_sudoku_4872 | 93..214....1..4...24.3...1.61.......4921568735.3.4..2...9.15.8....7....5.5...87.. | 935821467871564239246379518617283954492156873583947621729415386368792145154638792 | normal_sudoku_4872 | 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 . . 2 1 4 . .
. . 1 . . 4 . . .
2 4 . 3 . . . 1 .
6 1 . . . . . . .
4 9 2 1 5 6 8 7 3
5 . 3 . 4 . . 2 .
. . 9 . 1 5 . 8 .
. . . 7 . . . . 5
. 5 . . . 8 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 935821467871564239246379518617283954492156873583947621729415386368792145154638792 #1 Extreme (4444)
Locked Triple: 4,5,9 in r4c789 => r4c456,r6c79<>9
Naked Pair: 7,9 in r36c6 => r4c6<>7, r8c6<>9
2-String Kite: 7 in r3c6,r4c3 (connected by r4c5,r6c6) => r3c3<>7
Empty Rectangle: 7 in b1 (r4c35) => r2c5<>7
Locked Candidates Type 1 (Pointing): 7 in b2 => r3c9<>7
W-Wing: 8/7 in r2c1,r6c2 connected by 7 in r7c12 => r2c2<>8
XYZ-Wing: 5/6/9 in r1c8,r34c7 => r2c7<>5
Hidden Rectangle: 5/6 in r1c48,r2c48 => r2c4<>6
AIC: 3 3- r7c7 =3= r7c1 =7= r7c2 =2= r8c2 -2- r8c6 -3 => r8c78<>3
Discontinuous Nice Loop: 8 r2c4 -8- r4c4 -2- r9c4 =2= r9c9 -2- r2c9 =2= r2c7 =3= r2c8 =5= r2c4 => r2c4<>8
Discontinuous Nice Loop: 9 r2c4 -9- r6c4 -8- r6c2 -7- r7c2 =7= r7c1 =3= r7c7 -3- r2c7 =3= r2c8 =5= r2c4 => r2c4<>9
Naked Single: r2c4=5
Discontinuous Nice Loop: 6 r1c9 -6- r1c4 -8- r6c4 =8= r6c2 =7= r4c3 -7- r1c3 =7= r1c9 => r1c9<>6
Discontinuous Nice Loop: 6 r2c8 -6- r2c2 -7- r2c1 =7= r7c1 =3= r7c7 -3- r2c7 =3= r2c8 => r2c8<>6
Discontinuous Nice Loop: 8 r2c9 -8- r2c1 -7- r7c1 -3- r7c7 =3= r2c7 =2= r2c9 => r2c9<>8
Discontinuous Nice Loop: 8 r3c3 -8- r3c9 =8= r1c9 =7= r1c3 =5= r3c3 => r3c3<>8
Continuous Nice Loop: 6/9 8= r3c5 =7= r4c5 -7- r4c3 =7= r1c3 -7- r1c9 -8- r3c9 =8= r3c5 =7 => r3c5<>6, r3c5<>9
Sue de Coq: r3c79 - {5689} (r3c56 - {789}, r1c8 - {56}) => r2c79<>6
Discontinuous Nice Loop: 6 r7c2 -6- r2c2 =6= r2c5 -6- r1c4 -8- r4c4 -2- r4c6 =2= r8c6 -2- r8c2 =2= r7c2 => r7c2<>6
Discontinuous Nice Loop: 2 r7c4 -2- r7c2 -7- r7c1 -3- r7c7 =3= r2c7 =2= r2c9 -2- r9c9 =2= r9c4 -2- r7c4 => r7c4<>2
Discontinuous Nice Loop: 6 r7c4 -6- r1c4 =6= r2c5 -6- r2c2 =6= r8c2 -6- r9c3 -4- r9c4 =4= r7c4 => r7c4<>6
Naked Single: r7c4=4
Locked Candidates Type 2 (Claiming): 6 in r7 => r8c78,r9c89<>6
Hidden Single: r1c8=6
Naked Single: r1c4=8
Naked Single: r1c9=7
Full House: r1c3=5
Naked Single: r3c5=7
Naked Single: r4c4=2
Naked Single: r6c4=9
Full House: r9c4=6
Naked Single: r3c3=6
Naked Single: r3c6=9
Full House: r2c5=6
Naked Single: r4c6=3
Naked Single: r6c6=7
Full House: r4c5=8
Full House: r8c6=2
Naked Single: r9c3=4
Naked Single: r2c2=7
Full House: r2c1=8
Naked Single: r3c7=5
Full House: r3c9=8
Naked Single: r6c2=8
Full House: r4c3=7
Full House: r8c3=8
Naked Single: r7c2=2
Full House: r8c2=6
Naked Single: r4c7=9
Naked Single: r7c9=6
Naked Single: r4c9=4
Full House: r4c8=5
Naked Single: r8c7=1
Naked Single: r6c9=1
Full House: r6c7=6
Naked Single: r7c7=3
Full House: r2c7=2
Full House: r7c1=7
Naked Single: r8c1=3
Full House: r9c1=1
Naked Single: r9c8=9
Naked Single: r2c9=9
Full House: r2c8=3
Full House: r8c8=4
Full House: r8c5=9
Full House: r9c5=3
Full House: r9c9=2
|
normal_sudoku_5747 | .4.......7....1..3..38...9.3....6..147615.23.1..4.3..6.37.1...5.....53..5.....61. | 941532768768941523253867194382796451476158239195423876637214985819675342524389617 | normal_sudoku_5747 | 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 . . 3
. . 3 8 . . . 9 .
3 . . . . 6 . . 1
4 7 6 1 5 . 2 3 .
1 . . 4 . 3 . . 6
. 3 7 . 1 . . . 5
. . . . . 5 3 . .
5 . . . . . 6 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 941532768768941523253867194382796451476158239195423876637214985819675342524389617 #1 Extreme (16076)
Hidden Pair: 1,5 in r3c27 => r3c2<>2, r3c2<>6, r3c7<>4, r3c7<>7
Skyscraper: 6 in r3c5,r7c4 (connected by r37c1) => r12c4,r8c5<>6
Empty Rectangle: 9 in b9 (r5c69) => r7c6<>9
Finned Swordfish: 4 r247 c578 fr7c6 => r89c5<>4
Locked Candidates Type 1 (Pointing): 4 in b8 => r3c6<>4
Discontinuous Nice Loop: 5 r1c8 -5- r3c7 -1- r3c2 =1= r8c2 =6= r2c2 -6- r2c8 =6= r1c8 => r1c8<>5
Discontinuous Nice Loop: 4 r9c9 -4- r9c3 =4= r8c3 =1= r8c2 =6= r2c2 -6- r3c1 =6= r3c5 =4= r3c9 -4- r9c9 => r9c9<>4
Forcing Net Contradiction in c6 => r1c1<>6
r1c1=6 (r1c8<>6 r2c8=6 r2c8<>2) (r1c8<>6 r2c8=6 r2c8<>4) r3c1<>6 (r3c1=2 r2c2<>2) (r3c1=2 r2c3<>2) r3c5=6 r3c5<>4 r3c9=4 r2c7<>4 r2c5=4 r2c5<>2 r2c4=2 r1c6<>2
r1c1=6 r3c1<>6 r3c1=2 r3c6<>2
r1c1=6 (r2c2<>6 r8c2=6 r8c2<>1 r8c3=1 r8c3<>4) r3c1<>6 r3c5=6 r3c5<>4 r3c9=4 r8c9<>4 r8c8=4 (r7c7<>4) r7c8<>4 r7c6=4 r7c6<>2
r1c1=6 (r3c1<>6 r3c1=2 r7c1<>2) (r3c1<>6 r3c1=2 r8c1<>2) r2c2<>6 r8c2=6 (r8c2<>2) r8c2<>1 r8c3=1 (r8c3<>2) r8c3<>4 r9c3=4 r9c3<>2 r9c2=2 r9c6<>2
Forcing Net Contradiction in c8 => r8c2<>2
r8c2=2 r8c2<>6 r2c2=6 r2c8<>6 r1c8=6 r1c8<>7
r8c2=2 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r4c8<>7
r8c2=2 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r6c8<>7
r8c2=2 (r8c2<>1 r8c3=1 r8c3<>4) r8c2<>6 r2c2=6 r3c1<>6 r3c5=6 r3c5<>4 r3c9=4 r8c9<>4 r8c8=4 r8c8<>7
Forcing Net Contradiction in c8 => r8c2<>8
r8c2=8 r8c2<>6 r2c2=6 r2c8<>6 r1c8=6 r1c8<>7
r8c2=8 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r4c8<>7
r8c2=8 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r6c8<>7
r8c2=8 (r8c2<>1 r8c3=1 r8c3<>4) r8c2<>6 r2c2=6 r3c1<>6 r3c5=6 r3c5<>4 r3c9=4 r8c9<>4 r8c8=4 r8c8<>7
Forcing Net Contradiction in c8 => r8c2<>9
r8c2=9 r8c2<>6 r2c2=6 r2c8<>6 r1c8=6 r1c8<>7
r8c2=9 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r4c8<>7
r8c2=9 r8c2<>1 r8c3=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r6c8<>7
r8c2=9 (r8c2<>1 r8c3=1 r8c3<>4) r8c2<>6 r2c2=6 r3c1<>6 r3c5=6 r3c5<>4 r3c9=4 r8c9<>4 r8c8=4 r8c8<>7
Forcing Net Contradiction in r7c7 => r9c2<>9
r9c2=9 (r2c2<>9) (r7c1<>9) (r9c9<>9) (r9c6<>9) (r7c1<>9) r8c1<>9 r1c1=9 r1c6<>9 r5c6=9 r5c9<>9 r8c9=9 r7c7<>9 r7c4=9 (r2c4<>9) r7c4<>6 r7c1=6 r3c1<>6 r3c5=6 r3c5<>4 r3c9=4 (r2c7<>4) r2c8<>4 r2c5=4 r2c5<>9 r2c3=9 r1c1<>9 r78c1=9 r9c2<>9
Forcing Net Verity => r1c8<>2
r7c1=2 (r9c2<>2 r9c2=8 r8c1<>8 r1c1=8 r1c9<>8) (r9c2<>2 r9c2=8 r9c9<>8) (r9c2<>2 r9c2=8 r8c1<>8 r8c1=9 r8c9<>9) (r7c1<>9) r7c1<>6 r7c4=6 r7c4<>9 r7c7=9 r9c9<>9 r5c9=9 r5c9<>8 r8c9=8 (r8c9<>2) (r8c9<>4 r3c9=4 r3c9<>2) (r8c5<>8) r5c9<>8 r5c6=8 (r4c5<>8) r6c5<>8 r9c5=8 r9c2<>8 r9c2=2 r9c9<>2 r1c9=2 r1c8<>2
r7c4=2 (r7c6<>2) (r9c6<>2) r7c4<>6 r7c1=6 r3c1<>6 r3c1=2 r3c6<>2 r1c6=2 r1c8<>2
r7c6=2 r7c6<>4 r9c6=4 r9c3<>4 r8c3=4 r8c3<>1 r8c2=1 r8c2<>6 r2c2=6 r2c8<>6 r1c8=6 r1c8<>2
r7c8=2 r1c8<>2
Forcing Net Verity => r1c8<>8
r2c2=2 r9c2<>2 r9c2=8 (r7c1<>8) r8c1<>8 r1c1=8 r1c8<>8
r2c3=2 r13c1<>2 r78c1=2 r9c2<>2 r9c2=8 (r7c1<>8) r8c1<>8 r1c1=8 r1c8<>8
r2c4=2 r2c4<>5 r1c4=5 r1c4<>3 r1c5=3 r1c5<>6 r1c8=6 r1c8<>8
r2c5=2 (r3c6<>2 r3c6=7 r9c6<>7) (r3c6<>2 r3c6=7 r1c6<>7 r1c6=9 r5c6<>9 r5c6=8 r9c6<>8) (r3c6<>2 r3c6=7 r1c6<>7 r1c6=9 r9c6<>9) r2c5<>4 r3c5=4 r3c9<>4 r8c9=4 (r7c7<>4) r7c8<>4 r7c6=4 r9c6<>4 r9c6=2 r9c2<>2 r9c2=8 (r7c1<>8) r8c1<>8 r1c1=8 r1c8<>8
r2c8=2 r2c8<>6 r1c8=6 r1c8<>8
Forcing Net Contradiction in c6 => r2c5<>2
r2c5=2 r1c6<>2
r2c5=2 r3c6<>2
r2c5=2 r2c5<>4 r3c5=4 r3c9<>4 r8c9=4 (r7c7<>4) r7c8<>4 r7c6=4 r7c6<>2
r2c5=2 (r2c5<>6) r2c5<>4 r3c5=4 (r3c9<>4 r3c9=2 r1c9<>2) r3c5<>6 r1c5=6 r1c8<>6 r1c8=7 r1c9<>7 r1c9=8 r1c1<>8 r78c1=8 r9c2<>8 r9c2=2 r9c6<>2
Forcing Net Contradiction in c3 => r2c5<>9
r2c5=9 (r2c5<>6) r2c5<>4 r3c5=4 r3c5<>6 r1c5=6 (r1c5<>3 r1c4=3 r1c4<>5) r1c8<>6 r2c8=6 r2c2<>6 r8c2=6 r8c2<>1 r3c2=1 r3c7<>1 r3c7=5 r1c7<>5 r1c3=5 r1c3<>9
r2c5=9 r2c3<>9
r2c5=9 r2c2<>9 r46c2=9 r4c3<>9
r2c5=9 r2c2<>9 r46c2=9 r6c3<>9
r2c5=9 r2c5<>4 r3c5=4 r3c5<>6 r3c1=6 r2c2<>6 r8c2=6 r8c2<>1 r8c3=1 r8c3<>9
r2c5=9 r2c5<>4 r3c5=4 r3c9<>4 r8c9=4 (r7c7<>4) r7c8<>4 r7c6=4 r9c6<>4 r9c3=4 r9c3<>9
Forcing Net Contradiction in c1 => r1c8=6
r1c8<>6 (r2c8=6 r2c8<>2) r1c5=6 r2c5<>6 r2c5=4 r3c5<>4 r3c9=4 r3c9<>2 r1c9=2 r1c1<>2
r1c8<>6 r1c5=6 r3c5<>6 r3c1=6 r3c1<>2
r1c8<>6 (r1c5=6 r2c5<>6 r2c5=4 r3c5<>4 r3c9=4 r8c9<>4) r2c8=6 (r2c8<>2) r2c2<>6 r8c2=6 r8c2<>1 r8c3=1 r8c3<>4 r8c8=4 r8c8<>2 r7c8=2 r7c1<>2
r1c8<>6 r1c5=6 (r1c5<>9) r1c5<>3 r1c4=3 (r1c4<>9) r1c4<>5 r2c4=5 r2c4<>9 r1c6=9 (r1c1<>9) r5c6<>9 r5c9=9 (r4c7<>9) r6c7<>9 r7c7=9 r7c1<>9 r8c1=9 r8c1<>2
Hidden Pair: 4,6 in r23c5 => r3c5<>2, r3c5<>7
Forcing Net Contradiction in c6 => r2c2<>2
r2c2=2 (r9c2<>2 r9c2=8 r8c1<>8 r1c1=8 r1c9<>8) (r9c2<>2 r9c2=8 r9c9<>8) r3c1<>2 r3c1=6 r3c5<>6 r3c5=4 r3c9<>4 r8c9=4 r8c9<>8 r5c9=8 r5c6<>8
r2c2=2 r3c1<>2 r3c1=6 r3c5<>6 r3c5=4 r3c9<>4 r8c9=4 (r7c7<>4) r7c8<>4 r7c6=4 r7c6<>8
r2c2=2 r9c2<>2 r9c2=8 r9c6<>8
Forcing Net Contradiction in r2c8 => r2c2<>8
r2c2=8 (r9c2<>8 r9c2=2 r9c9<>2) r2c2<>6 r2c5=6 r3c5<>6 (r3c1=6 r3c1<>2 r1c1=2 r1c9<>2) r3c5=4 r3c9<>4 r8c9=4 r8c9<>2 r3c9=2 r2c8<>2
r2c2=8 (r2c7<>8) r2c2<>6 r8c2=6 r8c2<>1 r3c2=1 r3c7<>1 r3c7=5 r2c7<>5 r2c7=4 r2c8<>4
r2c2=8 r2c2<>6 r8c2=6 r8c2<>1 r3c2=1 r3c7<>1 r3c7=5 r2c8<>5
r2c2=8 r2c8<>8
Forcing Net Contradiction in r8c4 => r2c3<>5
r2c3=5 (r2c4<>5) (r2c2<>5) r3c2<>5 r3c2=1 r8c2<>1 r8c2=6 r2c2<>6 r2c2=9 r2c4<>9 r2c4=2 r8c4<>2
r2c3=5 r3c2<>5 r3c2=1 r8c2<>1 r8c2=6 r8c4<>6
r2c3=5 r3c2<>5 r3c2=1 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r46c8<>7 r8c8=7 r8c4<>7
r2c3=5 (r2c4<>5 r1c4=5 r1c4<>9) (r2c4<>5 r1c4=5 r1c4<>3 r1c5=3 r1c5<>9) (r2c2<>5) r3c2<>5 r3c2=1 r8c2<>1 r8c2=6 r2c2<>6 r2c2=9 (r1c1<>9) (r1c1<>9) r1c3<>9 r1c6=9 r5c6<>9 r5c9=9 (r4c7<>9) r6c7<>9 r7c7=9 r7c1<>9 r8c1=9 r8c4<>9
Forcing Net Contradiction in c9 => r7c1<>2
r7c1=2 (r7c1<>8) r9c2<>2 r9c2=8 r8c1<>8 r1c1=8 r1c9<>8
r7c1=2 (r9c2<>2 r9c2=8 r8c1<>8 r8c1=9 r8c9<>9) (r7c1<>9) r7c1<>6 r7c4=6 r7c4<>9 r7c7=9 r9c9<>9 r5c9=9 r5c9<>8
r7c1=2 r3c1<>2 r3c1=6 r3c5<>6 r3c5=4 r3c9<>4 r8c9=4 r8c9<>8
r7c1=2 r9c2<>2 r9c2=8 r9c9<>8
Forcing Chain Verity => r8c4<>2
r2c3=2 r13c1<>2 r8c1=2 r8c4<>2
r2c4=2 r8c4<>2
r2c8=2 r7c8<>2 r7c46=2 r8c4<>2
Forcing Chain Contradiction in r8c4 => r1c3<>9
r1c3=9 r1c3<>1 r8c3=1 r8c2<>1 r8c2=6 r8c4<>6
r1c3=9 r1c3<>1 r1c7=1 r1c7<>7 r46c7=7 r46c8<>7 r8c8=7 r8c4<>7
r1c3=9 r1c456<>9 r2c4=9 r8c4<>9
Forcing Chain Verity => r8c5<>2
r2c3=2 r13c1<>2 r8c1=2 r8c5<>2
r2c4=2 r4c4<>2 r46c5=2 r8c5<>2
r2c8=2 r7c8<>2 r7c46=2 r8c5<>2
Forcing Chain Verity => r1c1<>2
r7c4=2 r7c4<>6 r7c1=6 r3c1<>6 r3c1=2 r1c1<>2
r7c6=2 r7c6<>4 r7c78=4 r8c9<>4 r3c9=4 r3c5<>4 r3c5=6 r3c1<>6 r3c1=2 r1c1<>2
r7c8=2 r7c46<>2 r9c456=2 r9c2<>2 r9c2=8 r78c1<>8 r1c1=8 r1c1<>2
Grouped Discontinuous Nice Loop: 8 r1c3 =1= r8c3 -1- r8c2 -6- r2c2 =6= r3c1 =2= r8c1 -2- r9c2 -8- r78c1 =8= r1c1 -8- r1c3 => r1c3<>8
Forcing Net Contradiction in r7 => r1c3=1
r1c3<>1 r8c3=1 r8c2<>1 r8c2=6 (r7c1<>6) r2c2<>6 r2c5=6 r3c5<>6 r3c1=6 r3c1<>2 r8c1=2 r9c2<>2 r9c2=8 r7c1<>8 r7c1=9
r1c3<>1 r8c3=1 r8c2<>1 r8c2=6 r2c2<>6 r2c5=6 r3c5<>6 r3c1=6 r5c6=8 r5c9<>8 r5c9=9 (r4c7<>9) r6c7<>9 r7c7=9
Naked Single: r3c2=5
Naked Single: r3c7=1
Hidden Single: r8c2=1
Hidden Single: r2c2=6
Naked Single: r2c5=4
Naked Single: r3c1=2
Naked Single: r3c5=6
Naked Single: r3c6=7
Full House: r3c9=4
Locked Candidates Type 2 (Claiming): 9 in c2 => r46c3<>9
Finned X-Wing: 2 r27 c48 fr7c6 => r9c4<>2
Grouped Discontinuous Nice Loop: 5 r4c7 -5- r12c7 =5= r2c8 =2= r2c4 -2- r1c6 -9- r5c6 =9= r5c9 -9- r46c7 =9= r7c7 =4= r4c7 => r4c7<>5
Grouped Discontinuous Nice Loop: 8 r4c7 -8- r5c9 -9- r46c7 =9= r7c7 =4= r4c7 => r4c7<>8
Grouped Discontinuous Nice Loop: 2 r9c5 -2- r7c46 =2= r7c8 -2- r2c8 =2= r2c4 -2- r4c4 =2= r46c5 -2- r9c5 => r9c5<>2
Grouped Discontinuous Nice Loop: 8 r7c1 -8- r1c1 -9- r1c6 -2- r79c6 =2= r7c4 =6= r7c1 => r7c1<>8
Hidden Rectangle: 6/9 in r7c14,r8c14 => r8c4<>9
Sashimi X-Wing: 8 r57 c69 fr7c7 fr7c8 => r89c9<>8
W-Wing: 9/8 in r1c1,r5c6 connected by 8 in r15c9 => r1c6<>9
Naked Single: r1c6=2
Hidden Single: r2c8=2
Hidden Single: r7c4=2
Hidden Single: r7c1=6
Hidden Single: r8c4=6
Hidden Single: r7c7=9
Hidden Single: r5c9=9
Full House: r5c6=8
Naked Single: r7c6=4
Full House: r7c8=8
Full House: r9c6=9
Hidden Single: r4c7=4
Hidden Single: r1c9=8
Naked Single: r1c1=9
Full House: r2c3=8
Full House: r8c1=8
Naked Single: r2c7=5
Full House: r1c7=7
Full House: r2c4=9
Full House: r6c7=8
Naked Single: r1c5=3
Full House: r1c4=5
Naked Single: r8c5=7
Naked Single: r9c2=2
Naked Single: r4c4=7
Full House: r9c4=3
Full House: r9c5=8
Naked Single: r8c8=4
Naked Single: r8c9=2
Full House: r9c9=7
Full House: r9c3=4
Full House: r8c3=9
Naked Single: r6c2=9
Full House: r4c2=8
Naked Single: r4c8=5
Full House: r6c8=7
Naked Single: r6c5=2
Full House: r4c5=9
Full House: r4c3=2
Full House: r6c3=5
|
normal_sudoku_134 | ..214...9..65.......49..18.745296831..3714...2.1385.4..18........9...7..437629518 | 852143679196578423374962185745296831983714256261385947618457392529831764437629518 | normal_sudoku_134 | 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 4 . . . 9
. . 6 5 . . . . .
. . 4 9 . . 1 8 .
7 4 5 2 9 6 8 3 1
. . 3 7 1 4 . . .
2 . 1 3 8 5 . 4 .
. 1 8 . . . . . .
. . 9 . . . 7 . .
4 3 7 6 2 9 5 1 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 852143679196578423374962185745296831983714256261385947618457392529831764437629518 #1 Easy (196)
Naked Single: r7c4=4
Full House: r8c4=8
Hidden Single: r3c5=6
Hidden Single: r2c1=1
Hidden Single: r6c9=7
Hidden Single: r8c2=2
Naked Single: r8c8=6
Naked Single: r8c1=5
Full House: r7c1=6
Naked Single: r3c1=3
Naked Single: r8c5=3
Naked Single: r1c1=8
Full House: r5c1=9
Naked Single: r2c5=7
Full House: r7c5=5
Naked Single: r7c6=7
Full House: r8c6=1
Full House: r8c9=4
Naked Single: r6c2=6
Full House: r5c2=8
Full House: r6c7=9
Naked Single: r1c6=3
Naked Single: r2c2=9
Naked Single: r2c8=2
Naked Single: r3c6=2
Full House: r2c6=8
Naked Single: r1c7=6
Naked Single: r2c9=3
Full House: r2c7=4
Naked Single: r3c9=5
Full House: r1c8=7
Full House: r3c2=7
Full House: r1c2=5
Naked Single: r5c8=5
Full House: r7c8=9
Naked Single: r5c7=2
Full House: r5c9=6
Full House: r7c9=2
Full House: r7c7=3
|
normal_sudoku_192 | .8.2543.1.7.689....4.3179.8..4.91.....5736489.9..42...4....58....3.68.2...7.23... | 986254371371689542542317968634891257215736489798542613429175836153968724867423195 | normal_sudoku_192 | 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 5 4 3 . 1
. 7 . 6 8 9 . . .
. 4 . 3 1 7 9 . 8
. . 4 . 9 1 . . .
. . 5 7 3 6 4 8 9
. 9 . . 4 2 . . .
4 . . . . 5 8 . .
. . 3 . 6 8 . 2 .
. . 7 . 2 3 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 986254371371689542542317968634891257215736489798542613429175836153968724867423195 #1 Easy (238)
Full House: r7c5=7
Hidden Single: r1c8=7
Hidden Single: r2c1=3
Hidden Single: r4c2=3
Hidden Single: r9c1=8
Hidden Single: r6c3=8
Naked Single: r6c4=5
Full House: r4c4=8
Hidden Single: r3c8=6
Naked Single: r3c3=2
Full House: r3c1=5
Naked Single: r4c8=5
Naked Single: r2c3=1
Naked Single: r2c8=4
Hidden Single: r7c2=2
Naked Single: r5c2=1
Full House: r5c1=2
Naked Single: r8c2=5
Full House: r9c2=6
Naked Single: r7c3=9
Full House: r1c3=6
Full House: r8c1=1
Full House: r1c1=9
Naked Single: r7c4=1
Naked Single: r8c7=7
Naked Single: r7c8=3
Full House: r7c9=6
Naked Single: r8c9=4
Full House: r8c4=9
Full House: r9c4=4
Naked Single: r6c8=1
Full House: r9c8=9
Naked Single: r9c9=5
Full House: r9c7=1
Naked Single: r6c7=6
Naked Single: r2c9=2
Full House: r2c7=5
Full House: r4c7=2
Naked Single: r6c1=7
Full House: r4c1=6
Full House: r4c9=7
Full House: r6c9=3
|
normal_sudoku_5132 | 7.2.35.6.5....6..8....9..5.9..65.13.623.185.9..59.3.86...36..153..5..89..5..8.6.3 | 712835964594176328836294751948657132623418579175923486487369215361542897259781643 | normal_sudoku_5132 | 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 5 . 6 .
5 . . . . 6 . . 8
. . . . 9 . . 5 .
9 . . 6 5 . 1 3 .
6 2 3 . 1 8 5 . 9
. . 5 9 . 3 . 8 6
. . . 3 6 . . 1 5
3 . . 5 . . 8 9 .
. 5 . . 8 . 6 . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 712835964594176328836294751948657132623418579175923486487369215361542897259781643 #1 Extreme (5188)
Finned X-Wing: 2 r48 c69 fr8c5 => r79c6<>2
Finned X-Wing: 2 c48 r29 fr3c4 => r2c5<>2
2-String Kite: 2 in r4c9,r8c5 (connected by r4c6,r6c5) => r8c9<>2
Locked Candidates Type 2 (Claiming): 2 in r8 => r9c4<>2
Locked Candidates Type 2 (Claiming): 2 in c4 => r3c6<>2
Discontinuous Nice Loop: 1/4 r1c4 =8= r1c2 -8- r3c1 =8= r7c1 =2= r7c7 -2- r9c8 =2= r2c8 -2- r2c4 =2= r3c4 =8= r1c4 => r1c4<>1, r1c4<>4
Naked Single: r1c4=8
Forcing Chain Contradiction in r2c8 => r3c4<>4
r3c4=4 r3c4<>2 r2c4=2 r2c8<>2
r3c4=4 r5c4<>4 r5c8=4 r2c8<>4
r3c4=4 r2c5<>4 r2c5=7 r2c8<>7
Forcing Chain Contradiction in r2c8 => r3c4<>7
r3c4=7 r3c4<>2 r2c4=2 r2c8<>2
r3c4=7 r2c5<>7 r2c5=4 r2c8<>4
r3c4=7 r5c4<>7 r5c8=7 r2c8<>7
Forcing Chain Contradiction in r2c8 => r6c5<>4
r6c5=4 r6c5<>2 r6c7=2 r7c7<>2 r9c8=2 r2c8<>2
r6c5=4 r5c4<>4 r5c8=4 r2c8<>4
r6c5=4 r2c5<>4 r2c5=7 r2c8<>7
Sashimi Swordfish: 4 c458 r259 fr8c5 => r9c6<>4
Discontinuous Nice Loop: 7 r4c9 -7- r5c8 -4- r5c4 =4= r4c6 =2= r4c9 => r4c9<>7
Discontinuous Nice Loop: 7 r8c6 -7- r8c9 -4- r4c9 -2- r4c6 =2= r8c6 => r8c6<>7
Finned Franken Swordfish: 7 c59b6 r268 fr3c9 fr5c8 => r2c8<>7
AIC: 2 2- r4c9 =2= r3c9 -2- r2c8 -4- r2c5 -7- r6c5 -2 => r4c6,r6c7<>2
Hidden Single: r4c9=2
Hidden Single: r8c6=2
Hidden Single: r6c5=2
Locked Candidates Type 1 (Pointing): 1 in b8 => r9c13<>1
Naked Pair: 4,7 in r8c59 => r8c23<>4, r8c23<>7
Skyscraper: 7 in r2c5,r3c9 (connected by r8c59) => r2c7,r3c6<>7
Turbot Fish: 7 r4c6 =7= r5c4 -7- r5c8 =7= r9c8 => r9c6<>7
Empty Rectangle: 7 in b4 (r47c6) => r7c2<>7
Locked Candidates Type 1 (Pointing): 7 in b7 => r4c3<>7
W-Wing: 4/7 in r5c4,r8c5 connected by 7 in r2c45 => r9c4<>4
Turbot Fish: 4 r2c4 =4= r5c4 -4- r5c8 =4= r6c7 => r2c7<>4
W-Wing: 4/7 in r6c7,r8c9 connected by 7 in r3c79 => r7c7<>4
Turbot Fish: 4 r2c5 =4= r8c5 -4- r8c9 =4= r9c8 => r2c8<>4
Naked Single: r2c8=2
Hidden Single: r3c4=2
Hidden Single: r7c7=2
Hidden Single: r9c1=2
Remote Pair: 4/7 r2c5 -7- r8c5 -4- r8c9 -7- r9c8 -4- r5c8 -7- r5c4 => r2c4<>4, r2c4<>7
Naked Single: r2c4=1
Naked Single: r3c6=4
Full House: r2c5=7
Full House: r8c5=4
Naked Single: r9c4=7
Full House: r5c4=4
Full House: r4c6=7
Full House: r5c8=7
Full House: r9c8=4
Full House: r8c9=7
Full House: r6c7=4
Naked Single: r7c6=9
Full House: r9c6=1
Full House: r9c3=9
Naked Single: r3c9=1
Full House: r1c9=4
Naked Single: r1c7=9
Full House: r1c2=1
Naked Single: r6c1=1
Full House: r6c2=7
Naked Single: r2c3=4
Naked Single: r3c1=8
Full House: r7c1=4
Naked Single: r2c7=3
Full House: r2c2=9
Full House: r3c7=7
Naked Single: r8c2=6
Full House: r8c3=1
Naked Single: r4c3=8
Full House: r4c2=4
Naked Single: r3c3=6
Full House: r3c2=3
Full House: r7c2=8
Full House: r7c3=7
|
normal_sudoku_2669 | 6......9..2...4.63..9.6.5....3.2..862.6.58.14.8..4..5..6...2.75....7....7..51.... | 647835291125794863839261547453129786276358914981647352364982175518473629792516438 | normal_sudoku_2669 | 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 .
. 2 . . . 4 . 6 3
. . 9 . 6 . 5 . .
. . 3 . 2 . . 8 6
2 . 6 . 5 8 . 1 4
. 8 . . 4 . . 5 .
. 6 . . . 2 . 7 5
. . . . 7 . . . .
7 . . 5 1 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 647835291125794863839261547453129786276358914981647352364982175518473629792516438 #1 Extreme (3694)
Hidden Single: r1c6=5
Locked Candidates Type 1 (Pointing): 3 in b6 => r789c7<>3
Naked Triple: 1,7,9 in r5c2,r6c13 => r4c12<>1, r4c12<>9, r4c2<>7
Locked Candidates Type 1 (Pointing): 1 in b4 => r6c46<>1
Finned Franken Swordfish: 7 r24b4 c347 fr4c6 fr5c2 => r5c4<>7
AIC: 9 9- r4c7 -7- r5c7 =7= r5c2 =9= r6c1 -9 => r6c79<>9
Locked Candidates Type 1 (Pointing): 9 in b6 => r789c7<>9
Finned Swordfish: 9 r267 c145 fr6c6 => r45c4<>9
Naked Single: r5c4=3
Hidden Single: r6c7=3
Hidden Single: r6c9=2
Locked Candidates Type 1 (Pointing): 7 in b6 => r12c7<>7
Naked Triple: 1,7,8 in r13c9,r2c7 => r1c7<>1, r1c7<>8
Skyscraper: 3 in r1c2,r7c1 (connected by r17c5) => r3c1,r89c2<>3
Finned X-Wing: 7 r26 c34 fr6c6 => r4c4<>7
Naked Single: r4c4=1
Hidden Single: r3c6=1
Hidden Single: r3c2=3
Hidden Single: r1c5=3
Hidden Single: r7c1=3
Locked Candidates Type 1 (Pointing): 7 in b2 => r6c4<>7
Locked Candidates Type 2 (Claiming): 9 in r7 => r8c46,r9c6<>9
Locked Pair: 3,6 in r89c6 => r6c6,r8c4<>6
Hidden Single: r6c4=6
X-Wing: 1 c29 r18 => r18c3,r8c17<>1
Uniqueness Test 4: 8/9 in r2c45,r7c45 => r27c4<>8
XY-Chain: 8 8- r3c1 -4- r4c1 -5- r4c2 -4- r9c2 -9- r9c9 -8 => r3c9<>8
Naked Single: r3c9=7
XY-Wing: 2/8/4 in r3c48,r8c4 => r8c8<>4
XY-Chain: 4 4- r8c4 -8- r7c5 -9- r2c5 -8- r2c7 -1- r1c9 -8- r9c9 -9- r9c2 -4 => r8c123<>4
XY-Chain: 8 8- r2c7 -1- r1c9 -8- r9c9 -9- r9c2 -4- r4c2 -5- r4c1 -4- r3c1 -8 => r2c13<>8
Turbot Fish: 8 r2c7 =8= r2c5 -8- r7c5 =8= r8c4 => r8c7<>8
AIC: 2/4 2- r1c7 -4- r3c8 =4= r3c1 -4- r4c1 -5- r4c2 =5= r8c2 =1= r8c9 -1- r1c9 -8- r2c7 =8= r2c5 -8- r7c5 =8= r8c4 =4= r8c7 -4 => r8c7<>2, r1c7<>4
Naked Single: r1c7=2
Naked Single: r3c8=4
Naked Single: r3c1=8
Full House: r3c4=2
Hidden Single: r4c1=4
Naked Single: r4c2=5
XY-Wing: 5/9/1 in r28c1,r8c2 => r1c2<>1
Hidden Single: r1c9=1
Full House: r2c7=8
Naked Single: r2c5=9
Full House: r7c5=8
Naked Single: r2c4=7
Full House: r1c4=8
Naked Single: r8c4=4
Full House: r7c4=9
Naked Single: r8c7=6
Naked Single: r8c6=3
Full House: r9c6=6
Naked Single: r9c7=4
Naked Single: r8c8=2
Full House: r9c8=3
Naked Single: r7c7=1
Full House: r7c3=4
Naked Single: r9c2=9
Naked Single: r1c3=7
Full House: r1c2=4
Naked Single: r5c2=7
Full House: r8c2=1
Full House: r5c7=9
Full House: r4c7=7
Full House: r4c6=9
Full House: r6c6=7
Naked Single: r8c1=5
Naked Single: r9c9=8
Full House: r8c9=9
Full House: r8c3=8
Full House: r9c3=2
Naked Single: r6c3=1
Full House: r2c3=5
Full House: r2c1=1
Full House: r6c1=9
|
normal_sudoku_1160 | ..93.6857..68...41..3....2...8....3.9352614784217.....59417..8.3.2.5.....674..... | 149326857256897341783514926678945132935261478421783569594172683312658794867439215 | normal_sudoku_1160 | 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 . 6 8 5 7
. . 6 8 . . . 4 1
. . 3 . . . . 2 .
. . 8 . . . . 3 .
9 3 5 2 6 1 4 7 8
4 2 1 7 . . . . .
5 9 4 1 7 . . 8 .
3 . 2 . 5 . . . .
. 6 7 4 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 149326857256897341783514926678945132935261478421783569594172683312658794867439215 #1 Medium (288)
Naked Single: r4c2=7
Full House: r4c1=6
Naked Single: r2c2=5
Hidden Single: r2c7=3
Hidden Single: r4c7=1
Hidden Single: r8c4=6
Hidden Single: r8c7=7
Hidden Single: r8c9=4
Hidden Single: r4c9=2
Hidden Single: r6c8=6
Locked Candidates Type 1 (Pointing): 9 in b3 => r3c456<>9
Naked Single: r3c4=5
Full House: r4c4=9
Naked Single: r4c5=4
Full House: r4c6=5
Naked Single: r3c5=1
Naked Single: r1c5=2
Naked Single: r1c1=1
Full House: r1c2=4
Naked Single: r2c5=9
Naked Single: r9c1=8
Full House: r8c2=1
Full House: r3c2=8
Naked Single: r2c6=7
Full House: r2c1=2
Full House: r3c1=7
Full House: r3c6=4
Naked Single: r9c5=3
Full House: r6c5=8
Full House: r6c6=3
Naked Single: r8c8=9
Full House: r8c6=8
Full House: r9c8=1
Naked Single: r7c6=2
Full House: r9c6=9
Naked Single: r9c9=5
Full House: r9c7=2
Naked Single: r7c7=6
Full House: r7c9=3
Naked Single: r6c9=9
Full House: r3c9=6
Full House: r3c7=9
Full House: r6c7=5
|
normal_sudoku_372 | ..7342.8.42.6587..385791..2...26...72..1.3..4......21.742.39....36....295..42637. | 967342581421658793385791642194265837258173964673984215742839156836517429519426378 | normal_sudoku_372 | 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 4 2 . 8 .
4 2 . 6 5 8 7 . .
3 8 5 7 9 1 . . 2
. . . 2 6 . . . 7
2 . . 1 . 3 . . 4
. . . . . . 2 1 .
7 4 2 . 3 9 . . .
. 3 6 . . . . 2 9
5 . . 4 2 6 3 7 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 967342581421658793385791642194265837258173964673984215742839156836517429519426378 #1 Hard (396)
Hidden Single: r6c4=9
Hidden Single: r8c7=4
Naked Single: r3c7=6
Full House: r3c8=4
Hidden Single: r8c5=1
Naked Single: r8c1=8
Naked Single: r6c1=6
Naked Single: r8c4=5
Full House: r7c4=8
Full House: r8c6=7
Hidden Single: r9c9=8
Hidden Single: r1c2=6
Hidden Single: r5c8=6
Naked Single: r7c8=5
Naked Single: r7c7=1
Full House: r7c9=6
Naked Pair: 1,9 in r29c3 => r4c3<>1, r45c3<>9
Naked Single: r5c3=8
Naked Single: r5c5=7
Full House: r6c5=8
Hidden Single: r4c7=8
Hidden Single: r6c2=7
Bivalue Universal Grave + 1 => r4c2<>1, r4c2<>5
Naked Single: r4c2=9
Naked Single: r4c1=1
Full House: r1c1=9
Full House: r2c3=1
Naked Single: r4c8=3
Full House: r2c8=9
Full House: r2c9=3
Naked Single: r5c2=5
Full House: r9c2=1
Full House: r9c3=9
Full House: r5c7=9
Full House: r1c7=5
Full House: r6c9=5
Full House: r1c9=1
Naked Single: r4c3=4
Full House: r4c6=5
Full House: r6c6=4
Full House: r6c3=3
|
normal_sudoku_4715 | .3...4..9476.9..3.9.1...4..7.9......36..1.9.412...9.5.6..2.1.98.9.86.14..1.94.3.. | 532674819476198532981325467759436281368512974124789653643251798297863145815947326 | normal_sudoku_4715 | 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 . . 9
4 7 6 . 9 . . 3 .
9 . 1 . . . 4 . .
7 . 9 . . . . . .
3 6 . . 1 . 9 . 4
1 2 . . . 9 . 5 .
6 . . 2 . 1 . 9 8
. 9 . 8 6 . 1 4 .
. 1 . 9 4 . 3 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 532674819476198532981325467759436281368512974124789653643251798297863145815947326 #1 Extreme (2250)
Locked Candidates Type 1 (Pointing): 2 in b1 => r1c578<>2
Skyscraper: 2 in r2c7,r3c5 (connected by r4c57) => r2c6,r3c89<>2
Discontinuous Nice Loop: 8 r3c5 -8- r2c6 =8= r2c7 =2= r4c7 -2- r4c5 =2= r3c5 => r3c5<>8
Discontinuous Nice Loop: 8 r5c6 -8- r2c6 =8= r2c7 =2= r4c7 -2- r5c8 =2= r5c6 => r5c6<>8
2-String Kite: 8 in r3c2,r5c8 (connected by r4c2,r5c3) => r3c8<>8
Grouped Discontinuous Nice Loop: 5 r1c4 -5- r2c6 -8- r3c6 =8= r3c2 =5= r1c13 -5- r1c4 => r1c4<>5
Grouped Discontinuous Nice Loop: 5 r1c5 -5- r2c6 -8- r3c6 =8= r3c2 =5= r1c13 -5- r1c5 => r1c5<>5
XY-Wing: 5/8/7 in r1c5,r29c6 => r3c6,r7c5<>7
Locked Candidates Type 1 (Pointing): 7 in b8 => r5c6<>7
Sashimi Swordfish: 5 c257 r347 fr1c7 fr2c7 => r3c9<>5
Locked Pair: 6,7 in r3c89 => r1c78,r3c46<>6, r1c78,r3c45<>7
Hidden Single: r4c6=6
Hidden Single: r1c4=6
Hidden Single: r6c7=6
Hidden Single: r1c8=1
Hidden Single: r2c4=1
Hidden Single: r1c5=7
Hidden Single: r7c7=7
Hidden Single: r4c9=1
Hidden Single: r6c9=3
Naked Single: r6c5=8
Naked Single: r6c3=4
Full House: r6c4=7
Naked Single: r5c4=5
Naked Single: r3c4=3
Full House: r4c4=4
Naked Single: r5c3=8
Full House: r4c2=5
Naked Single: r5c6=2
Full House: r4c5=3
Full House: r5c8=7
Naked Single: r3c2=8
Full House: r7c2=4
Naked Single: r7c5=5
Full House: r3c5=2
Full House: r7c3=3
Naked Single: r3c8=6
Naked Single: r3c6=5
Full House: r3c9=7
Full House: r2c6=8
Naked Single: r9c6=7
Full House: r8c6=3
Naked Single: r9c8=2
Full House: r4c8=8
Full House: r4c7=2
Naked Single: r8c9=5
Full House: r9c9=6
Full House: r2c9=2
Full House: r2c7=5
Full House: r1c7=8
Naked Single: r9c3=5
Full House: r9c1=8
Naked Single: r8c1=2
Full House: r1c1=5
Full House: r1c3=2
Full House: r8c3=7
|
normal_sudoku_3561 | 584.....16139...4.972.1.6.5..1.59.7.7.8.649....97....6896..23..42758..6.135.....8 | 584326791613975842972418635361859274758264913249731586896142357427583169135697428 | normal_sudoku_3561 | 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 8 4 . . . . . 1
6 1 3 9 . . . 4 .
9 7 2 . 1 . 6 . 5
. . 1 . 5 9 . 7 .
7 . 8 . 6 4 9 . .
. . 9 7 . . . . 6
8 9 6 . . 2 3 . .
4 2 7 5 8 . . 6 .
1 3 5 . . . . . 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 584326791613975842972418635361859274758264913249731586896142357427583169135697428 #1 Easy (156)
Naked Single: r8c7=1
Naked Single: r8c9=9
Full House: r8c6=3
Naked Single: r5c2=5
Naked Single: r7c8=5
Naked Single: r9c8=2
Naked Single: r3c6=8
Naked Single: r6c2=4
Full House: r4c2=6
Naked Single: r3c8=3
Full House: r3c4=4
Naked Single: r6c6=1
Naked Single: r1c8=9
Naked Single: r5c8=1
Full House: r6c8=8
Naked Single: r7c4=1
Naked Single: r9c4=6
Naked Single: r9c6=7
Naked Single: r1c6=6
Full House: r2c6=5
Naked Single: r7c5=4
Full House: r7c9=7
Full House: r9c7=4
Full House: r9c5=9
Naked Single: r2c9=2
Naked Single: r4c7=2
Naked Single: r1c7=7
Full House: r2c7=8
Full House: r2c5=7
Full House: r6c7=5
Naked Single: r5c9=3
Full House: r4c9=4
Full House: r5c4=2
Naked Single: r4c1=3
Full House: r4c4=8
Full House: r1c4=3
Full House: r6c5=3
Full House: r6c1=2
Full House: r1c5=2
|
normal_sudoku_2547 | .138.......65..3...97.....69.8.3..1.1.4..9..3375....9..32.41.65..92...3..51...72. | 513876942846592371297413586928635417164789253375124698732941865689257134451368729 | normal_sudoku_2547 | 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 8 . . . . .
. . 6 5 . . 3 . .
. 9 7 . . . . . 6
9 . 8 . 3 . . 1 .
1 . 4 . . 9 . . 3
3 7 5 . . . . 9 .
. 3 2 . 4 1 . 6 5
. . 9 2 . . . 3 .
. 5 1 . . . 7 2 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 513876942846592371297413586928635417164789253375124698732941865689257134451368729 #1 Extreme (1978)
Locked Candidates Type 1 (Pointing): 9 in b2 => r9c5<>9
Locked Candidates Type 1 (Pointing): 2 in b4 => r2c2<>2
Locked Candidates Type 1 (Pointing): 6 in b4 => r8c2<>6
Locked Candidates Type 2 (Claiming): 4 in c8 => r1c79,r2c9,r3c7<>4
Naked Triple: 1,4,8 in r8c279 => r8c1<>4, r8c156<>8
Locked Candidates Type 1 (Pointing): 8 in b8 => r9c19<>8
Hidden Pair: 1,9 in r2c59 => r2c59<>2, r2c59<>7, r2c9<>8
2-String Kite: 7 in r2c6,r4c9 (connected by r1c9,r2c8) => r4c6<>7
Continuous Nice Loop: 6/8 9= r9c4 =3= r9c6 =8= r6c6 -8- r6c9 =8= r8c9 -8- r7c7 -9- r7c4 =9= r9c4 =3 => r9c46<>6, r6c57,r8c7<>8
Locked Candidates Type 2 (Claiming): 6 in c4 => r46c6,r56c5<>6
Naked Pair: 1,2 in r36c5 => r15c5<>2, r2c5<>1
Naked Single: r2c5=9
Naked Single: r2c9=1
Hidden Single: r8c7=1
Locked Candidates Type 1 (Pointing): 4 in b9 => r46c9<>4
W-Wing: 7/6 in r1c5,r8c1 connected by 6 in r9c15 => r8c5<>7
Skyscraper: 7 in r4c9,r5c5 (connected by r1c59) => r4c4,r5c8<>7
Hidden Single: r4c9=7
Skyscraper: 2 in r1c9,r3c5 (connected by r6c59) => r1c6,r3c7<>2
Locked Candidates Type 1 (Pointing): 2 in b3 => r1c1<>2
Hidden Pair: 2,9 in r1c79 => r1c7<>5
Sue de Coq: r6c456 - {12468} (r6c9 - {28}, r4c4 - {46}) => r4c6<>4, r5c4<>6, r6c7<>2
Naked Single: r5c4=7
Naked Single: r7c4=9
Naked Single: r7c7=8
Full House: r7c1=7
Naked Single: r9c4=3
Naked Single: r3c7=5
Naked Single: r8c9=4
Full House: r9c9=9
Naked Single: r8c1=6
Naked Single: r9c6=8
Naked Single: r8c2=8
Full House: r9c1=4
Full House: r9c5=6
Naked Single: r1c9=2
Full House: r6c9=8
Naked Single: r8c5=5
Full House: r8c6=7
Naked Single: r2c2=4
Naked Single: r1c1=5
Naked Single: r1c5=7
Naked Single: r1c7=9
Naked Single: r5c8=5
Naked Single: r5c5=8
Naked Single: r2c6=2
Naked Single: r1c8=4
Full House: r1c6=6
Naked Single: r2c1=8
Full House: r2c8=7
Full House: r3c8=8
Full House: r3c1=2
Naked Single: r3c5=1
Full House: r6c5=2
Naked Single: r4c6=5
Naked Single: r6c6=4
Full House: r3c6=3
Full House: r3c4=4
Naked Single: r4c4=6
Full House: r6c4=1
Full House: r6c7=6
Naked Single: r4c2=2
Full House: r4c7=4
Full House: r5c7=2
Full House: r5c2=6
|
normal_sudoku_1479 | .....1.....3.4...712.....9....8...7.817.6..539.....28..4.3.7..57.54.6.3.....5..4. | 479521368583649127126783594652834971817962453934175286248397615795416832361258749 | normal_sudoku_1479 | 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 . 4 . . . 7
1 2 . . . . . 9 .
. . . 8 . . . 7 .
8 1 7 . 6 . . 5 3
9 . . . . . 2 8 .
. 4 . 3 . 7 . . 5
7 . 5 4 . 6 . 3 .
. . . . 5 . . 4 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 479521368583649127126783594652834971817962453934175286248397615795416832361258749 #1 Extreme (8058)
Hidden Single: r1c2=7
Hidden Single: r9c7=7
Locked Candidates Type 1 (Pointing): 2 in b4 => r4c56<>2
Grouped Discontinuous Nice Loop: 6 r4c3 -6- r4c7 =6= r46c9 -6- r9c9 =6= r7c78 -6- r7c1 -2- r4c1 =2= r4c3 => r4c3<>6
Forcing Chain Contradiction in r9c4 => r1c4<>2
r1c4=2 r1c89<>2 r2c8=2 r2c8<>1 r7c8=1 r7c3<>1 r9c3=1 r9c4<>1
r1c4=2 r9c4<>2
r1c4=2 r5c4<>2 r5c4=9 r9c4<>9
Forcing Chain Contradiction in r3 => r7c3<>2
r7c3=2 r4c3<>2 r4c3=4 r6c3<>4 r6c3=6 r3c3<>6
r7c3=2 r7c3<>1 r9c3=1 r9c4<>1 r6c4=1 r6c4<>7 r3c4=7 r3c4<>6
r7c3=2 r7c1<>2 r7c1=6 r7c8<>6 r12c8=6 r3c7<>6
r7c3=2 r7c1<>2 r7c1=6 r7c8<>6 r12c8=6 r3c9<>6
Forcing Chain Contradiction in r6c9 => r7c3<>6
r7c3=6 r7c3<>1 r9c3=1 r9c4<>1 r6c4=1 r6c9<>1
r7c3=6 r6c3<>6 r6c3=4 r6c9<>4
r7c3=6 r7c78<>6 r9c9=6 r6c9<>6
Forcing Chain Verity => r9c9<>1
r1c5=2 r1c89<>2 r2c8=2 r2c8<>1 r7c8=1 r9c9<>1
r7c5=2 r7c1<>2 r7c1=6 r7c78<>6 r9c9=6 r9c9<>1
r8c5=2 r8c5<>1 r8c79=1 r9c9<>1
Forcing Net Contradiction in r7 => r1c3<>6
r1c3=6 (r6c3<>6 r6c3=4 r3c3<>4 r3c3=8 r3c5<>8) (r1c3<>9 r2c2=9 r8c2<>9 r8c2=8 r8c5<>8) (r1c8<>6 r1c8=2 r1c9<>2) (r1c9<>6) (r1c1<>6) r2c1<>6 r2c1=5 r1c1<>5 r1c1=4 r1c9<>4 r1c9=8 r1c5<>8 r7c5=8
r1c3=6 (r3c3<>6) r6c3<>6 r6c3=4 r3c3<>4 r3c3=8 r7c3<>8 r7c7=8
Forcing Net Contradiction in c9 => r1c7<>4
r1c7=4 r5c7<>4 r5c7=9 r4c9<>9
r1c7=4 (r1c7<>3 r1c5=3 r3c6<>3 r3c7=3 r3c7<>5 r2c7=5 r2c7<>8) (r1c7<>3 r1c5=3 r1c5<>2) r5c7<>4 r5c7=9 r5c4<>9 r5c4=2 r2c4<>2 r2c6=2 r2c6<>8 r2c2=8 r8c2<>8 r8c2=9 r8c9<>9
r1c7=4 (r1c1<>4 r4c1=4 r4c3<>4 r4c3=2 r9c3<>2) (r1c1<>4 r4c1=4 r4c1<>3 r9c1=3 r9c1<>2) (r1c7<>3 r1c5=3 r1c5<>2) r5c7<>4 r5c7=9 r5c4<>9 r5c4=2 (r9c4<>2) r2c4<>2 r2c6=2 r9c6<>2 r9c9=2 r9c9<>9
Forcing Chain Contradiction in r1 => r4c9<>4
r4c9=4 r4c1<>4 r1c1=4 r1c1<>5
r4c9=4 r45c7<>4 r3c7=4 r3c7<>5 r3c46=5 r1c4<>5
r4c9=4 r45c7<>4 r3c7=4 r3c7<>3 r1c7=3 r1c7<>5
Forcing Net Contradiction in r3 => r1c7<>6
r1c7=6 (r3c7<>6) (r3c9<>6) (r1c7<>5) r1c7<>3 r1c5=3 (r3c5<>3) r3c6<>3 r3c7=3 r3c7<>5 r2c7=5 r2c1<>5 r2c1=6 r3c3<>6 r3c4=6 r3c4<>5
r1c7=6 (r3c7<>6) (r3c9<>6) (r1c7<>5) r1c7<>3 r1c5=3 (r3c5<>3) r3c6<>3 r3c7=3 r3c7<>5 r2c7=5 r2c1<>5 r2c1=6 r3c3<>6 r3c4=6 r3c4<>7 r3c5=7 r6c5<>7 r6c4=7 r6c4<>5 r123c4=5 r3c6<>5
r1c7=6 r1c7<>3 r1c5=3 (r3c5<>3) r3c6<>3 r3c7=3 r3c7<>5
Forcing Net Verity => r2c8<>6
r2c8=1 r2c8<>6
r7c8=1 (r7c3<>1 r9c3=1 r9c4<>1) (r8c7<>1) r8c9<>1 r8c5=1 (r4c5<>1 r4c9=1 r4c9<>9) r8c5<>2 r8c9=2 r8c9<>9 r9c9=9 r9c4<>9 r9c4=2 (r2c4<>2) r5c4<>2 r5c6=2 r2c6<>2 r2c8=2 r2c8<>6
Forcing Chain Contradiction in r7c8 => r7c5<>2
r7c5=2 r1c5<>2 r1c89=2 r2c8<>2 r2c8=1 r7c8<>1
r7c5=2 r7c8<>2
r7c5=2 r7c1<>2 r7c1=6 r7c8<>6
Grouped Continuous Nice Loop: 1/8/9 2= r8c5 =1= r8c79 -1- r7c8 =1= r2c8 =2= r1c89 -2- r1c5 =2= r8c5 =1 => r7c7<>1, r8c5<>8, r8c5<>9
Finned Franken Swordfish: 8 r28b8 c267 fr7c5 fr8c9 => r7c7<>8
Grouped Discontinuous Nice Loop: 9 r9c2 -9- r8c2 -8- r7c3 =8= r7c5 =9= r9c46 -9- r9c2 => r9c2<>9
Grouped Discontinuous Nice Loop: 9 r9c3 -9- r9c46 =9= r7c5 =8= r7c3 =1= r9c3 => r9c3<>9
Sashimi Swordfish: 9 c359 r147 fr8c9 fr9c9 => r7c7<>9
Naked Single: r7c7=6
Naked Single: r7c1=2
Naked Single: r7c8=1
Naked Single: r2c8=2
Full House: r1c8=6
Hidden Single: r4c3=2
Hidden Single: r2c7=1
Hidden Single: r9c3=1
Hidden Single: r8c5=1
Hidden Single: r1c5=2
Hidden Single: r6c4=1
Hidden Single: r4c9=1
Hidden Single: r8c9=2
Hidden Single: r1c7=3
Hidden Single: r6c5=7
Hidden Single: r3c4=7
Hidden Single: r6c9=6
Naked Single: r6c3=4
Hidden Single: r9c9=9
Full House: r8c7=8
Full House: r8c2=9
Naked Single: r9c4=2
Naked Single: r7c3=8
Full House: r7c5=9
Full House: r9c6=8
Naked Single: r5c4=9
Naked Single: r1c3=9
Full House: r3c3=6
Naked Single: r4c5=3
Full House: r3c5=8
Naked Single: r1c4=5
Full House: r2c4=6
Naked Single: r5c7=4
Full House: r4c7=9
Full House: r3c7=5
Full House: r5c6=2
Naked Single: r2c1=5
Naked Single: r6c6=5
Full House: r4c6=4
Full House: r6c2=3
Naked Single: r3c9=4
Full House: r3c6=3
Full House: r2c6=9
Full House: r2c2=8
Full House: r1c1=4
Full House: r1c9=8
Naked Single: r4c1=6
Full House: r4c2=5
Full House: r9c2=6
Full House: r9c1=3
|
normal_sudoku_1206 | .7856..215.1..26...62.1..5..4..3.5...2.67..94..7....3..14.9.2.57.....91.2..851.4. | 978563421531482679462917358149238567823675194657149832314796285785324916296851743 | normal_sudoku_1206 | 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 5 6 . . 2 1
5 . 1 . . 2 6 . .
. 6 2 . 1 . . 5 .
. 4 . . 3 . 5 . .
. 2 . 6 7 . . 9 4
. . 7 . . . . 3 .
. 1 4 . 9 . 2 . 5
7 . . . . . 9 1 .
2 . . 8 5 1 . 4 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 978563421531482679462917358149238567823675194657149832314796285785324916296851743 #1 Hard (506)
Locked Pair: 1,8 in r56c7 => r3c7,r4c89,r6c9<>8
Locked Candidates Type 1 (Pointing): 7 in b8 => r7c8<>7
Locked Candidates Type 2 (Claiming): 4 in r2 => r13c6,r3c4<>4
Naked Pair: 3,9 in r29c2 => r6c2<>9, r8c2<>3
Skyscraper: 6 in r6c1,r9c3 (connected by r69c9) => r4c3,r7c1<>6
Naked Single: r4c3=9
Naked Single: r4c6=8
Naked Single: r5c6=5
Naked Single: r5c3=3
Naked Single: r9c3=6
Full House: r8c3=5
Naked Single: r8c2=8
Naked Single: r6c2=5
Naked Single: r7c1=3
Full House: r9c2=9
Full House: r2c2=3
Naked Single: r7c4=7
Naked Single: r7c6=6
Full House: r7c8=8
Naked Single: r2c8=7
Full House: r4c8=6
Naked Single: r4c1=1
Naked Single: r6c9=2
Naked Single: r4c4=2
Full House: r4c9=7
Naked Single: r5c1=8
Full House: r5c7=1
Full House: r6c1=6
Full House: r6c7=8
Naked Single: r6c5=4
Naked Single: r9c9=3
Full House: r9c7=7
Full House: r8c9=6
Naked Single: r2c5=8
Full House: r8c5=2
Naked Single: r6c6=9
Full House: r6c4=1
Naked Single: r2c9=9
Full House: r2c4=4
Full House: r3c9=8
Naked Single: r1c6=3
Naked Single: r8c4=3
Full House: r3c4=9
Full House: r3c6=7
Full House: r8c6=4
Naked Single: r1c7=4
Full House: r1c1=9
Full House: r3c1=4
Full House: r3c7=3
|
normal_sudoku_6767 | ..9..8.5..6.54.9..5..9....3.....4.272.1.75...7..2..3.5.178.35.66..7...3..8.4..... | 429368751163547982578912463895134627231675894746289315917823546654791238382456179 | normal_sudoku_6767 | 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 .
. 6 . 5 4 . 9 . .
5 . . 9 . . . . 3
. . . . . 4 . 2 7
2 . 1 . 7 5 . . .
7 . . 2 . . 3 . 5
. 1 7 8 . 3 5 . 6
6 . . 7 . . . 3 .
. 8 . 4 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 429368751163547982578912463895134627231675894746289315917823546654791238382456179 #1 Extreme (2746)
Hidden Single: r7c5=2
Locked Candidates Type 1 (Pointing): 3 in b2 => r1c12<>3
Locked Candidates Type 2 (Claiming): 8 in r5 => r4c7,r6c8<>8
Locked Candidates Type 2 (Claiming): 3 in c2 => r4c13<>3
Naked Triple: 1,3,6 in r1c45,r3c5 => r23c6<>1, r3c6<>6
W-Wing: 6/1 in r3c5,r4c7 connected by 1 in r14c4 => r3c7,r4c5<>6
W-Wing: 1/6 in r3c5,r4c7 connected by 6 in r1c7,r3c8 => r3c7,r4c5<>1
Hidden Pair: 1,6 in r3c58 => r3c8<>4, r3c8<>7, r3c8<>8
Finned Swordfish: 1 r368 c568 fr8c7 fr8c9 => r9c8<>1
Multi Colors 1: 1 (r1c1) / (r2c1), (r1c4,r4c7) / (r4c4,r6c8) => r2c8<>1
Sue de Coq: r56c8 - {14689} (r279c8 - {4789}, r4c7 - {16}) => r5c7<>6
Skyscraper: 6 in r3c5,r5c4 (connected by r35c8) => r1c4,r6c5<>6
Locked Candidates Type 1 (Pointing): 6 in b2 => r9c5<>6
Hidden Single: r9c6=6
2-String Kite: 1 in r4c7,r8c6 (connected by r4c4,r6c6) => r8c7<>1
Simple Colors Trap: 1 (r1c4,r3c8,r4c7) / (r3c5,r4c4,r6c8) => r1c5<>1
XY-Chain: 8 8- r2c8 -7- r9c8 -9- r7c8 -4- r7c1 -9- r4c1 -8 => r2c1<>8
Hidden Single: r4c1=8
Hidden Single: r6c5=8
Locked Candidates Type 1 (Pointing): 9 in b4 => r8c2<>9
AIC: 4 4- r1c1 -1- r1c4 =1= r4c4 -1- r6c6 -9- r6c2 -4 => r13c2<>4
Locked Pair: 2,7 in r13c2 => r23c3,r8c2<>2
Naked Pair: 2,7 in r3c26 => r3c7<>2, r3c7<>7
Naked Pair: 4,8 in r35c7 => r18c7<>4, r8c7<>8
Naked Single: r8c7=2
Hidden Single: r8c9=8
Hidden Single: r9c3=2
Hidden Single: r7c8=4
Full House: r7c1=9
Naked Single: r9c1=3
Naked Single: r2c1=1
Full House: r1c1=4
Naked Single: r2c9=2
Naked Single: r3c3=8
Naked Single: r1c9=1
Naked Single: r2c6=7
Naked Single: r2c3=3
Full House: r2c8=8
Naked Single: r3c7=4
Naked Single: r1c4=3
Naked Single: r3c8=6
Full House: r1c7=7
Naked Single: r9c9=9
Full House: r5c9=4
Naked Single: r3c6=2
Naked Single: r5c7=8
Naked Single: r1c5=6
Full House: r3c5=1
Full House: r1c2=2
Full House: r3c2=7
Naked Single: r5c4=6
Full House: r4c4=1
Naked Single: r5c8=9
Full House: r5c2=3
Naked Single: r9c7=1
Full House: r9c8=7
Full House: r9c5=5
Full House: r4c7=6
Full House: r6c8=1
Naked Single: r6c6=9
Full House: r4c5=3
Full House: r8c5=9
Full House: r8c6=1
Naked Single: r4c3=5
Full House: r4c2=9
Naked Single: r6c2=4
Full House: r6c3=6
Full House: r8c3=4
Full House: r8c2=5
|
normal_sudoku_6427 | 395..874.867..31..241...9....9.36..1..6.81.7..185..6..153.6.8..972......684..5.17 | 395128746867943152241657938729436581536281479418579623153762894972814365684395217 | normal_sudoku_6427 | 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 5 . . 8 7 4 .
8 6 7 . . 3 1 . .
2 4 1 . . . 9 . .
. . 9 . 3 6 . . 1
. . 6 . 8 1 . 7 .
. 1 8 5 . . 6 . .
1 5 3 . 6 . 8 . .
9 7 2 . . . . . .
6 8 4 . . 5 . 1 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 395128746867943152241657938729436581536281479418579623153762894972814365684395217 #1 Easy (160)
Naked Single: r4c2=2
Full House: r5c2=3
Naked Single: r3c6=7
Naked Single: r8c6=4
Naked Single: r3c4=6
Naked Single: r3c5=5
Naked Single: r8c5=1
Naked Single: r1c5=2
Naked Single: r1c4=1
Full House: r1c9=6
Naked Single: r9c5=9
Naked Single: r2c5=4
Full House: r2c4=9
Full House: r6c5=7
Naked Single: r7c6=2
Full House: r6c6=9
Naked Single: r4c4=4
Full House: r5c4=2
Naked Single: r6c1=4
Naked Single: r7c4=7
Naked Single: r7c8=9
Full House: r7c9=4
Naked Single: r9c4=3
Full House: r8c4=8
Full House: r9c7=2
Naked Single: r4c7=5
Naked Single: r5c1=5
Full House: r4c1=7
Full House: r4c8=8
Naked Single: r5c7=4
Full House: r5c9=9
Full House: r8c7=3
Naked Single: r3c8=3
Full House: r3c9=8
Naked Single: r8c9=5
Full House: r8c8=6
Naked Single: r6c8=2
Full House: r2c8=5
Full House: r2c9=2
Full House: r6c9=3
|
normal_sudoku_1669 | 4...2.16.6823.1957.1....24.92....681...8..4....8..23.58792..534.54.738.6.6...47.. | 493725168682341957517698243925437681136859472748162395879216534254973816361584729 | normal_sudoku_1669 | 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 . 1 6 .
6 8 2 3 . 1 9 5 7
. 1 . . . . 2 4 .
9 2 . . . . 6 8 1
. . . 8 . . 4 . .
. . 8 . . 2 3 . 5
8 7 9 2 . . 5 3 4
. 5 4 . 7 3 8 . 6
. 6 . . . 4 7 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 493725168682341957517698243925437681136859472748162395879216534254973816361584729 #1 Easy (156)
Full House: r2c5=4
Naked Single: r7c6=6
Full House: r7c5=1
Naked Single: r5c2=3
Naked Single: r6c2=4
Full House: r1c2=9
Naked Single: r8c4=9
Naked Single: r9c4=5
Full House: r9c5=8
Naked Single: r1c4=7
Naked Single: r3c4=6
Naked Single: r4c4=4
Full House: r6c4=1
Naked Single: r6c1=7
Naked Single: r4c3=5
Naked Single: r6c8=9
Full House: r6c5=6
Naked Single: r1c3=3
Naked Single: r4c5=3
Full House: r4c6=7
Naked Single: r5c1=1
Full House: r5c3=6
Naked Single: r5c9=2
Full House: r5c8=7
Naked Single: r1c9=8
Full House: r1c6=5
Full House: r3c9=3
Full House: r9c9=9
Naked Single: r3c1=5
Full House: r3c3=7
Full House: r9c3=1
Naked Single: r8c1=2
Full House: r8c8=1
Full House: r9c8=2
Full House: r9c1=3
Naked Single: r3c5=9
Full House: r3c6=8
Full House: r5c6=9
Full House: r5c5=5
|
normal_sudoku_713 | 265.1.....4...2..........2..1.278....52.938713..1.52.9....29.1552.3.1....9175.3.2 | 265417938143982756879536124916278543452693871387145269734829615528361497691754382 | normal_sudoku_713 | 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 5 . 1 . . . .
. 4 . . . 2 . . .
. . . . . . . 2 .
. 1 . 2 7 8 . . .
. 5 2 . 9 3 8 7 1
3 . . 1 . 5 2 . 9
. . . . 2 9 . 1 5
5 2 . 3 . 1 . . .
. 9 1 7 5 . 3 . 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 265417938143982756879536124916278543452693871387145269734829615528361497691754382 #1 Extreme (4162)
Locked Candidates Type 2 (Claiming): 3 in r1 => r2c89,r3c9<>3
Naked Pair: 4,6 in r6c58 => r6c3<>4, r6c3<>6
Grouped Discontinuous Nice Loop: 8 r2c8 -8- r9c8 =8= r9c1 -8- r7c123 =8= r7c4 -8- r1c4 =8= r1c89 -8- r2c8 => r2c8<>8
Forcing Chain Contradiction in r9c1 => r7c4<>4
r7c4=4 r5c4<>4 r5c1=4 r9c1<>4
r7c4=4 r9c6<>4 r9c6=6 r9c1<>6
r7c4=4 r7c4<>8 r7c123=8 r9c1<>8
Turbot Fish: 4 r6c8 =4= r6c5 -4- r8c5 =4= r9c6 => r9c8<>4
AIC: 6 6- r3c6 =6= r9c6 =4= r8c5 -4- r6c5 -6 => r23c5<>6
Almost Locked Set XZ-Rule: A=r1c46,r23c5,r3c6 {346789}, B=r1c789,r23c9 {346789}, X=9, Z=6 => r3c7<>6
Almost Locked Set XY-Wing: A=r1c467 {4789}, B=r6c238 {4678}, C=r236c5 {3468}, X,Y=6,8, Z=4 => r1c8<>4
Almost Locked Set XY-Wing: A=r4c789 {3456}, B=r59c1 {468}, C=r69c8 {468}, X,Y=4,8, Z=6 => r4c1<>6
Almost Locked Set Chain: 7- r1c467 {4789} -8- r23c5 {348} -4- r68c5 {468} -8- r1c6,r23c5 {3478} -7 => r1c9<>7
Almost Locked Set Chain: 6- r5c1 {46} -4- r5c4 {46} -6- r6c5 {46} -4- r6c8 {46} -6- r9c8 {68} -8- r59c1 {468} -6 => r7c1<>6
Forcing Chain Contradiction in r9c1 => r7c4=8
r7c4<>8 r7c4=6 r9c6<>6 r9c6=4 r9c1<>4
r7c4<>8 r7c4=6 r5c4<>6 r5c1=6 r9c1<>6
r7c4<>8 r7c123=8 r9c1<>8
Locked Candidates Type 2 (Claiming): 8 in r1 => r23c9<>8
Naked Pair: 4,6 in r68c5 => r3c5<>4
Naked Triple: 4,7,9 in r1c467 => r1c8<>9, r1c9<>4
Remote Pair: 6/4 r6c8 -4- r6c5 -6- r8c5 -4- r9c6 => r9c8<>6
Naked Single: r9c8=8
Naked Single: r1c8=3
Naked Single: r1c9=8
Hidden Single: r8c3=8
Naked Single: r6c3=7
Naked Single: r6c2=8
Hidden Single: r4c9=3
Locked Pair: 3,9 in r23c3 => r23c1,r4c3<>9, r3c2,r7c3<>3
Naked Single: r3c2=7
Full House: r7c2=3
Hidden Single: r4c1=9
Hidden Single: r7c1=7
Hidden Single: r1c6=7
Naked Pair: 4,6 in r3c69 => r3c47<>4, r3c4<>6
Remote Pair: 4/6 r3c9 -6- r3c6 -4- r9c6 -6- r9c1 -4- r7c3 -6- r7c7 => r1c7,r8c9<>4, r2c7,r8c9<>6
Naked Single: r1c7=9
Full House: r1c4=4
Naked Single: r8c9=7
Naked Single: r3c6=6
Full House: r9c6=4
Full House: r8c5=6
Full House: r9c1=6
Full House: r7c3=4
Full House: r7c7=6
Naked Single: r5c4=6
Full House: r6c5=4
Full House: r5c1=4
Full House: r4c3=6
Full House: r6c8=6
Naked Single: r2c9=6
Full House: r3c9=4
Naked Single: r8c7=4
Full House: r8c8=9
Naked Single: r2c8=5
Full House: r4c8=4
Full House: r4c7=5
Naked Single: r2c4=9
Full House: r3c4=5
Naked Single: r3c7=1
Full House: r2c7=7
Naked Single: r2c3=3
Full House: r3c3=9
Naked Single: r3c1=8
Full House: r2c1=1
Full House: r2c5=8
Full House: r3c5=3
|
normal_sudoku_3237 | 9.524867..27.9.8456......92....627.9.927..4687.64.952.2......54.7..24..6.....32.7 | 915248673327691845648357192854162739192735468736489521281976354573824916469513287 | normal_sudoku_3237 | 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 2 4 8 6 7 .
. 2 7 . 9 . 8 4 5
6 . . . . . . 9 2
. . . . 6 2 7 . 9
. 9 2 7 . . 4 6 8
7 . 6 4 . 9 5 2 .
2 . . . . . . 5 4
. 7 . . 2 4 . . 6
. . . . . 3 2 . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 915248673327691845648357192854162739192735468736489521281976354573824916469513287 #1 Hard (836)
Naked Pair: 1,3 in r1c2,r2c1 => r3c23<>1, r3c23<>3
Remote Pair: 1/3 r1c2 -3- r1c9 -1- r6c9 -3- r4c8 => r4c2<>1, r4c2<>3
Skyscraper: 3 in r2c4,r5c5 (connected by r25c1) => r3c5,r4c4<>3
2-String Kite: 5 in r4c2,r8c4 (connected by r8c1,r9c2) => r4c4<>5
Locked Candidates Type 1 (Pointing): 5 in b5 => r5c1<>5
Naked Pair: 1,3 in r25c1 => r489c1<>1, r48c1<>3
Remote Pair: 1/3 r4c8 -3- r6c9 -1- r1c9 -3- r1c2 -1- r2c1 -3- r5c1 => r4c3<>1, r4c3<>3
Hidden Single: r4c8=3
Full House: r6c9=1
Full House: r1c9=3
Full House: r1c2=1
Full House: r3c7=1
Naked Single: r2c1=3
Naked Single: r5c1=1
Naked Single: r5c6=5
Full House: r5c5=3
Naked Single: r3c6=7
Naked Single: r6c5=8
Full House: r4c4=1
Full House: r6c2=3
Naked Single: r3c5=5
Naked Single: r2c4=6
Full House: r2c6=1
Full House: r3c4=3
Full House: r7c6=6
Naked Single: r9c5=1
Full House: r7c5=7
Naked Single: r7c2=8
Naked Single: r9c8=8
Full House: r8c8=1
Naked Single: r3c2=4
Full House: r3c3=8
Naked Single: r7c4=9
Naked Single: r8c1=5
Naked Single: r4c2=5
Full House: r9c2=6
Naked Single: r4c3=4
Full House: r4c1=8
Full House: r9c1=4
Naked Single: r7c7=3
Full House: r7c3=1
Full House: r8c7=9
Naked Single: r9c4=5
Full House: r8c4=8
Full House: r9c3=9
Full House: r8c3=3
|
normal_sudoku_6744 | ..36..985489235761..58974..25....1..9317...488..1..3...9.3.......84..2..3.257.8.. | 723641985489235761615897423254983176931762548876154392197328654568419237342576819 | normal_sudoku_6744 | 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 . . 9 8 5
4 8 9 2 3 5 7 6 1
. . 5 8 9 7 4 . .
2 5 . . . . 1 . .
9 3 1 7 . . . 4 8
8 . . 1 . . 3 . .
. 9 . 3 . . . . .
. . 8 4 . . 2 . .
3 . 2 5 7 . 8 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 723641985489235761615897423254983176931762548876154392197328654568419237342576819 #1 Easy (160)
Full House: r4c4=9
Naked Single: r4c8=7
Naked Single: r4c9=6
Naked Single: r4c3=4
Naked Single: r5c7=5
Full House: r7c7=6
Naked Single: r4c5=8
Full House: r4c6=3
Naked Single: r7c3=7
Full House: r6c3=6
Full House: r6c2=7
Naked Single: r7c9=4
Naked Single: r9c9=9
Naked Single: r6c9=2
Full House: r6c8=9
Naked Single: r9c8=1
Naked Single: r3c9=3
Full House: r3c8=2
Full House: r8c9=7
Naked Single: r6c6=4
Full House: r6c5=5
Naked Single: r7c8=5
Full House: r8c8=3
Naked Single: r9c6=6
Full House: r9c2=4
Naked Single: r1c6=1
Full House: r1c5=4
Naked Single: r7c1=1
Naked Single: r5c6=2
Full House: r5c5=6
Naked Single: r8c5=1
Full House: r7c5=2
Full House: r7c6=8
Full House: r8c6=9
Naked Single: r1c1=7
Full House: r1c2=2
Naked Single: r3c1=6
Full House: r3c2=1
Full House: r8c2=6
Full House: r8c1=5
|
normal_sudoku_3740 | 9..725....4..1......5.34.2..5918.342.......5...3...6.8.7.49.1..198.6..3...4..12.9 | 931725864247618593685934721759186342816342957423579618572493186198267435364851279 | normal_sudoku_3740 | 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 . . 7 2 5 . . .
. 4 . . 1 . . . .
. . 5 . 3 4 . 2 .
. 5 9 1 8 . 3 4 2
. . . . . . . 5 .
. . 3 . . . 6 . 8
. 7 . 4 9 . 1 . .
1 9 8 . 6 . . 3 .
. . 4 . . 1 2 . 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 931725864247618593685934721759186342816342957423579618572493186198267435364851279 #1 Hard (718)
Locked Candidates Type 1 (Pointing): 2 in b7 => r7c6<>2
Locked Candidates Type 1 (Pointing): 8 in b9 => r12c8<>8
Locked Candidates Type 2 (Claiming): 2 in c2 => r5c13,r6c1<>2
Naked Pair: 1,6 in r1c38 => r1c29<>1, r1c29<>6
Naked Triple: 2,5,7 in r8c46,r9c5 => r9c4<>5
Hidden Triple: 2,3,5 in r279c1 => r279c1<>6, r2c1<>7, r2c1<>8
Skyscraper: 1 in r1c3,r6c2 (connected by r16c8) => r3c2,r5c3<>1
Hidden Single: r3c9=1
Naked Single: r1c8=6
Naked Single: r5c9=7
Naked Single: r1c3=1
Naked Single: r7c8=8
Naked Single: r5c3=6
Naked Single: r5c5=4
Naked Single: r5c7=9
Full House: r6c8=1
Naked Single: r7c6=3
Naked Single: r9c8=7
Full House: r2c8=9
Naked Single: r4c1=7
Full House: r4c6=6
Naked Single: r7c3=2
Full House: r2c3=7
Naked Single: r5c1=8
Naked Single: r6c2=2
Naked Single: r5c6=2
Naked Single: r9c4=8
Naked Single: r9c5=5
Full House: r6c5=7
Naked Single: r6c1=4
Full House: r5c2=1
Full House: r5c4=3
Naked Single: r2c6=8
Naked Single: r7c1=5
Full House: r7c9=6
Naked Single: r3c1=6
Naked Single: r8c6=7
Full House: r8c4=2
Full House: r6c6=9
Full House: r6c4=5
Naked Single: r2c4=6
Full House: r3c4=9
Naked Single: r9c1=3
Full House: r2c1=2
Full House: r9c2=6
Naked Single: r2c7=5
Full House: r2c9=3
Naked Single: r3c2=8
Full House: r1c2=3
Full House: r3c7=7
Naked Single: r8c7=4
Full House: r1c7=8
Full House: r1c9=4
Full House: r8c9=5
|
normal_sudoku_2867 | 4369872519712.3.6.285..1..3..3.9..2...4.2...7....36.4.6.75...8.54.3.....31...2..5 | 436987251971253864285641793753498126864125937192736548627514389548379612319862475 | normal_sudoku_2867 | 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 6 9 8 7 2 5 1
9 7 1 2 . 3 . 6 .
2 8 5 . . 1 . . 3
. . 3 . 9 . . 2 .
. . 4 . 2 . . . 7
. . . . 3 6 . 4 .
6 . 7 5 . . . 8 .
5 4 . 3 . . . . .
3 1 . . . 2 . . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 436987251971253864285641793753498126864125937192736548627514389548379612319862475 #1 Medium (534)
Hidden Single: r2c5=5
Hidden Single: r7c7=3
Hidden Single: r5c8=3
Hidden Single: r7c5=1
Hidden Single: r8c8=1
Locked Candidates Type 1 (Pointing): 4 in b2 => r3c7<>4
Locked Candidates Type 1 (Pointing): 7 in b5 => r9c4<>7
Locked Candidates Type 1 (Pointing): 8 in b7 => r6c3<>8
Naked Pair: 1,8 in r5c14 => r5c67<>8, r5c7<>1
Naked Single: r5c6=5
Naked Triple: 6,8,9 in r46c9,r5c7 => r4c7<>6, r46c7<>8, r6c7<>9
Hidden Single: r2c7=8
Full House: r2c9=4
Hidden Single: r9c7=4
Hidden Single: r7c6=4
Naked Single: r4c6=8
Full House: r8c6=9
Naked Single: r4c9=6
Naked Single: r5c4=1
Naked Single: r4c2=5
Naked Single: r5c7=9
Naked Single: r8c9=2
Naked Single: r5c1=8
Full House: r5c2=6
Naked Single: r6c4=7
Full House: r4c4=4
Naked Single: r4c7=1
Full House: r4c1=7
Full House: r6c1=1
Naked Single: r3c7=7
Full House: r3c8=9
Full House: r9c8=7
Naked Single: r6c9=8
Full House: r7c9=9
Full House: r6c7=5
Full House: r8c7=6
Full House: r7c2=2
Full House: r6c2=9
Full House: r6c3=2
Naked Single: r8c3=8
Full House: r8c5=7
Full House: r9c3=9
Naked Single: r3c4=6
Full House: r3c5=4
Full House: r9c5=6
Full House: r9c4=8
|
normal_sudoku_1398 | .79..4....6.2..9..8..963..76..43...145....2.....6.5.4.7..3..1...8.74269393651.... | 279154836365287914814963527628439751453871269197625348742396185581742693936518472 | normal_sudoku_1398 | 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 . . 4 . . .
. 6 . 2 . . 9 . .
8 . . 9 6 3 . . 7
6 . . 4 3 . . . 1
4 5 . . . . 2 . .
. . . 6 . 5 . 4 .
7 . . 3 . . 1 . .
. 8 . 7 4 2 6 9 3
9 3 6 5 1 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 279154836365287914814963527628439751453871269197625348742396185581742693936518472 #1 Easy (250)
Naked Single: r9c6=8
Naked Single: r7c5=9
Full House: r7c6=6
Hidden Single: r6c5=2
Hidden Single: r1c1=2
Hidden Single: r3c8=2
Naked Single: r9c8=7
Naked Single: r9c7=4
Full House: r9c9=2
Naked Single: r3c7=5
Hidden Single: r2c9=4
Hidden Single: r1c5=5
Hidden Single: r7c9=5
Full House: r7c8=8
Naked Single: r4c8=5
Hidden Single: r2c5=8
Full House: r5c5=7
Naked Single: r1c4=1
Full House: r2c6=7
Full House: r5c4=8
Naked Single: r4c6=9
Full House: r5c6=1
Naked Single: r4c2=2
Naked Single: r5c3=3
Naked Single: r7c2=4
Full House: r7c3=2
Naked Single: r5c8=6
Full House: r5c9=9
Naked Single: r6c1=1
Naked Single: r3c2=1
Full House: r6c2=9
Full House: r3c3=4
Naked Single: r1c8=3
Full House: r2c8=1
Naked Single: r6c9=8
Full House: r1c9=6
Full House: r1c7=8
Naked Single: r8c1=5
Full House: r2c1=3
Full House: r2c3=5
Full House: r8c3=1
Naked Single: r4c7=7
Full House: r4c3=8
Full House: r6c3=7
Full House: r6c7=3
|
normal_sudoku_1227 | ...1.7........21.9143958627...86.91..1879..32...21..6...4.2..9.9...862.1....79.56 | 296147385587632149143958627372865914618794532459213768764521893935486271821379456 | normal_sudoku_1227 | 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 . 7 . . .
. . . . . 2 1 . 9
1 4 3 9 5 8 6 2 7
. . . 8 6 . 9 1 .
. 1 8 7 9 . . 3 2
. . . 2 1 . . 6 .
. . 4 . 2 . . 9 .
9 . . . 8 6 2 . 1
. . . . 7 9 . 5 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 296147385587632149143958627372865914618794532459213768764521893935486271821379456 #1 Easy (228)
Hidden Single: r2c4=6
Hidden Single: r5c1=6
Hidden Single: r6c7=7
Hidden Single: r7c6=1
Hidden Single: r9c3=1
Hidden Single: r8c8=7
Naked Single: r8c3=5
Naked Single: r2c3=7
Naked Single: r6c3=9
Naked Single: r8c2=3
Full House: r8c4=4
Naked Single: r4c3=2
Full House: r1c3=6
Naked Single: r6c2=5
Naked Single: r9c4=3
Full House: r7c4=5
Naked Single: r2c2=8
Naked Single: r4c2=7
Naked Single: r2c1=5
Naked Single: r2c8=4
Full House: r1c8=8
Full House: r2c5=3
Full House: r1c5=4
Naked Single: r9c2=2
Naked Single: r7c2=6
Full House: r1c2=9
Full House: r1c1=2
Naked Single: r9c1=8
Full House: r7c1=7
Full House: r9c7=4
Naked Single: r5c7=5
Full House: r5c6=4
Naked Single: r1c7=3
Full House: r1c9=5
Full House: r7c7=8
Full House: r7c9=3
Naked Single: r4c9=4
Full House: r6c9=8
Naked Single: r6c6=3
Full House: r4c6=5
Full House: r4c1=3
Full House: r6c1=4
|
normal_sudoku_3737 | ..6....29.3.62.48.2.49.83.6...4.68.26.289.134.4831269...72....8..1......4...8..6. | 786143529935627481214958376193476852672895134548312697357264918861739245429581763 | normal_sudoku_3737 | 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 9
. 3 . 6 2 . 4 8 .
2 . 4 9 . 8 3 . 6
. . . 4 . 6 8 . 2
6 . 2 8 9 . 1 3 4
. 4 8 3 1 2 6 9 .
. . 7 2 . . . . 8
. . 1 . . . . . .
4 . . . 8 . . 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 786143529935627481214958376193476852672895134548312697357264918861739245429581763 #1 Hard (808)
Naked Pair: 5,7 in r5c2,r6c1 => r4c123<>5, r4c12<>7
Naked Pair: 5,7 in r34c5 => r178c5<>5, r18c5<>7
Naked Triple: 1,5,7 in r1c4,r2c6,r3c5 => r1c6<>1, r1c6<>5, r1c6<>7
Remote Pair: 5/7 r3c5 -7- r4c5 -5- r5c6 -7- r5c2 => r3c2<>5, r3c2<>7
Naked Single: r3c2=1
Naked Single: r4c2=9
Naked Single: r4c3=3
Naked Single: r4c1=1
Hidden Single: r1c4=1
Hidden Single: r7c8=1
Hidden Single: r2c9=1
Hidden Single: r9c6=1
Hidden Single: r8c8=4
Hidden Single: r9c9=3
Locked Candidates Type 2 (Claiming): 5 in c4 => r78c6<>5
Locked Candidates Type 2 (Claiming): 7 in c4 => r8c6<>7
Naked Pair: 5,7 in r8c49 => r8c127<>5, r8c7<>7
Remote Pair: 5/7 r1c7 -7- r3c8 -5- r3c5 -7- r2c6 -5- r5c6 -7- r4c5 -5- r4c8 -7- r6c9 -5- r6c1 -7- r5c2 => r1c2,r2c1<>5, r1c2,r2c1<>7
Naked Single: r1c2=8
Naked Single: r2c1=9
Naked Single: r2c3=5
Full House: r1c1=7
Full House: r2c6=7
Full House: r9c3=9
Naked Single: r1c7=5
Full House: r3c8=7
Full House: r3c5=5
Full House: r4c8=5
Full House: r4c5=7
Full House: r5c6=5
Full House: r6c9=7
Full House: r6c1=5
Full House: r5c2=7
Full House: r8c9=5
Naked Single: r7c7=9
Naked Single: r7c1=3
Full House: r8c1=8
Naked Single: r8c4=7
Full House: r9c4=5
Naked Single: r8c7=2
Full House: r9c7=7
Full House: r9c2=2
Naked Single: r7c6=4
Naked Single: r8c2=6
Full House: r7c2=5
Full House: r7c5=6
Naked Single: r1c6=3
Full House: r1c5=4
Full House: r8c5=3
Full House: r8c6=9
|
normal_sudoku_2052 | .7.38...23....5.......9....5.6..3..7734..9..8.2.47.5.....9.78.5..7..12.4.5..4..7. | 679384152342165789815792346596813427734259618128476593461927835987531264253648971 | normal_sudoku_2052 | 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 . . . 2
3 . . . . 5 . . .
. . . . 9 . . . .
5 . 6 . . 3 . . 7
7 3 4 . . 9 . . 8
. 2 . 4 7 . 5 . .
. . . 9 . 7 8 . 5
. . 7 . . 1 2 . 4
. 5 . . 4 . . 7 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 679384152342165789815792346596813427734259618128476593461927835987531264253648971 #1 Extreme (14918)
Empty Rectangle: 2 in b1 (r39c6) => r9c3<>2
Grouped Discontinuous Nice Loop: 8 r9c3 -8- r8c12 =8= r8c4 =5= r8c5 =3= r8c8 -3- r9c79 =3= r9c3 => r9c3<>8
Forcing Chain Verity => r3c3<>2
r2c3=8 r2c8<>8 r3c8=8 r3c8<>5 r3c3=5 r3c3<>2
r3c3=8 r3c3<>2
r6c3=8 r6c6<>8 r9c6=8 r9c6<>2 r3c6=2 r3c3<>2
Grouped Discontinuous Nice Loop: 1 r2c3 -1- r2c45 =1= r3c4 =7= r3c7 =3= r9c7 -3- r9c3 =3= r7c3 =2= r2c3 => r2c3<>1
Forcing Net Contradiction in b3 => r2c7<>1
r2c7=1 (r1c7<>1) r5c7<>1 r5c7=6 (r1c7<>6) (r6c8<>6) r6c9<>6 r6c6=6 r1c6<>6 r1c6=4 r1c7<>4 r1c7=9
r2c7=1 (r2c9<>1) (r2c7<>7 r2c4=7 r2c4<>6) (r2c5<>1 r3c4=1 r3c4<>6) r5c7<>1 r5c7=6 (r6c8<>6) r6c9<>6 r6c6=6 (r1c6<>6) r3c6<>6 r2c5=6 r2c9<>6 r2c9=9
Forcing Net Contradiction in c9 => r3c4<>2
r3c4=2 (r3c4<>1) r3c4<>7 r3c7=7 r2c7<>7 r2c4=7 r2c4<>1 r2c5=1 r2c9<>1
r3c4=2 (r3c4<>7 r3c7=7 r2c7<>7 r2c4=7 r2c4<>1 r2c5=1 r2c2<>1) (r2c5<>2 r2c3=2 r7c3<>2) r3c6<>2 r9c6=2 (r9c6<>8 r6c6=8 r4c4<>8 r4c4=1 r4c2<>1) r7c5<>2 r7c1=2 r7c1<>4 r7c2=4 r7c2<>1 r3c2=1 r3c9<>1
r3c4=2 (r3c4<>7 r3c7=7 r2c7<>7 r2c4=7 r2c4<>1 r2c5=1 r5c5<>1) (r5c4<>2) (r4c4<>2) r3c6<>2 r9c6=2 r9c6<>8 r6c6=8 r4c4<>8 r4c4=1 (r5c4<>1) r4c5<>1 r4c5=2 r5c5<>2 r5c8=2 r5c8<>1 r5c7=1 r6c9<>1
r3c4=2 (r3c6<>2 r9c6=2 r7c5<>2 r7c1=2 r7c1<>1) (r3c6<>2 r9c6=2 r7c5<>2 r7c1=2 r7c1<>4 r7c2=4 r7c2<>1) r3c4<>7 r3c7=7 r3c7<>3 r9c7=3 (r7c8<>3) r8c8<>3 r8c5=3 r7c5<>3 r7c3=3 r7c3<>1 r7c8=1 r9c9<>1
Forcing Net Contradiction in c8 => r1c8<>4
r1c8=4 r1c8<>1
r1c8=4 r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>8 r2c8=8 r2c8<>1
r1c8=4 r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>1
r1c8=4 (r4c8<>4 r4c7=4 r4c7<>9) r1c6<>4 r1c6=6 r6c6<>6 r6c6=8 r4c4<>8 r4c2=8 r4c2<>9 r4c8=9 r4c8<>1
r1c8=4 r1c6<>4 r1c6=6 r6c6<>6 r5c45=6 r5c7<>6 r5c7=1 r5c8<>1
r1c8=4 (r1c6<>4 r1c6=6 r6c6<>6 r6c6=8 r6c3<>8) (r1c6<>4 r3c6=4 r3c6<>2 r3c1=2 r2c3<>2) r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>8 r2c8=8 r2c3<>8 r2c3=9 r6c3<>9 r6c3=1 r6c8<>1
r1c8=4 (r2c8<>4 r2c2=4 r7c2<>4) (r2c8<>4 r2c2=4 r2c2<>6) r1c6<>4 (r1c6=6 r1c1<>6) r3c6=4 r3c6<>2 r3c1=2 r3c1<>6 r3c2=6 r7c2<>6 r7c2=1 r7c8<>1
Forcing Net Contradiction in b1 => r4c7<>1
r4c7=1 (r1c7<>1) r5c7<>1 r5c7=6 (r1c7<>6) (r6c8<>6) r6c9<>6 r6c6=6 r1c6<>6 r1c6=4 r1c7<>4 r1c7=9 r1c1<>9
r4c7=1 (r1c7<>1) r5c7<>1 r5c7=6 (r1c7<>6) (r6c8<>6) r6c9<>6 r6c6=6 r1c6<>6 r1c6=4 r1c7<>4 r1c7=9 r1c3<>9
r4c7=1 (r4c7<>9) r4c7<>4 r4c8=4 r4c8<>9 r4c2=9 r2c2<>9
r4c7=1 (r4c4<>1) r4c5<>1 r4c5=2 r4c4<>2 r4c4=8 r6c6<>8 r9c6=8 r9c6<>2 r3c6=2 (r2c4<>2) r2c5<>2 r2c3=2 r2c3<>9
Forcing Net Contradiction in b9 => r1c7<>4
r1c7=4 (r2c8<>4 r2c2=4 r7c2<>4) (r2c8<>4 r2c2=4 r2c2<>6) r1c6<>4 (r1c6=6 r1c1<>6) r3c6=4 r3c6<>2 r3c1=2 r3c1<>6 r3c2=6 r7c2<>6 r7c2=1 r7c8<>1
r1c7=4 r1c6<>4 r1c6=6 r6c6<>6 r5c45=6 r5c7<>6 r5c7=1 r9c7<>1
r1c7=4 (r4c7<>4 r4c7=9 r9c7<>9) (r4c7<>4 r4c7=9 r4c2<>9) (r2c7<>4) r2c8<>4 r2c2=4 r2c2<>9 r8c2=9 (r9c1<>9) r9c3<>9 r9c9=9 r9c9<>1
Forcing Net Contradiction in r4 => r2c3<>9
r2c3=9 r2c3<>2 r7c3=2 r7c3<>3 r9c3=3 r9c7<>3 r3c7=3 (r3c7<>4) r3c7<>7 r3c4=7 r2c4<>7 r2c7=7 r2c7<>4 r4c7=4
r2c3=9 (r2c3<>8) r2c3<>2 r7c3=2 (r7c1<>2) r9c1<>2 r3c1=2 r3c6<>2 r9c6=2 r9c6<>8 r6c6=8 r6c3<>8 r3c3=8 (r2c3<>8 r2c8=8 r2c8<>4) r3c3<>5 r3c8=5 r3c8<>4 r4c8=4
Forcing Net Contradiction in r2 => r2c7<>6
r2c7=6 r2c7<>7 r2c4=7 r2c4<>2 r2c3=2
r2c7=6 (r2c5<>6) (r2c9<>6) (r1c7<>6) r5c7<>6 r5c7=1 r1c7<>1 r1c7=9 r2c9<>9 r2c9=1 r2c5<>1 r2c5=2
Forcing Net Contradiction in c2 => r2c8<>1
r2c8=1 (r2c8<>9) (r2c8<>4) r2c8<>8 r3c8=8 (r3c3<>8 r3c3=5 r1c3<>5 r1c8=5 r1c8<>9) r3c8<>4 r4c8=4 r4c7<>4 r4c7=9 (r1c7<>9) r2c7<>9 r2c9=9 r2c2<>9
r2c8=1 (r2c8<>4) r2c8<>8 r3c8=8 r3c8<>4 r4c8=4 r4c7<>4 r4c7=9 r4c2<>9
r2c8=1 (r2c8<>9) (r2c8<>4) r2c8<>8 r3c8=8 (r3c3<>8 r3c3=5 r1c3<>5 r1c8=5 r1c8<>9) r3c8<>4 r4c8=4 (r4c8<>9) r4c7<>4 r4c7=9 r6c8<>9 r8c8=9 r8c2<>9
Forcing Net Contradiction in c2 => r2c8<>6
r2c8=6 (r2c8<>9) (r2c8<>4) r2c8<>8 r3c8=8 (r3c8<>5 r3c3=5 r1c3<>5 r1c8=5 r1c8<>9) r3c8<>4 r4c8=4 r4c7<>4 r4c7=9 (r1c7<>9) r2c7<>9 r2c9=9 r2c2<>9
r2c8=6 (r2c8<>4) r2c8<>8 r3c8=8 r3c8<>4 r4c8=4 r4c7<>4 r4c7=9 r4c2<>9
r2c8=6 (r2c8<>9) (r2c8<>4) r2c8<>8 r3c8=8 (r3c8<>5 r3c3=5 r1c3<>5 r1c8=5 r1c8<>9) r3c8<>4 r4c8=4 (r4c8<>9) r4c7<>4 r4c7=9 r6c8<>9 r8c8=9 r8c2<>9
Forcing Net Contradiction in c2 => r2c9<>1
r2c9=1 r2c2<>1
r2c9=1 (r2c4<>1) r2c5<>1 r3c4=1 r3c2<>1
r2c9=1 (r1c7<>1) (r3c7<>1) (r2c4<>1) r2c5<>1 r3c4=1 r3c4<>7 r3c7=7 r3c7<>3 r9c7=3 r9c7<>1 r5c7=1 r5c45<>1 r4c45=1 r4c2<>1
r2c9=1 (r1c8<>1) (r3c8<>1) (r1c7<>1) (r3c7<>1) (r2c4<>1) r2c5<>1 r3c4=1 r3c4<>7 r3c7=7 r3c7<>3 r9c7=3 r9c7<>1 r5c7=1 (r4c8<>1) (r5c8<>1) r6c8<>1 r7c8=1 r7c2<>1
XYZ-Wing: 1/6/9 in r15c7,r2c9 => r3c7<>6
Forcing Net Contradiction in r3 => r1c8<>9
r1c8=9 (r1c7<>9) r2c9<>9 (r2c2=9 r4c2<>9 r4c7=9 r6c9<>9) r2c9=6 (r6c9<>6) (r3c9<>6) r1c7<>6 r1c7=1 (r5c7<>1 r5c7=6 r6c9<>6 r6c6=6 r6c6<>8 r9c6=8 r9c4<>8) r3c9<>1 r3c9=3 r6c9<>3 r6c9=1 (r6c3<>1 r4c2=1 r4c5<>1 r4c5=2 r7c5<>2) r6c9<>3 r6c8=3 r8c8<>3 r8c5=3 r7c5<>3 r7c5=6 (r7c2<>6 r7c2=4 r7c1<>4) r9c4<>6 r9c4=2 r9c6<>2 r3c6=2 r3c6<>4 r1c6=4 r1c1<>4 r3c1=4 r3c1<>1
r1c8=9 (r1c7<>9) r2c9<>9 (r2c2=9 r4c2<>9 r4c7=9 r6c9<>9) r2c9=6 (r6c9<>6) (r3c9<>6) r1c7<>6 r1c7=1 r3c9<>1 r3c9=3 r6c9<>3 r6c9=1 (r6c1<>1) r6c3<>1 r4c2=1 r3c2<>1
r1c8=9 (r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>8 r2c8=8 r2c3<>8) (r6c8<>9) (r8c8<>9) (r2c7<>9) (r2c8<>9) r2c9<>9 r2c2=9 (r4c2<>9 r4c7=9 r6c9<>9) r8c2<>9 r8c1=9 r6c1<>9 r6c3=9 r6c3<>8 r3c3=8 r3c3<>1
r1c8=9 (r2c9<>9 r2c9=6 r2c5<>6) r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>8 r2c8=8 r2c3<>8 r2c3=2 r2c5<>2 r2c5=1 r3c4<>1
r1c8=9 (r1c7<>9) r2c9<>9 r2c9=6 r1c7<>6 r1c7=1 r3c7<>1
r1c8=9 r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 r3c8<>1
r1c8=9 (r1c7<>9) r2c9<>9 r2c9=6 r1c7<>6 r1c7=1 r3c9<>1
Forcing Net Contradiction in c2 => r1c8=5
r1c8<>5 r1c3=5 (r1c3<>9) r3c3<>5 r3c8=5 (r3c8<>4) r3c8<>8 r2c8=8 r2c8<>4 r4c8=4 r4c7<>4 r4c7=9 r1c7<>9 r1c1=9 r2c2<>9
r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 (r3c8<>4) r3c8<>8 r2c8=8 r2c8<>4 r4c8=4 r4c7<>4 r4c7=9 r4c2<>9
r1c8<>5 r1c3=5 r3c3<>5 r3c8=5 (r3c8<>4) r3c8<>8 r2c8=8 (r2c8<>9) r2c8<>4 r4c8=4 (r4c8<>9) r4c7<>4 r4c7=9 r6c8<>9 r8c8=9 r8c2<>9
Hidden Single: r3c3=5
Continuous Nice Loop: 6/8 8= r9c6 =2= r3c6 -2- r3c1 =2= r2c3 =8= r6c3 -8- r6c6 =8= r9c6 =2 => r9c6<>6, r6c1<>8
Grouped Discontinuous Nice Loop: 6 r6c9 -6- r6c6 -8- r6c3 =8= r2c3 =2= r7c3 =3= r9c3 -3- r9c79 =3= r78c8 -3- r6c8 =3= r6c9 => r6c9<>6
Forcing Chain Contradiction in c2 => r1c6=4
r1c6<>4 r1c6=6 r6c6<>6 r6c8=6 r5c7<>6 r5c7=1 r1c7<>1 r1c13=1 r2c2<>1
r1c6<>4 r1c6=6 r6c6<>6 r6c8=6 r5c7<>6 r5c7=1 r1c7<>1 r1c13=1 r3c2<>1
r1c6<>4 r1c6=6 r6c6<>6 r6c6=8 r6c3<>8 r4c2=8 r4c2<>1
r1c6<>4 r1c1=4 r7c1<>4 r7c2=4 r7c2<>1
Grouped Discontinuous Nice Loop: 6 r9c1 -6- r9c9 =6= r23c9 -6- r1c7 =6= r1c1 -6- r9c1 => r9c1<>6
Forcing Chain Contradiction in r9 => r1c1<>9
r1c1=9 r6c1<>9 r6c1=1 r9c1<>1
r1c1=9 r1c3<>9 r1c3=1 r9c3<>1
r1c1=9 r1c1<>6 r1c7=6 r5c7<>6 r5c7=1 r9c7<>1
r1c1=9 r1c1<>6 r1c7=6 r23c9<>6 r9c9=6 r9c9<>1
Finned Franken Swordfish: 9 c19b1 r269 fr1c3 fr8c1 => r9c3<>9
Almost Locked Set XZ-Rule: A=r1689c1 {12689}, B=r79c3 {123}, X=2, Z=1 => r7c1<>1
Almost Locked Set Chain: 1- r5c7 {16} -6- r6c1389 {13689} -8- r1279c3 {12389} -9- r15c7 {169} -1 => r39c7<>1
Forcing Chain Contradiction in c2 => r1c1=6
r1c1<>6 r1c1=1 r2c2<>1
r1c1<>6 r1c1=1 r3c2<>1
r1c1<>6 r1c1=1 r1c7<>1 r5c7=1 r5c45<>1 r4c45=1 r4c2<>1
r1c1<>6 r1c7=6 r23c9<>6 r9c9=6 r9c9<>1 r7c8=1 r7c2<>1
Continuous Nice Loop: 1/6 9= r6c3 =8= r6c6 =6= r6c8 -6- r5c7 -1- r1c7 -9- r1c3 =9= r6c3 =8 => r6c3<>1, r5c8<>6
Discontinuous Nice Loop: 1 r3c8 -1- r1c7 -9- r1c3 =9= r6c3 =8= r2c3 -8- r2c8 =8= r3c8 => r3c8<>1
Grouped Discontinuous Nice Loop: 1 r7c2 -1- r7c8 =1= r9c9 -1- r3c9 =1= r1c7 -1- r1c3 =1= r79c3 -1- r7c2 => r7c2<>1
Sashimi Jellyfish: 1 r1679 c1389 fr1c7 => r3c9<>1
Hidden Single: r1c7=1
Full House: r1c3=9
Naked Single: r5c7=6
Naked Single: r6c3=8
Naked Single: r2c3=2
Naked Single: r6c6=6
Naked Single: r3c6=2
Full House: r9c6=8
Hidden Single: r4c4=8
Locked Candidates Type 2 (Claiming): 1 in c3 => r9c1<>1
Empty Rectangle: 6 in b2 (r9c49) => r2c9<>6
Naked Single: r2c9=9
Locked Candidates Type 1 (Pointing): 6 in b3 => r3c4<>6
Skyscraper: 9 in r6c8,r9c7 (connected by r69c1) => r4c7,r8c8<>9
Naked Single: r4c7=4
Naked Single: r2c7=7
Naked Single: r3c7=3
Full House: r9c7=9
Naked Single: r3c9=6
Naked Single: r9c1=2
Naked Single: r7c1=4
Naked Single: r9c4=6
Naked Single: r7c2=6
Naked Single: r2c4=1
Naked Single: r8c4=5
Naked Single: r2c5=6
Full House: r3c4=7
Full House: r5c4=2
Naked Single: r8c5=3
Full House: r7c5=2
Naked Single: r4c5=1
Full House: r5c5=5
Full House: r5c8=1
Naked Single: r8c8=6
Naked Single: r4c2=9
Full House: r4c8=2
Full House: r6c1=1
Naked Single: r6c9=3
Full House: r6c8=9
Full House: r9c9=1
Full House: r7c8=3
Full House: r9c3=3
Full House: r7c3=1
Naked Single: r8c2=8
Full House: r8c1=9
Full House: r3c1=8
Naked Single: r2c2=4
Full House: r2c8=8
Full House: r3c8=4
Full House: r3c2=1
|
normal_sudoku_5781 | 5.2..9.8.7...8.4....12.5.393..7..5.11.4953.78.75.2.394..8.9...591.5..8..25....96. | 542379186793186452861245739389764521124953678675821394438697215916532847257418963 | normal_sudoku_5781 | 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 . . 9 . 8 .
7 . . . 8 . 4 . .
. . 1 2 . 5 . 3 9
3 . . 7 . . 5 . 1
1 . 4 9 5 3 . 7 8
. 7 5 . 2 . 3 9 4
. . 8 . 9 . . . 5
9 1 . 5 . . 8 . .
2 5 . . . . 9 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 542379186793186452861245739389764521124953678675821394438697215916532847257418963 #1 Easy (214)
Naked Single: r4c8=2
Full House: r5c7=6
Full House: r5c2=2
Naked Single: r8c8=4
Naked Single: r3c7=7
Naked Single: r7c8=1
Full House: r2c8=5
Naked Single: r1c7=1
Full House: r7c7=2
Naked Single: r1c9=6
Full House: r2c9=2
Hidden Single: r1c5=7
Hidden Single: r7c6=7
Hidden Single: r9c5=1
Hidden Single: r8c6=2
Hidden Single: r8c5=3
Naked Single: r8c9=7
Full House: r8c3=6
Full House: r9c9=3
Naked Single: r4c3=9
Naked Single: r7c1=4
Naked Single: r9c3=7
Full House: r2c3=3
Full House: r7c2=3
Full House: r7c4=6
Naked Single: r1c2=4
Full House: r1c4=3
Naked Single: r2c4=1
Naked Single: r2c6=6
Full House: r2c2=9
Full House: r3c5=4
Full House: r4c5=6
Naked Single: r6c4=8
Full House: r9c4=4
Full House: r9c6=8
Naked Single: r4c2=8
Full House: r4c6=4
Full House: r6c1=6
Full House: r6c6=1
Full House: r3c2=6
Full House: r3c1=8
|
normal_sudoku_4843 | 3.21...6.9.5....141.......221.8.745.4...1..2...6..41...24..169.59...2.416314..2.5 | 342158967965723814187946532213897456479615328856234179724581693598362741631479285 | normal_sudoku_4843 | 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 1 . . . 6 .
9 . 5 . . . . 1 4
1 . . . . . . . 2
2 1 . 8 . 7 4 5 .
4 . . . 1 . . 2 .
. . 6 . . 4 1 . .
. 2 4 . . 1 6 9 .
5 9 . . . 2 . 4 1
6 3 1 4 . . 2 . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 342158967965723814187946532213897456479615328856234179724581693598362741631479285 #1 Extreme (2928)
Naked Pair: 7,8 in r38c3 => r5c3<>7, r5c3<>8
Forcing Chain Contradiction in c8 => r3c5<>8
r3c5=8 r3c8<>8
r3c5=8 r3c3<>8 r8c3=8 r7c1<>8 r6c1=8 r6c8<>8
r3c5=8 r789c5<>8 r9c6=8 r9c8<>8
Forcing Chain Contradiction in r8c7 => r3c8<>7
r3c8=7 r3c8<>3 r23c7=3 r8c7<>3
r3c8=7 r3c3<>7 r8c3=7 r8c7<>7
r3c8=7 r9c8<>7 r9c8=8 r8c7<>8
Skyscraper: 7 in r7c1,r9c8 (connected by r6c18) => r7c9<>7
Grouped Discontinuous Nice Loop: 8 r8c5 -8- r8c3 -7- r8c7 =7= r9c8 =8= r9c56 -8- r8c5 => r8c5<>8
Almost Locked Set XY-Wing: A=r6c18 {378}, B=r123c2 {4678}, C=r3c38 {378}, X,Y=3,7, Z=8 => r6c2<>8
Forcing Chain Contradiction in r8c7 => r3c8=3
r3c8<>3 r23c7=3 r8c7<>3
r3c8<>3 r3c8=8 r9c8<>8 r9c8=7 r8c7<>7
r3c8<>3 r3c8=8 r3c3<>8 r8c3=8 r8c7<>8
Naked Pair: 7,8 in r6c18 => r6c29<>7, r6c9<>8
Naked Single: r6c2=5
Remote Pair: 8/7 r7c1 -7- r6c1 -8- r6c8 -7- r9c8 => r7c9<>8
Naked Single: r7c9=3
Naked Single: r6c9=9
Naked Single: r4c9=6
Hidden Single: r5c7=3
Naked Single: r5c3=9
Naked Single: r4c3=3
Full House: r4c5=9
Hidden Single: r2c6=3
Hidden Single: r3c4=9
Hidden Single: r9c6=9
Hidden Single: r1c7=9
Hidden Single: r3c7=5
Locked Candidates Type 1 (Pointing): 8 in b8 => r12c5<>8
Naked Pair: 7,8 in r8c37 => r8c45<>7
Remote Pair: 7/8 r2c7 -8- r1c9 -7- r5c9 -8- r5c2 -7- r6c1 -8- r6c8 -7- r9c8 -8- r9c5 => r2c25<>7, r2c2<>8
Naked Single: r2c2=6
Naked Single: r2c5=2
Naked Single: r2c4=7
Full House: r2c7=8
Full House: r1c9=7
Full House: r8c7=7
Full House: r5c9=8
Full House: r9c8=8
Full House: r6c8=7
Full House: r9c5=7
Naked Single: r6c5=3
Naked Single: r7c4=5
Naked Single: r8c3=8
Full House: r3c3=7
Full House: r7c1=7
Full House: r6c1=8
Full House: r5c2=7
Full House: r6c4=2
Full House: r7c5=8
Naked Single: r8c5=6
Full House: r8c4=3
Full House: r5c4=6
Full House: r5c6=5
Naked Single: r3c5=4
Full House: r1c5=5
Naked Single: r1c6=8
Full House: r1c2=4
Full House: r3c2=8
Full House: r3c6=6
|
normal_sudoku_192 | ......1.4.1.2.....4...5..78..9.......64719..27.1.8..6.5....7..6.4..3......38.5.4. | 375698124918274653426351978259463817864719532731582469582147396147936285693825741 | normal_sudoku_192 | 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
. 1 . 2 . . . . .
4 . . . 5 . . 7 8
. . 9 . . . . . .
. 6 4 7 1 9 . . 2
7 . 1 . 8 . . 6 .
5 . . . . 7 . . 6
. 4 . . 3 . . . .
. . 3 8 . 5 . 4 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 375698124918274653426351978259463817864719532731582469582147396147936285693825741 #1 Extreme (6904)
Locked Candidates Type 1 (Pointing): 5 in b4 => r1c2<>5
Locked Candidates Type 2 (Claiming): 5 in r5 => r4c789,r6c79<>5
Discontinuous Nice Loop: 6 r1c3 -6- r3c3 -2- r3c7 =2= r1c8 =5= r1c3 => r1c3<>6
Finned X-Wing: 6 r19 c15 fr1c4 fr1c6 => r2c5<>6
Discontinuous Nice Loop: 8 r1c3 -8- r1c6 =8= r2c6 =4= r2c5 =7= r2c3 =5= r1c3 => r1c3<>8
Discontinuous Nice Loop: 4 r6c6 -4- r6c7 =4= r4c7 =7= r4c9 =1= r4c8 -1- r7c8 =1= r7c4 =4= r7c5 -4- r2c5 =4= r2c6 -4- r6c6 => r6c6<>4
Grouped Discontinuous Nice Loop: 3 r2c1 -3- r2c9 =3= r46c9 -3- r5c78 =3= r5c1 -3- r2c1 => r2c1<>3
Grouped Discontinuous Nice Loop: 3 r3c7 -3- r7c7 =3= r7c8 =1= r7c4 =4= r7c5 -4- r2c5 =4= r2c6 =3= r2c789 -3- r3c7 => r3c7<>3
Almost Locked Set XZ-Rule: A=r1245c1 {23689}, B=r37c3 {268}, X=6, Z=8 => r8c1<>8
Forcing Chain Contradiction in r9c9 => r1c6=8
r1c6<>8 r2c6=8 r2c6<>4 r2c5=4 r7c5<>4 r7c4=4 r7c4<>1 r7c8=1 r9c9<>1
r1c6<>8 r2c6=8 r2c6<>4 r2c5=4 r2c5<>7 r2c3=7 r8c3<>7 r9c2=7 r9c9<>7
r1c6<>8 r2c6=8 r2c6<>4 r4c6=4 r4c7<>4 r6c7=4 r6c7<>9 r6c9=9 r9c9<>9
Discontinuous Nice Loop: 6 r2c1 -6- r3c3 -2- r7c3 -8- r2c3 =8= r2c1 => r2c1<>6
Almost Locked Set XY-Wing: A=r7c3 {28}, B=r245c1 {2389}, C=r2c356789 {3456789}, X,Y=8,9, Z=2 => r89c1<>2
Almost Locked Set XZ-Rule: A=r6c69 {239}, B=r8c146 {1269}, X=2, Z=9 => r8c9<>9
Forcing Chain Contradiction in r9c9 => r2c6=4
r2c6<>4 r2c5=4 r7c5<>4 r7c4=4 r7c4<>1 r7c8=1 r9c9<>1
r2c6<>4 r2c5=4 r2c5<>7 r2c3=7 r8c3<>7 r9c2=7 r9c9<>7
r2c6<>4 r4c6=4 r4c7<>4 r6c7=4 r6c7<>9 r6c9=9 r9c9<>9
Locked Candidates Type 2 (Claiming): 3 in r2 => r1c8<>3
Almost Locked Set XY-Wing: A=r3c3467 {12369}, B=r1245c1 {23689}, C=r1c45,r2c5 {3679}, X,Y=3,6, Z=9 => r3c2<>9
Almost Locked Set XY-Wing: A=r7c2378 {12389}, B=r12c5 {679}, C=r9c2579 {12679}, X,Y=1,6, Z=9 => r7c5<>9
Empty Rectangle: 9 in b8 (r3c47) => r9c7<>9
Discontinuous Nice Loop: 2 r1c2 -2- r1c8 =2= r3c7 -2- r9c7 -7- r9c2 =7= r1c2 => r1c2<>2
Discontinuous Nice Loop: 7 r1c3 -7- r1c2 =7= r9c2 -7- r9c7 -2- r3c7 =2= r1c8 =5= r1c3 => r1c3<>7
Grouped Discontinuous Nice Loop: 9 r9c9 -9- r9c5 =9= r78c4 -9- r3c4 =9= r3c7 -9- r6c7 =9= r6c9 -9- r9c9 => r9c9<>9
Grouped Discontinuous Nice Loop: 6 r3c6 =1= r3c4 -1- r7c4 =1= r7c8 -1- r9c9 -7- r9c2 =7= r8c3 =6= r89c1 -6- r1c1 =6= r1c45 -6- r3c6 => r3c6<>6
Almost Locked Set XZ-Rule: A=r9c1279 {12679}, B=r1245c1 {23689}, X=6, Z=9 => r8c1<>9
Finned X-Wing: 9 r38 c47 fr8c8 => r7c7<>9
Grouped AIC: 2 2- r4c1 =2= r1c1 -2- r1c8 =2= r3c7 =9= r3c4 -9- r78c4 =9= r9c5 -9- r9c12 =9= r7c2 =8= r4c2 =5= r6c2 =2= r6c6 -2 => r4c56,r6c2<>2
Hidden Single: r6c6=2
Naked Pair: 1,6 in r8c16 => r8c34<>6, r8c489<>1
Naked Single: r8c4=9
Hidden Single: r3c7=9
Hidden Single: r7c8=9
Hidden Single: r6c9=9
Hidden Single: r1c8=2
Naked Single: r1c3=5
Hidden Single: r2c7=6
Hidden Single: r7c4=1
Naked Single: r8c6=6
Naked Single: r4c6=3
Full House: r3c6=1
Naked Single: r8c1=1
Naked Single: r9c5=2
Full House: r7c5=4
Naked Single: r9c7=7
Naked Single: r4c5=6
Naked Single: r8c9=5
Naked Single: r9c2=9
Naked Single: r9c9=1
Full House: r9c1=6
Naked Single: r2c9=3
Full House: r4c9=7
Full House: r2c8=5
Naked Single: r8c8=8
Naked Single: r4c8=1
Full House: r5c8=3
Naked Single: r8c7=2
Full House: r7c7=3
Full House: r8c3=7
Naked Single: r5c1=8
Full House: r5c7=5
Naked Single: r6c7=4
Full House: r4c7=8
Naked Single: r2c3=8
Naked Single: r2c1=9
Full House: r2c5=7
Full House: r1c5=9
Naked Single: r4c1=2
Full House: r1c1=3
Naked Single: r6c4=5
Full House: r4c4=4
Full House: r4c2=5
Full House: r6c2=3
Naked Single: r7c3=2
Full House: r3c3=6
Full House: r7c2=8
Naked Single: r1c2=7
Full House: r1c4=6
Full House: r3c2=2
Full House: r3c4=3
|
normal_sudoku_2706 | 67..3...1..2..6...5..9..4....7.6..2.9..4.21..25...3..8..5.1...3.6.3.8.5.7.....81. | 679534281142786395538921476317869524986452137254173968895217643461398752723645819 | normal_sudoku_2706 | 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 . . . 1
. . 2 . . 6 . . .
5 . . 9 . . 4 . .
. . 7 . 6 . . 2 .
9 . . 4 . 2 1 . .
2 5 . . . 3 . . 8
. . 5 . 1 . . . 3
. 6 . 3 . 8 . 5 .
7 . . . . . 8 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 679534281142786395538921476317869524986452137254173968895217643461398752723645819 #1 Extreme (2594)
X-Wing: 3 c17 r24 => r2c28,r4c2<>3
2-String Kite: 1 in r3c6,r6c3 (connected by r4c6,r6c4) => r3c3<>1
W-Wing: 8/3 in r3c3,r5c2 connected by 3 in r9c23 => r23c2,r5c3<>8
Locked Candidates Type 2 (Claiming): 8 in c3 => r2c1<>8
Finned X-Wing: 2 r38 c59 fr8c7 => r9c9<>2
Finned Swordfish: 4 r167 c368 fr7c1 fr7c2 => r89c3<>4
AIC: 1/8 1- r2c4 =1= r3c6 -1- r3c2 -3- r5c2 -8- r5c5 =8= r4c4 -8 => r4c4<>1, r2c4<>8
AIC: 3/6 6- r5c3 =6= r6c3 =1= r6c4 -1- r2c4 =1= r3c6 -1- r3c2 -3- r3c8 =3= r5c8 -3 => r5c3<>3, r5c8<>6
Naked Single: r5c3=6
AIC: 4 4- r2c5 =4= r1c6 -4- r1c3 =4= r6c3 =1= r8c3 -1- r8c1 -4 => r2c1,r8c5<>4
Naked Pair: 1,3 in r2c1,r3c2 => r2c2<>1, r3c3<>3
Naked Single: r3c3=8
Hidden Single: r9c3=3
Naked Triple: 2,7,9 in r368c5 => r25c5<>7, r9c5<>2, r9c5<>9
Locked Candidates Type 1 (Pointing): 7 in b5 => r6c78<>7
Naked Pair: 5,8 in r4c4,r5c5 => r4c6<>5
X-Wing: 1 c26 r34 => r4c1<>1
X-Wing: 2 c59 r38 => r8c7<>2
XY-Wing: 1/9/7 in r34c6,r6c5 => r3c5<>7
Naked Single: r3c5=2
Hidden Single: r1c7=2
Hidden Single: r8c9=2
Hidden Single: r8c1=4
Naked Single: r7c1=8
Naked Single: r4c1=3
Full House: r2c1=1
Naked Single: r5c2=8
Naked Single: r3c2=3
Naked Single: r5c5=5
Naked Single: r4c4=8
Naked Single: r5c9=7
Full House: r5c8=3
Naked Single: r9c5=4
Naked Single: r1c4=5
Naked Single: r3c9=6
Naked Single: r2c5=8
Naked Single: r1c6=4
Naked Single: r2c4=7
Full House: r3c6=1
Full House: r3c8=7
Naked Single: r9c9=9
Naked Single: r1c3=9
Full House: r1c8=8
Full House: r2c2=4
Naked Single: r2c8=9
Naked Single: r6c4=1
Naked Single: r4c6=9
Full House: r6c5=7
Full House: r8c5=9
Naked Single: r2c9=5
Full House: r2c7=3
Full House: r4c9=4
Naked Single: r8c7=7
Full House: r8c3=1
Full House: r6c3=4
Full House: r4c2=1
Full House: r4c7=5
Naked Single: r9c2=2
Full House: r7c2=9
Naked Single: r9c6=5
Full House: r7c6=7
Full House: r9c4=6
Full House: r7c4=2
Naked Single: r6c8=6
Full House: r6c7=9
Full House: r7c7=6
Full House: r7c8=4
|
normal_sudoku_1967 | 973.41.8.126....3.8542......97.....3685.3.7.42.1.75968..89....65.9.16.7...2.8.... | 973641285126758439854293617497862153685139724231475968318927546549316872762584391 | 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 | 9 7 3 . 4 1 . 8 .
1 2 6 . . . . 3 .
8 5 4 2 . . . . .
. 9 7 . . . . . 3
6 8 5 . 3 . 7 . 4
2 . 1 . 7 5 9 6 8
. . 8 9 . . . . 6
5 . 9 . 1 6 . 7 .
. . 2 . 8 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 973641285126758439854293617497862153685139724231475968318927546549316872762584391 #1 Easy (164)
Naked Single: r4c1=4
Full House: r6c2=3
Full House: r6c4=4
Naked Single: r5c4=1
Naked Single: r8c9=2
Naked Single: r8c2=4
Naked Single: r8c4=3
Full House: r8c7=8
Naked Single: r5c8=2
Full House: r5c6=9
Naked Single: r1c9=5
Naked Single: r7c2=1
Full House: r9c2=6
Naked Single: r1c4=6
Full House: r1c7=2
Naked Single: r2c7=4
Naked Single: r3c5=9
Naked Single: r4c4=8
Naked Single: r2c5=5
Naked Single: r3c8=1
Naked Single: r4c6=2
Full House: r4c5=6
Full House: r7c5=2
Naked Single: r2c4=7
Full House: r9c4=5
Naked Single: r3c7=6
Naked Single: r3c9=7
Full House: r2c9=9
Full House: r2c6=8
Full House: r3c6=3
Full House: r9c9=1
Naked Single: r4c8=5
Full House: r4c7=1
Naked Single: r9c7=3
Full House: r7c7=5
Naked Single: r7c8=4
Full House: r9c8=9
Naked Single: r9c1=7
Full House: r7c1=3
Full House: r7c6=7
Full House: r9c6=4
|
normal_sudoku_1720 | 35.....21.1.....9.79.12....6.....1.9.....9.....97..635137948256.6....843284.3.917 | 356894721412657398798123564623485179571369482849712635137948256965271843284536917 | normal_sudoku_1720 | 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 . . . . . 2 1
. 1 . . . . . 9 .
7 9 . 1 2 . . . .
6 . . . . . 1 . 9
. . . . . 9 . . .
. . 9 7 . . 6 3 5
1 3 7 9 4 8 2 5 6
. 6 . . . . 8 4 3
2 8 4 . 3 . 9 1 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 356894721412657398798123564623485179571369482849712635137948256965271843284536917 #1 Easy (208)
Naked Single: r8c3=5
Full House: r8c1=9
Naked Single: r8c4=2
Hidden Single: r5c3=1
Hidden Single: r1c5=9
Hidden Single: r5c9=2
Hidden Single: r3c8=6
Naked Single: r3c3=8
Naked Single: r1c3=6
Naked Single: r2c1=4
Full House: r2c3=2
Full House: r4c3=3
Naked Single: r3c9=4
Full House: r2c9=8
Naked Single: r6c1=8
Full House: r5c1=5
Naked Single: r1c7=7
Naked Single: r6c5=1
Naked Single: r1c6=4
Full House: r1c4=8
Naked Single: r5c7=4
Naked Single: r8c5=7
Full House: r8c6=1
Naked Single: r6c6=2
Full House: r6c2=4
Naked Single: r5c2=7
Full House: r4c2=2
Naked Single: r4c6=5
Naked Single: r5c8=8
Full House: r4c8=7
Naked Single: r3c6=3
Full House: r3c7=5
Full House: r2c7=3
Naked Single: r4c4=4
Full House: r4c5=8
Naked Single: r9c6=6
Full House: r2c6=7
Full House: r9c4=5
Naked Single: r5c5=6
Full House: r2c5=5
Full House: r2c4=6
Full House: r5c4=3
|
normal_sudoku_266 | 31..4........8.1...821....523...9.6.9482....7..783.9.2..3......87.3..25.5....8..3 | 319542678756983124482167395235479861948216537167835942623751489871394256594628713 | normal_sudoku_266 | 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 . . 4 . . . .
. . . . 8 . 1 . .
. 8 2 1 . . . . 5
2 3 . . . 9 . 6 .
9 4 8 2 . . . . 7
. . 7 8 3 . 9 . 2
. . 3 . . . . . .
8 7 . 3 . . 2 5 .
5 . . . . 8 . . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 319542678756983124482167395235479861948216537167835942623751489871394256594628713 #1 Extreme (7848)
Locked Candidates Type 1 (Pointing): 2 in b2 => r7c6<>2
Locked Candidates Type 1 (Pointing): 6 in b4 => r6c6<>6
Hidden Pair: 2,3 in r2c68 => r2c6<>5, r2c6<>6, r2c68<>7, r2c8<>4, r2c8<>9
Discontinuous Nice Loop: 1 r4c5 -1- r4c3 -5- r6c2 =5= r6c6 =4= r4c4 =7= r4c5 => r4c5<>1
2-String Kite: 1 in r4c9,r7c1 (connected by r4c3,r6c1) => r7c9<>1
Grouped Discontinuous Nice Loop: 5 r4c4 -5- r4c7 =5= r5c7 =3= r5c8 -3- r2c8 -2- r2c6 =2= r1c6 =5= r12c4 -5- r4c4 => r4c4<>5
Grouped Discontinuous Nice Loop: 1 r7c5 -1- r7c1 =1= r6c1 =6= r6c2 =5= r6c6 -5- r45c5 =5= r7c5 => r7c5<>1
Almost Locked Set XY-Wing: A=r179c7 {4678}, B=r1247c9 {14689}, C=r4c3457 {14578}, X,Y=1,8, Z=4 => r8c9<>4
Finned Franken Swordfish: 9 r38b1 c359 fr2c2 fr3c8 => r2c9<>9
Grouped Discontinuous Nice Loop: 6 r2c1 -6- r2c9 -4- r2c13 =4= r3c1 =7= r2c1 => r2c1<>6
Forcing Chain Verity => r2c3<>4
r2c9=4 r2c3<>4
r4c9=4 r4c4<>4 r6c6=4 r8c6<>4 r8c3=4 r2c3<>4
r7c9=4 r7c1<>4 r23c1=4 r2c3<>4
Locked Candidates Type 1 (Pointing): 4 in b1 => r7c1<>4
Naked Pair: 1,6 in r67c1 => r3c1<>6
AIC: 4 4- r2c9 =4= r2c1 =7= r2c4 -7- r4c4 -4- r6c6 =4= r6c8 -4 => r3c8,r4c9<>4
Forcing Chain Contradiction in r8 => r2c1=7
r2c1<>7 r2c1=4 r2c9<>4 r2c9=6 r2c2<>6 r12c3=6 r8c3<>6
r2c1<>7 r2c1=4 r2c9<>4 r2c9=6 r3c7<>6 r3c56=6 r12c4<>6 r79c4=6 r8c5<>6
r2c1<>7 r2c1=4 r2c9<>4 r2c9=6 r3c7<>6 r3c56=6 r12c4<>6 r79c4=6 r8c6<>6
r2c1<>7 r2c1=4 r2c9<>4 r2c9=6 r8c9<>6
Naked Single: r3c1=4
Hidden Single: r2c9=4
Forcing Chain Contradiction in r8c6 => r4c4=4
r4c4<>4 r4c7=4 r4c7<>8 r4c9=8 r4c9<>1 r8c9=1 r8c6<>1
r4c4<>4 r6c6=4 r8c6<>4
r4c4<>4 r4c7=4 r4c7<>5 r5c7=5 r5c7<>3 r3c7=3 r3c7<>6 r3c56=6 r12c4<>6 r79c4=6 r8c6<>6
Hidden Single: r6c8=4
Hidden Single: r4c5=7
Almost Locked Set Chain: 5- r5c578 {1356} -6- r38c5 {169} -1- r178c9 {1689} -8- r4c9,r5c78 {1358} -5 => r5c6<>5
W-Wing: 6/1 in r5c6,r7c1 connected by 1 in r6c16 => r7c6<>6
Discontinuous Nice Loop: 6 r1c6 -6- r5c6 -1- r5c8 -3- r2c8 -2- r2c6 =2= r1c6 => r1c6<>6
Grouped Discontinuous Nice Loop: 6 r8c6 -6- r5c6 -1- r5c8 -3- r5c7 =3= r3c7 =6= r3c56 -6- r12c4 =6= r79c4 -6- r8c6 => r8c6<>6
Discontinuous Nice Loop: 6 r7c7 -6- r7c1 -1- r6c1 =1= r6c6 -1- r8c6 -4- r7c6 =4= r7c7 => r7c7<>6
Discontinuous Nice Loop: 8 r7c7 -8- r4c7 =8= r4c9 =1= r8c9 -1- r8c6 -4- r7c6 =4= r7c7 => r7c7<>8
Discontinuous Nice Loop: 6 r9c3 -6- r7c1 -1- r6c1 =1= r6c6 -1- r8c6 -4- r8c3 =4= r9c3 => r9c3<>6
Grouped Discontinuous Nice Loop: 9 r9c3 -9- r79c2 =9= r2c2 =5= r6c2 -5- r6c6 -1- r8c6 -4- r8c3 =4= r9c3 => r9c3<>9
Almost Locked Set Chain: 6- r5c6 {16} -1- r6c26 {156} -6- r279c2 {2569} -5- r2c4,r3c5 {569} -6 => r3c6<>6
Hidden Single: r5c6=6
2-String Kite: 1 in r5c5,r8c9 (connected by r4c9,r5c8) => r8c5<>1
Naked Pair: 6,9 in r38c5 => r79c5<>6, r79c5<>9
Discontinuous Nice Loop: 9 r7c8 -9- r3c8 =9= r3c5 =6= r3c7 =3= r5c7 =5= r4c7 =8= r4c9 -8- r7c9 =8= r7c8 => r7c8<>9
Discontinuous Nice Loop: 6 r9c2 -6- r6c2 -5- r6c6 -1- r5c5 =1= r9c5 =2= r9c2 => r9c2<>6
Skyscraper: 6 in r3c5,r9c4 (connected by r39c7) => r12c4,r8c5<>6
Naked Single: r8c5=9
Naked Single: r3c5=6
Hidden Single: r3c8=9
Hidden Single: r7c9=9
Hidden Single: r9c2=9
Hidden Single: r7c8=8
Hidden Single: r9c5=2
Naked Single: r7c5=5
Full House: r5c5=1
Full House: r6c6=5
Naked Single: r5c8=3
Full House: r5c7=5
Naked Single: r6c2=6
Full House: r6c1=1
Full House: r4c3=5
Full House: r7c1=6
Naked Single: r2c8=2
Naked Single: r4c7=8
Full House: r4c9=1
Naked Single: r2c2=5
Full House: r7c2=2
Naked Single: r7c4=7
Naked Single: r1c8=7
Full House: r9c8=1
Naked Single: r2c6=3
Naked Single: r8c9=6
Full House: r1c9=8
Naked Single: r2c4=9
Full House: r2c3=6
Full House: r1c3=9
Naked Single: r7c7=4
Full House: r7c6=1
Full House: r9c7=7
Naked Single: r9c4=6
Full House: r9c3=4
Full House: r1c4=5
Full House: r8c6=4
Full House: r8c3=1
Naked Single: r1c6=2
Full House: r1c7=6
Full House: r3c7=3
Full House: r3c6=7
|
normal_sudoku_3509 | ...14.5.9..19.3..8..98..6..7.........263.7.9...351.2.79...3......87....4.6.....5. | 382146579671953428549872631715629843426387195893514267954231786238765914167498352 | normal_sudoku_3509 | 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 . 5 . 9
. . 1 9 . 3 . . 8
. . 9 8 . . 6 . .
7 . . . . . . . .
. 2 6 3 . 7 . 9 .
. . 3 5 1 . 2 . 7
9 . . . 3 . . . .
. . 8 7 . . . . 4
. 6 . . . . . 5 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 382146579671953428549872631715629843426387195893514267954231786238765914167498352 #1 Extreme (2428)
Naked Single: r5c5=8
X-Wing: 6 c49 r47 => r4c568,r7c68<>6
Naked Pair: 2,9 in r49c5 => r238c5<>2, r8c5<>9
Locked Candidates Type 1 (Pointing): 2 in b2 => r4789c6<>2
X-Wing: 2 r28 c18 => r1c18,r3c18,r7c8,r9c1<>2
Hidden Rectangle: 4/9 in r4c26,r6c26 => r6c2<>4
Sue de Coq: r1c123 - {23678} (r1c6 - {26}, r23c2,r3c1 - {3457}) => r2c1<>4, r2c1<>5
Discontinuous Nice Loop: 2/4 r4c4 =6= r4c9 -6- r7c9 =6= r8c8 =2= r8c1 -2- r2c1 -6- r2c5 =6= r8c5 -6- r7c4 =6= r4c4 => r4c4<>2, r4c4<>4
Naked Single: r4c4=6
Hidden Single: r4c5=2
Naked Single: r9c5=9
Hidden Single: r7c9=6
Hidden Single: r6c8=6
Hidden Single: r8c7=9
Locked Candidates Type 1 (Pointing): 4 in b5 => r79c6<>4
Locked Candidates Type 1 (Pointing): 8 in b6 => r4c2<>8
Uniqueness Test 4: 4/9 in r4c26,r6c26 => r4c2<>4
Sue de Coq: r123c8 - {12347} (r8c8 - {123}, r2c7 - {47}) => r47c8<>1, r4c8<>3
AIC: 7 7- r7c8 -8- r4c8 =8= r4c7 =3= r9c7 =7= r9c3 -7 => r7c23,r9c7<>7
Hidden Single: r9c3=7
Naked Single: r1c3=2
Naked Single: r1c6=6
Naked Single: r2c1=6
Hidden Single: r3c6=2
Hidden Single: r2c8=2
Hidden Single: r8c1=2
Hidden Single: r7c4=2
Full House: r9c4=4
Hidden Single: r8c5=6
Hidden Single: r9c9=2
Skyscraper: 4 in r2c2,r5c1 (connected by r25c7) => r3c1<>4
Locked Candidates Type 1 (Pointing): 4 in b1 => r7c2<>4
Hidden Single: r7c3=4
Full House: r4c3=5
Hidden Single: r5c9=5
Hidden Single: r3c1=5
Naked Single: r3c5=7
Full House: r2c5=5
2-String Kite: 3 in r1c1,r8c8 (connected by r8c2,r9c1) => r1c8<>3
Naked Single: r1c8=7
Naked Single: r2c7=4
Full House: r2c2=7
Naked Single: r7c8=8
Naked Single: r5c7=1
Full House: r5c1=4
Naked Single: r4c8=4
Naked Single: r4c9=3
Full House: r3c9=1
Full House: r4c7=8
Full House: r3c8=3
Full House: r3c2=4
Full House: r8c8=1
Naked Single: r7c7=7
Full House: r9c7=3
Naked Single: r6c1=8
Naked Single: r4c6=9
Full House: r4c2=1
Full House: r6c2=9
Full House: r6c6=4
Naked Single: r8c6=5
Full House: r8c2=3
Naked Single: r9c1=1
Full House: r1c1=3
Full House: r7c2=5
Full House: r7c6=1
Full House: r1c2=8
Full House: r9c6=8
|
normal_sudoku_2081 | 5......84478.9125.6...48..774.815.3..8....54.3.54..87..37.8.4.58.4.527..1...74..8 | 591237684478691253623548197746815932289763541315429876937186425864352719152974368 | normal_sudoku_2081 | 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 . . . . . . 8 4
4 7 8 . 9 1 2 5 .
6 . . . 4 8 . . 7
7 4 . 8 1 5 . 3 .
. 8 . . . . 5 4 .
3 . 5 4 . . 8 7 .
. 3 7 . 8 . 4 . 5
8 . 4 . 5 2 7 . .
1 . . . 7 4 . . 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 591237684478691253623548197746815932289763541315429876937186425864352719152974368 #1 Medium (336)
Hidden Single: r3c4=5
Hidden Single: r9c2=5
Locked Candidates Type 1 (Pointing): 2 in b2 => r1c23<>2
Locked Candidates Type 1 (Pointing): 1 in b6 => r8c9<>1
Locked Candidates Type 1 (Pointing): 3 in b8 => r125c4<>3
Naked Single: r2c4=6
Full House: r2c9=3
Hidden Single: r1c7=6
Naked Single: r4c7=9
Naked Single: r3c7=1
Full House: r9c7=3
Full House: r3c8=9
Naked Single: r9c4=9
Naked Single: r3c2=2
Full House: r3c3=3
Naked Single: r7c4=1
Naked Single: r7c6=6
Full House: r8c4=3
Naked Single: r6c6=9
Naked Single: r7c8=2
Full House: r7c1=9
Full House: r5c1=2
Naked Single: r9c8=6
Full House: r8c8=1
Full House: r8c9=9
Full House: r8c2=6
Full House: r9c3=2
Naked Single: r4c3=6
Full House: r4c9=2
Naked Single: r5c4=7
Full House: r1c4=2
Naked Single: r6c2=1
Full House: r1c2=9
Full House: r5c3=9
Full House: r1c3=1
Naked Single: r5c6=3
Full House: r1c6=7
Full House: r1c5=3
Naked Single: r6c9=6
Full House: r5c9=1
Full House: r5c5=6
Full House: r6c5=2
|
normal_sudoku_6432 | 52963.7..347..9...6..7.2..9.53..7..6.94.26..7762.1..8..3..6.57.4752.......6.73..4 | 529634718347189265681752349153847926894326157762915483938461572475298631216573894 | normal_sudoku_6432 | 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 9 6 3 . 7 . .
3 4 7 . . 9 . . .
6 . . 7 . 2 . . 9
. 5 3 . . 7 . . 6
. 9 4 . 2 6 . . 7
7 6 2 . 1 . . 8 .
. 3 . . 6 . 5 7 .
4 7 5 2 . . . . .
. . 6 . 7 3 . . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 529634718347189265681752349153847926894326157762915483938461572475298631216573894 #1 Easy (194)
Hidden Single: r9c4=5
Hidden Single: r6c6=5
Naked Single: r6c9=3
Naked Single: r5c7=1
Naked Single: r5c1=8
Full House: r4c1=1
Naked Single: r5c8=5
Full House: r5c4=3
Hidden Single: r2c9=5
Naked Single: r2c5=8
Naked Single: r2c4=1
Naked Single: r8c5=9
Naked Single: r1c6=4
Full House: r3c5=5
Full House: r4c5=4
Naked Single: r1c8=1
Full House: r1c9=8
Naked Single: r6c4=9
Full House: r4c4=8
Full House: r6c7=4
Full House: r7c4=4
Naked Single: r8c9=1
Full House: r7c9=2
Naked Single: r3c7=3
Naked Single: r8c6=8
Full House: r7c6=1
Naked Single: r7c1=9
Full House: r7c3=8
Full House: r9c1=2
Full House: r3c3=1
Full House: r9c2=1
Full House: r3c2=8
Full House: r3c8=4
Naked Single: r9c8=9
Full House: r9c7=8
Naked Single: r8c7=6
Full House: r8c8=3
Naked Single: r4c8=2
Full House: r2c8=6
Full House: r2c7=2
Full House: r4c7=9
|
normal_sudoku_1793 | 785931..6...68..7.94675...8..439..8..9.176542.7.248.......1.83.....2...4.17.6.... | 785931426123684975946752318264395781398176542571248693652419837839527164417863259 | normal_sudoku_1793 | 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 5 9 3 1 . . 6
. . . 6 8 . . 7 .
9 4 6 7 5 . . . 8
. . 4 3 9 . . 8 .
. 9 . 1 7 6 5 4 2
. 7 . 2 4 8 . . .
. . . . 1 . 8 3 .
. . . . 2 . . . 4
. 1 7 . 6 . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 785931426123684975946752318264395781398176542571248693652419837839527164417863259 #1 Easy (168)
Full House: r4c6=5
Naked Single: r3c6=2
Full House: r2c6=4
Naked Single: r1c8=2
Full House: r1c7=4
Naked Single: r3c8=1
Full House: r3c7=3
Naked Single: r2c7=9
Full House: r2c9=5
Naked Single: r9c7=2
Naked Single: r9c9=9
Naked Single: r7c9=7
Naked Single: r9c6=3
Naked Single: r9c8=5
Naked Single: r4c9=1
Full House: r6c9=3
Naked Single: r7c6=9
Full House: r8c6=7
Naked Single: r8c8=6
Full House: r6c8=9
Full House: r8c7=1
Naked Single: r6c7=6
Full House: r4c7=7
Naked Single: r6c3=1
Full House: r6c1=5
Naked Single: r7c3=2
Naked Single: r2c3=3
Naked Single: r2c2=2
Full House: r2c1=1
Naked Single: r5c3=8
Full House: r5c1=3
Full House: r8c3=9
Naked Single: r4c2=6
Full House: r4c1=2
Naked Single: r8c1=8
Naked Single: r7c2=5
Full House: r8c2=3
Full House: r8c4=5
Naked Single: r9c1=4
Full House: r7c1=6
Full House: r7c4=4
Full House: r9c4=8
|
normal_sudoku_6675 | 18..549.7.74.9851.9.5....488..9.14.541.58..9.25943687154....18..918.57..7.8....5. | 182654937374298516965173248837921465416587392259436871543762189691845723728319654 | normal_sudoku_6675 | 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 8 . . 5 4 9 . 7
. 7 4 . 9 8 5 1 .
9 . 5 . . . . 4 8
8 . . 9 . 1 4 . 5
4 1 . 5 8 . . 9 .
2 5 9 4 3 6 8 7 1
5 4 . . . . 1 8 .
. 9 1 8 . 5 7 . .
7 . 8 . . . . 5 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 182654937374298516965173248837921465416587392259436871543762189691845723728319654 #1 Extreme (4576)
Empty Rectangle: 2 in b2 (r39c2) => r9c4<>2
Finned Swordfish: 2 c267 r359 fr7c6 => r9c5<>2
Sashimi Swordfish: 2 r248 c589 fr2c4 => r3c5<>2
Grouped Discontinuous Nice Loop: 6 r7c4 =7= r3c4 =1= r3c5 =6= r123c4 -6- r7c4 => r7c4<>6
Finned Franken Swordfish: 3 c18b4 r148 fr2c1 fr5c3 => r1c3<>3
W-Wing: 6/3 in r4c2,r8c1 connected by 3 in r2c1,r3c2 => r9c2<>6
Sashimi Swordfish: 6 c128 r148 fr2c1 fr3c2 => r1c3<>6
Naked Single: r1c3=2
Hidden Single: r9c2=2
Hidden Rectangle: 3/9 in r7c69,r9c69 => r7c9<>3
Discontinuous Nice Loop: 6 r7c9 -6- r9c7 -3- r9c6 -9- r9c9 =9= r7c9 => r7c9<>6
Grouped Discontinuous Nice Loop: 3 r7c4 -3- r7c3 =3= r8c1 -3- r2c1 =3= r3c2 -3- r3c6 =3= r123c4 -3- r7c4 => r7c4<>3
Discontinuous Nice Loop: 7 r7c6 -7- r7c4 -2- r2c4 =2= r2c9 -2- r3c7 =2= r5c7 -2- r5c6 -7- r7c6 => r7c6<>7
Forcing Chain Contradiction in r4c8 => r2c4<>3
r2c4=3 r2c4<>2 r2c9=2 r3c7<>2 r5c7=2 r4c8<>2
r2c4=3 r1c4<>3 r1c8=3 r4c8<>3
r2c4=3 r2c1<>3 r2c1=6 r3c2<>6 r4c2=6 r4c8<>6
W-Wing: 6/3 in r1c8,r3c2 connected by 3 in r2c19 => r3c7<>6
Turbot Fish: 6 r1c8 =6= r2c9 -6- r2c1 =6= r8c1 => r8c8<>6
Finned X-Wing: 3 r28 c19 fr8c8 => r9c9<>3
Discontinuous Nice Loop: 3 r4c3 -3- r7c3 =3= r8c1 -3- r8c8 -2- r4c8 =2= r4c5 =7= r4c3 => r4c3<>3
Discontinuous Nice Loop: 2 r7c4 -2- r2c4 -6- r2c1 =6= r8c1 -6- r7c3 =6= r7c5 =7= r7c4 => r7c4<>2
Naked Single: r7c4=7
Locked Candidates Type 2 (Claiming): 2 in c4 => r3c6<>2
XY-Wing: 3/7/2 in r3c67,r5c6 => r5c7<>2
Hidden Single: r3c7=2
Hidden Single: r2c4=2
Remote Pair: 3/6 r1c8 -6- r2c9 -3- r2c1 -6- r8c1 => r8c8<>3
Naked Single: r8c8=2
Naked Single: r7c9=9
Hidden Single: r4c5=2
Full House: r5c6=7
Naked Single: r7c5=6
Naked Single: r3c6=3
Naked Single: r7c3=3
Full House: r7c6=2
Full House: r9c6=9
Full House: r8c1=6
Full House: r2c1=3
Full House: r3c2=6
Full House: r2c9=6
Full House: r4c2=3
Full House: r1c8=3
Full House: r1c4=6
Full House: r4c8=6
Full House: r4c3=7
Full House: r5c3=6
Naked Single: r8c5=4
Full House: r8c9=3
Naked Single: r3c4=1
Full House: r3c5=7
Full House: r9c5=1
Full House: r9c4=3
Naked Single: r9c9=4
Full House: r5c9=2
Full House: r5c7=3
Full House: r9c7=6
|
normal_sudoku_2652 | 9....46..3....8...6.1..7.855..241.9.194...5.228.....147...62...4.2......856479123 | 978524631325618749641397285563241897194783562287956314739162458412835976856479123 | normal_sudoku_2652 | 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 . . . . 4 6 . .
3 . . . . 8 . . .
6 . 1 . . 7 . 8 5
5 . . 2 4 1 . 9 .
1 9 4 . . . 5 . 2
2 8 . . . . . 1 4
7 . . . 6 2 . . .
4 . 2 . . . . . .
8 5 6 4 7 9 1 2 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 978524631325618749641397285563241897194783562287956314739162458412835976856479123 #1 Easy (212)
Hidden Single: r1c3=8
Hidden Single: r2c4=6
Hidden Single: r4c2=6
Hidden Single: r7c3=9
Naked Single: r7c9=8
Naked Single: r4c9=7
Naked Single: r7c7=4
Naked Single: r1c9=1
Naked Single: r4c3=3
Full House: r4c7=8
Full House: r6c3=7
Full House: r2c3=5
Naked Single: r6c7=3
Full House: r5c8=6
Naked Single: r7c8=5
Naked Single: r2c9=9
Full House: r8c9=6
Naked Single: r5c6=3
Naked Single: r8c8=7
Full House: r8c7=9
Naked Single: r3c7=2
Full House: r2c7=7
Naked Single: r5c5=8
Full House: r5c4=7
Naked Single: r8c6=5
Full House: r6c6=6
Naked Single: r1c8=3
Full House: r2c8=4
Naked Single: r3c2=4
Naked Single: r1c4=5
Naked Single: r2c2=2
Full House: r1c2=7
Full House: r1c5=2
Full House: r2c5=1
Naked Single: r6c4=9
Full House: r6c5=5
Naked Single: r8c5=3
Full House: r3c5=9
Full House: r3c4=3
Naked Single: r7c4=1
Full House: r7c2=3
Full House: r8c2=1
Full House: r8c4=8
|
normal_sudoku_6136 | 2.38....1.59.21.73.1...3.2....23...77..1.8354....472.......27.8...3...42...7.413. | 263875491459621873817493526584239617792168354631547289345912768178356942926784135 | normal_sudoku_6136 | 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 . 3 8 . . . . 1
. 5 9 . 2 1 . 7 3
. 1 . . . 3 . 2 .
. . . 2 3 . . . 7
7 . . 1 . 8 3 5 4
. . . . 4 7 2 . .
. . . . . 2 7 . 8
. . . 3 . . . 4 2
. . . 7 . 4 1 3 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 263875491459621873817493526584239617792168354631547289345912768178356942926784135 #1 Extreme (2690)
Locked Candidates Type 1 (Pointing): 8 in b3 => r4c7<>8
Naked Pair: 6,9 in r4c7,r6c9 => r46c8<>6, r46c8<>9
Hidden Rectangle: 2/6 in r5c23,r9c23 => r9c2<>6
Finned Franken Swordfish: 9 c48b6 r367 fr1c8 fr4c7 => r3c7<>9
Forcing Net Verity => r6c4=5
r1c6=5 r4c6<>5 r6c4=5
r1c6=6 (r1c6<>9) (r2c4<>6) (r3c4<>6) r1c8<>6 r7c8=6 (r8c7<>6) (r9c9<>6) r7c4<>6 r6c4=6 r6c9<>6 r3c9=6 r3c9<>5 r9c9=5 r8c7<>5 r8c7=9 r8c6<>9 r4c6=9 r4c6<>5 r6c4=5
r1c6=9 (r1c6<>6) (r1c8<>9 r7c8=9 r8c7<>9) (r3c4<>9) r3c5<>9 r3c9=9 r3c9<>5 r9c9=5 r8c7<>5 r8c7=6 r8c6<>6 r4c6=6 r4c6<>5 r6c4=5
Naked Pair: 6,9 in r4c67 => r4c123<>6, r4c12<>9
Naked Pair: 6,9 in r7c48 => r7c1235<>6, r7c125<>9
Skyscraper: 9 in r1c8,r3c4 (connected by r7c48) => r1c56,r3c9<>9
2-String Kite: 9 in r5c2,r8c6 (connected by r4c6,r5c5) => r8c2<>9
Empty Rectangle: 9 in b4 (r69c9) => r9c2<>9
Locked Candidates Type 1 (Pointing): 9 in b7 => r6c1<>9
W-Wing: 6/9 in r4c7,r7c8 connected by 9 in r1c78 => r8c7<>6
W-Wing: 6/9 in r5c5,r7c4 connected by 9 in r3c45 => r89c5<>6
Turbot Fish: 6 r1c8 =6= r7c8 -6- r7c4 =6= r8c6 => r1c6<>6
Naked Single: r1c6=5
Naked Pair: 6,9 in r7c4,r8c6 => r89c5<>9
Remote Pair: 6/9 r1c8 -9- r7c8 -6- r7c4 -9- r8c6 -6- r4c6 -9- r4c7 => r123c7<>6, r1c7<>9
Naked Single: r1c7=4
Naked Single: r2c7=8
Naked Single: r3c7=5
Naked Single: r3c9=6
Full House: r1c8=9
Naked Single: r8c7=9
Full House: r4c7=6
Naked Single: r6c9=9
Full House: r9c9=5
Full House: r7c8=6
Naked Single: r8c6=6
Full House: r4c6=9
Full House: r5c5=6
Naked Single: r9c5=8
Naked Single: r7c4=9
Naked Single: r1c5=7
Full House: r1c2=6
Naked Single: r5c3=2
Full House: r5c2=9
Naked Single: r9c2=2
Naked Single: r3c4=4
Full House: r2c4=6
Full House: r3c5=9
Full House: r2c1=4
Naked Single: r9c3=6
Full House: r9c1=9
Naked Single: r3c1=8
Full House: r3c3=7
Hidden Single: r8c2=7
Hidden Single: r6c1=6
Hidden Single: r8c3=8
Naked Single: r6c3=1
Naked Single: r4c1=5
Naked Single: r6c8=8
Full House: r4c8=1
Full House: r6c2=3
Naked Single: r4c3=4
Full House: r4c2=8
Full House: r7c2=4
Full House: r7c3=5
Naked Single: r8c1=1
Full House: r7c1=3
Full House: r7c5=1
Full House: r8c5=5
|
normal_sudoku_4712 | .....3..4......8.96..8...2.....7...82865.49...1.6...52..21...8615......386...7... | 728913564541762839693845721935271648286534917417698352372159486159486273864327195 | normal_sudoku_4712 | 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
. . . . . . 8 . 9
6 . . 8 . . . 2 .
. . . . 7 . . . 8
2 8 6 5 . 4 9 . .
. 1 . 6 . . . 5 2
. . 2 1 . . . 8 6
1 5 . . . . . . 3
8 6 . . . 7 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 728913564541762839693845721935271648286534917417698352372159486159486273864327195 #1 Extreme (12834) bf
Hidden Single: r1c3=8
Locked Candidates Type 1 (Pointing): 7 in b4 => r6c7<>7
Hidden Pair: 6,8 in r8c56 => r8c56<>2, r8c5<>4, r8c56<>9
Discontinuous Nice Loop: 4 r8c7 -4- r6c7 -3- r5c8 =3= r5c5 =1= r4c6 =2= r4c4 -2- r8c4 =2= r8c7 => r8c7<>4
Forcing Chain Contradiction in r3 => r1c2<>7
r1c2=7 r3c2<>7
r1c2=7 r3c3<>7
r1c2=7 r1c2<>2 r2c2=2 r2c6<>2 r4c6=2 r4c6<>1 r5c5=1 r5c5<>3 r5c8=3 r2c8<>3 r3c7=3 r3c7<>7
r1c2=7 r1c2<>2 r2c2=2 r2c6<>2 r4c6=2 r4c6<>1 r5c5=1 r5c9<>1 r5c9=7 r3c9<>7
Forcing Net Contradiction in c3 => r4c6<>9
r4c6=9 (r3c6<>9) r7c6<>9 r7c6=5 r3c6<>5 r3c6=1 r3c3<>1 r2c3=1 r2c3<>3
r4c6=9 (r6c6<>9 r6c6=8 r6c5<>8 r6c5=3 r6c7<>3) r4c6<>1 r5c5=1 r5c5<>3 r5c8=3 r4c7<>3 r3c7=3 r3c3<>3
r4c6=9 (r4c6<>1 r5c5=1 r5c9<>1 r5c9=7 r3c9<>7 r3c9=5 r3c3<>5) (r3c6<>9) r7c6<>9 r7c6=5 r3c6<>5 r3c6=1 r3c3<>1 r2c3=1 r2c3<>5 r4c3=5 r4c3<>3
r4c6=9 (r6c5<>9) r6c6<>9 r6c6=8 r6c5<>8 r6c5=3 r6c3<>3
r4c6=9 r4c6<>2 r4c4=2 r4c4<>3 r9c4=3 r9c3<>3
Forcing Net Contradiction in c8 => r6c3<>9
r6c3=9 (r6c3<>4) r6c3<>7 r6c1=7 r6c1<>4 r6c7=4 r4c8<>4
r6c3=9 (r8c3<>9) (r4c1<>9) (r4c2<>9) r4c3<>9 r4c4=9 r8c4<>9 r8c8=9 r8c8<>4
r6c3=9 (r9c3<>9) (r4c1<>9) (r4c2<>9) r4c3<>9 r4c4=9 r4c4<>3 r9c4=3 r9c3<>3 r9c3=4 r9c8<>4
Brute Force: r4c8=4
Naked Single: r6c7=3
Hidden Single: r4c7=6
Hidden Single: r2c8=3
Hidden Single: r5c5=3
Hidden Single: r4c6=1
Hidden Single: r1c8=6
Hidden Single: r9c4=3
Hidden Single: r4c4=2
Hidden Single: r2c6=2
Hidden Single: r8c7=2
Hidden Single: r9c5=2
Hidden Single: r1c2=2
Hidden Single: r2c5=6
Naked Single: r8c5=8
Naked Single: r6c5=9
Full House: r6c6=8
Naked Single: r8c6=6
Hidden Single: r2c3=1
Hidden Single: r2c1=5
Hidden Single: r4c3=5
Hidden Single: r3c3=3
Locked Candidates Type 1 (Pointing): 4 in b1 => r7c2<>4
Locked Candidates Type 1 (Pointing): 5 in b8 => r7c7<>5
Locked Candidates Type 2 (Claiming): 9 in c3 => r7c12<>9
Hidden Single: r7c6=9
Full House: r3c6=5
Naked Single: r8c4=4
Full House: r7c5=5
Naked Single: r1c5=1
Full House: r3c5=4
Naked Single: r2c4=7
Full House: r1c4=9
Full House: r2c2=4
Naked Single: r1c1=7
Full House: r1c7=5
Full House: r3c2=9
Naked Single: r6c1=4
Full House: r6c3=7
Naked Single: r4c2=3
Full House: r4c1=9
Full House: r7c1=3
Full House: r7c2=7
Full House: r7c7=4
Naked Single: r8c3=9
Full House: r8c8=7
Full House: r9c3=4
Naked Single: r9c7=1
Full House: r3c7=7
Full House: r3c9=1
Naked Single: r5c8=1
Full House: r9c8=9
Full House: r9c9=5
Full House: r5c9=7
|
normal_sudoku_2709 | 1.23.87..87..491....3..12.9..89325.7.2...4913....176.8..5..68.1.6...3452....753.6 | 192358764876249135453761289618932547527684913349517628935426871761893452284175396 | normal_sudoku_2709 | 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 3 . 8 7 . .
8 7 . . 4 9 1 . .
. . 3 . . 1 2 . 9
. . 8 9 3 2 5 . 7
. 2 . . . 4 9 1 3
. . . . 1 7 6 . 8
. . 5 . . 6 8 . 1
. 6 . . . 3 4 5 2
. . . . 7 5 3 . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 192358764876249135453761289618932547527684913349517628935426871761893452284175396 #1 Easy (156)
Naked Single: r4c8=4
Full House: r6c8=2
Naked Single: r6c4=5
Naked Single: r2c3=6
Naked Single: r2c9=5
Full House: r1c9=4
Naked Single: r9c8=9
Full House: r7c8=7
Naked Single: r1c8=6
Naked Single: r4c1=6
Full House: r4c2=1
Naked Single: r2c4=2
Full House: r2c8=3
Full House: r3c8=8
Naked Single: r5c3=7
Naked Single: r1c5=5
Full House: r1c2=9
Naked Single: r7c4=4
Naked Single: r5c1=5
Naked Single: r3c5=6
Full House: r3c4=7
Naked Single: r7c2=3
Naked Single: r3c1=4
Full House: r3c2=5
Naked Single: r5c5=8
Full House: r5c4=6
Naked Single: r6c2=4
Full House: r9c2=8
Naked Single: r9c1=2
Naked Single: r8c5=9
Full House: r7c5=2
Full House: r7c1=9
Naked Single: r6c3=9
Full House: r6c1=3
Full House: r8c1=7
Naked Single: r9c4=1
Full House: r8c4=8
Full House: r8c3=1
Full House: r9c3=4
|
normal_sudoku_3637 | 8.52.3.4.4..8....39321....7648321.7.5..9..3.2..956....7864321591.36......547..... | 875293641461875293932146587648321975517984362329567418786432159193658724254719836 | normal_sudoku_3637 | 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 2 . 3 . 4 .
4 . . 8 . . . . 3
9 3 2 1 . . . . 7
6 4 8 3 2 1 . 7 .
5 . . 9 . . 3 . 2
. . 9 5 6 . . . .
7 8 6 4 3 2 1 5 9
1 . 3 6 . . . . .
. 5 4 7 . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 875293641461875293932146587648321975517984362329567418786432159193658724254719836 #1 Easy (156)
Naked Single: r4c9=5
Full House: r4c7=9
Naked Single: r9c1=2
Full House: r6c1=3
Full House: r8c2=9
Naked Single: r1c7=6
Naked Single: r1c9=1
Naked Single: r3c8=8
Naked Single: r9c7=8
Naked Single: r1c2=7
Full House: r1c5=9
Naked Single: r3c7=5
Naked Single: r6c8=1
Naked Single: r8c8=2
Naked Single: r6c7=4
Naked Single: r8c9=4
Naked Single: r9c6=9
Naked Single: r9c9=6
Full House: r6c9=8
Full House: r5c8=6
Naked Single: r2c3=1
Full House: r2c2=6
Full House: r5c3=7
Naked Single: r5c2=1
Full House: r6c2=2
Full House: r6c6=7
Naked Single: r9c5=1
Full House: r9c8=3
Full House: r2c8=9
Full House: r2c7=2
Full House: r8c7=7
Naked Single: r3c5=4
Full House: r3c6=6
Naked Single: r2c6=5
Full House: r2c5=7
Naked Single: r5c5=8
Full House: r5c6=4
Full House: r8c6=8
Full House: r8c5=5
|
normal_sudoku_5413 | ......5.....925.1.1.58.....7.32581.4218..7.53.54...7283.1...2.5.7253..4154.1.2... | 986413572437925816125876439793258164218647953654391728361784295872539641549162387 | normal_sudoku_5413 | 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 . .
. . . 9 2 5 . 1 .
1 . 5 8 . . . . .
7 . 3 2 5 8 1 . 4
2 1 8 . . 7 . 5 3
. 5 4 . . . 7 2 8
3 . 1 . . . 2 . 5
. 7 2 5 3 . . 4 1
5 4 . 1 . 2 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 986413572437925816125876439793258164218647953654391728361784295872539641549162387 #1 Extreme (4834)
Naked Pair: 6,7 in r2c39 => r2c127<>6
Turbot Fish: 8 r1c8 =8= r2c7 -8- r8c7 =8= r8c1 => r1c1<>8
Empty Rectangle: 9 in b1 (r4c28) => r1c8<>9
Almost Locked Set Chain: 6- r2c1279 {34678} -7- r2c3 {67} -6- r9c3 {69} -9- r29c9 {679} -6 => r13c9<>6
Forcing Chain Verity => r1c8<>6
r1c1=6 r1c8<>6
r6c1=6 r4c2<>6 r4c8=6 r1c8<>6
r8c1=6 r8c1<>8 r8c7=8 r2c7<>8 r1c8=8 r1c8<>6
Forcing Chain Contradiction in r8c1 => r3c7<>6
r3c7=6 r5c7<>6 r4c8=6 r4c2<>6 r6c1=6 r8c1<>6
r3c7=6 r3c7<>4 r2c7=4 r2c1<>4 r2c1=8 r8c1<>8
r3c7=6 r2c9<>6 r2c3=6 r9c3<>6 r9c3=9 r8c1<>9
Forcing Chain Contradiction in r8c1 => r3c7<>9
r3c7=9 r13c9<>9 r9c9=9 r9c3<>9 r9c3=6 r8c1<>6
r3c7=9 r3c7<>4 r2c7=4 r2c1<>4 r2c1=8 r8c1<>8
r3c7=9 r5c7<>9 r5c5=9 r6c56<>9 r6c1=9 r8c1<>9
Forcing Chain Verity => r8c1<>6
r5c7=9 r5c7<>6 r4c8=6 r4c2<>6 r6c1=6 r8c1<>6
r8c7=9 r8c7<>8 r8c1=8 r8c1<>6
r9c7=9 r9c3<>9 r9c3=6 r8c1<>6
Turbot Fish: 6 r4c8 =6= r4c2 -6- r7c2 =6= r9c3 => r9c8<>6
Sashimi X-Wing: 6 r58 c67 fr5c4 fr5c5 => r6c6<>6
Multi Colors 1: 6 (r1c1,r4c2,r5c7) / (r4c8,r6c1), (r2c3,r3c8,r9c9) / (r2c9) => r2c3,r3c8<>6
Naked Single: r2c3=7
Naked Single: r2c9=6
W-Wing: 9/6 in r1c3,r4c2 connected by 6 in r16c1 => r13c2<>9
Locked Candidates Type 1 (Pointing): 9 in b1 => r1c9<>9
Almost Locked Set XZ-Rule: A=r8c16 {689}, B=r1c13,r2c1 {4689}, X=8, Z=6 => r1c6<>6
Almost Locked Set XZ-Rule: A=r58c7 {689}, B=r8c1,r9c3 {689}, X=8, Z=6 => r9c7<>6
AIC: 9 9- r7c2 =9= r4c2 =6= r4c8 -6- r7c8 =6= r8c7 -6- r8c6 -9 => r7c56,r8c1<>9
Naked Single: r8c1=8
Naked Single: r2c1=4
Hidden Single: r3c7=4
Locked Pair: 6,9 in r1c13 => r1c245,r3c2<>6
Naked Pair: 6,9 in r58c7 => r9c7<>9
X-Wing: 6 c28 r47 => r7c456<>6
Naked Single: r7c6=4
Naked Single: r7c4=7
Naked Single: r7c5=8
Locked Candidates Type 2 (Claiming): 6 in c4 => r56c5<>6
Naked Pair: 6,9 in r7c8,r8c7 => r9c89<>9
Naked Single: r9c9=7
Naked Single: r1c9=2
Full House: r3c9=9
Hidden Single: r3c2=2
Remote Pair: 9/6 r6c1 -6- r4c2 -9- r4c8 -6- r5c7 -9- r8c7 -6- r7c8 -9- r7c2 -6- r9c3 -9- r9c5 -6- r8c6 => r5c5,r6c6<>9
Naked Single: r5c5=4
Naked Single: r5c4=6
Full House: r5c7=9
Full House: r4c8=6
Full House: r4c2=9
Full House: r6c1=6
Full House: r1c1=9
Naked Single: r6c4=3
Full House: r1c4=4
Naked Single: r8c7=6
Full House: r8c6=9
Full House: r9c5=6
Naked Single: r7c8=9
Full House: r7c2=6
Full House: r9c3=9
Full House: r1c3=6
Naked Single: r6c6=1
Full House: r6c5=9
Naked Single: r3c5=7
Full House: r1c5=1
Naked Single: r1c6=3
Full House: r3c6=6
Full House: r3c8=3
Naked Single: r1c2=8
Full House: r1c8=7
Full House: r2c7=8
Full House: r9c8=8
Full House: r2c2=3
Full House: r9c7=3
|
normal_sudoku_2428 | .8.93..463.4...198.6.8.435..9....42.723....8141....6.....326814.32......14.5.7... | 281935746354762198967814352896153427723649581415278639579326814632481975148597263 | normal_sudoku_2428 | 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 3 . . 4 6
3 . 4 . . . 1 9 8
. 6 . 8 . 4 3 5 .
. 9 . . . . 4 2 .
7 2 3 . . . . 8 1
4 1 . . . . 6 . .
. . . 3 2 6 8 1 4
. 3 2 . . . . . .
1 4 . 5 . 7 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 281935746354762198967814352896153427723649581415278639579326814632481975148597263 #1 Hard (862)
Locked Candidates Type 1 (Pointing): 6 in b4 => r4c45<>6
Locked Candidates Type 1 (Pointing): 5 in b9 => r8c1<>5
Locked Candidates Type 2 (Claiming): 2 in r2 => r1c6<>2
Locked Candidates Type 2 (Claiming): 9 in r7 => r8c1,r9c3<>9
Naked Pair: 5,9 in r5c67 => r5c5<>5, r5c5<>9
Naked Triple: 2,5,9 in r137c1 => r4c1<>5
Locked Candidates Type 1 (Pointing): 5 in b4 => r17c3<>5
2-String Kite: 8 in r4c1,r9c5 (connected by r8c1,r9c3) => r4c5<>8
W-Wing: 1/7 in r1c3,r3c5 connected by 7 in r1c7,r3c9 => r1c6,r3c3<>1
Naked Single: r1c6=5
Naked Single: r1c1=2
Naked Single: r2c6=2
Naked Single: r5c6=9
Naked Single: r1c7=7
Full House: r1c3=1
Full House: r3c9=2
Naked Single: r3c1=9
Naked Single: r5c7=5
Naked Single: r3c3=7
Full House: r2c2=5
Full House: r3c5=1
Full House: r7c2=7
Naked Single: r7c1=5
Full House: r7c3=9
Naked Single: r8c7=9
Full House: r9c7=2
Naked Single: r9c9=3
Naked Single: r4c9=7
Naked Single: r9c8=6
Naked Single: r4c4=1
Naked Single: r4c5=5
Naked Single: r6c8=3
Full House: r6c9=9
Full House: r8c9=5
Full House: r8c8=7
Naked Single: r9c3=8
Full House: r8c1=6
Full House: r9c5=9
Full House: r4c1=8
Naked Single: r8c4=4
Naked Single: r6c6=8
Naked Single: r4c3=6
Full House: r6c3=5
Full House: r4c6=3
Full House: r8c6=1
Full House: r8c5=8
Naked Single: r5c4=6
Full House: r5c5=4
Naked Single: r6c5=7
Full House: r2c5=6
Full House: r2c4=7
Full House: r6c4=2
|
normal_sudoku_415 | ..6.89.15..4.56.82..82.7.36....9.65.63.....98..9...32...192..63..3....718.5.31249 | 326489715174356982958217436482193657637542198519678324741925863293864571865731249 | normal_sudoku_415 | 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 5
. . 4 . 5 6 . 8 2
. . 8 2 . 7 . 3 6
. . . . 9 . 6 5 .
6 3 . . . . . 9 8
. . 9 . . . 3 2 .
. . 1 9 2 . . 6 3
. . 3 . . . . 7 1
8 . 5 . 3 1 2 4 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 326489715174356982958217436482193657637542198519678324741925863293864571865731249 #1 Easy (204)
Hidden Single: r5c7=1
Hidden Single: r4c6=3
Hidden Single: r9c4=7
Full House: r9c2=6
Hidden Single: r5c6=2
Naked Single: r5c3=7
Full House: r4c3=2
Naked Single: r5c5=4
Full House: r5c4=5
Naked Single: r3c5=1
Naked Single: r8c5=6
Full House: r6c5=7
Naked Single: r6c6=8
Naked Single: r2c4=3
Full House: r1c4=4
Naked Single: r6c9=4
Full House: r4c9=7
Naked Single: r4c4=1
Full House: r6c4=6
Full House: r8c4=8
Naked Single: r1c7=7
Naked Single: r4c1=4
Full House: r4c2=8
Naked Single: r8c7=5
Full House: r7c7=8
Naked Single: r1c2=2
Full House: r1c1=3
Naked Single: r2c7=9
Full House: r3c7=4
Naked Single: r7c1=7
Naked Single: r8c6=4
Full House: r7c6=5
Full House: r7c2=4
Naked Single: r2c1=1
Full House: r2c2=7
Naked Single: r8c2=9
Full House: r8c1=2
Naked Single: r6c1=5
Full House: r3c1=9
Full House: r3c2=5
Full House: r6c2=1
|
normal_sudoku_1745 | ...59.6......2.9..9.746..........165......379.516.9482163742598...9...46.9...6... | 314598627685327914927461853839274165246185379751639482163742598578913246492856731 | normal_sudoku_1745 | 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 9 . 6 . .
. . . . 2 . 9 . .
9 . 7 4 6 . . . .
. . . . . . 1 6 5
. . . . . . 3 7 9
. 5 1 6 . 9 4 8 2
1 6 3 7 4 2 5 9 8
. . . 9 . . . 4 6
. 9 . . . 6 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 314598627685327914927461853839274165246185379751639482163742598578913246492856731 #1 Medium (590)
Hidden Single: r3c8=5
Hidden Single: r3c7=8
Hidden Single: r4c3=9
Hidden Single: r3c2=2
Hidden Single: r1c8=2
Locked Candidates Type 1 (Pointing): 7 in b2 => r4c6<>7
Locked Candidates Type 1 (Pointing): 7 in b3 => r9c9<>7
Locked Candidates Type 1 (Pointing): 1 in b9 => r9c45<>1
Locked Candidates Type 1 (Pointing): 3 in b9 => r9c45<>3
Naked Single: r9c4=8
Naked Single: r9c5=5
Hidden Single: r5c6=5
Hidden Single: r4c6=4
Naked Pair: 1,3 in r2c4,r3c6 => r12c6<>1, r12c6<>3
Naked Pair: 1,3 in r2c8,r3c9 => r12c9<>1, r12c9<>3
Hidden Single: r1c2=1
Hidden Single: r1c1=3
Naked Single: r6c1=7
Full House: r6c5=3
Naked Single: r4c4=2
Naked Single: r8c5=1
Full House: r8c6=3
Naked Single: r4c1=8
Naked Single: r5c4=1
Full House: r2c4=3
Naked Single: r5c5=8
Full House: r4c5=7
Full House: r4c2=3
Naked Single: r3c6=1
Full House: r3c9=3
Naked Single: r5c2=4
Naked Single: r2c8=1
Full House: r9c8=3
Naked Single: r9c9=1
Naked Single: r2c2=8
Full House: r8c2=7
Naked Single: r1c3=4
Naked Single: r2c6=7
Full House: r1c6=8
Full House: r1c9=7
Full House: r2c9=4
Naked Single: r8c7=2
Full House: r9c7=7
Naked Single: r9c3=2
Full House: r9c1=4
Naked Single: r8c1=5
Full House: r8c3=8
Naked Single: r5c3=6
Full House: r2c3=5
Full House: r2c1=6
Full House: r5c1=2
|
normal_sudoku_945 | ..6.5..4......18....4936.5.76....4..9...8467...5.6..3....6.5.2.....2.3.4..2..35.. | 196258743253471896874936251768392415931584672425167938389645127517829364642713589 | normal_sudoku_945 | 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 . 5 . . 4 .
. . . . . 1 8 . .
. . 4 9 3 6 . 5 .
7 6 . . . . 4 . .
9 . . . 8 4 6 7 .
. . 5 . 6 . . 3 .
. . . 6 . 5 . 2 .
. . . . 2 . 3 . 4
. . 2 . . 3 5 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 196258743253471896874936251768392415931584672425167938389645127517829364642713589 #1 Extreme (5450)
Locked Candidates Type 1 (Pointing): 8 in b2 => r1c12<>8
Hidden Pair: 3,5 in r45c4 => r45c4<>1, r45c4<>2
Finned Swordfish: 8 r367 c129 fr7c3 => r8c12,r9c12<>8
Grouped Discontinuous Nice Loop: 7 r7c2 -7- r8c23 =7= r8c46 -7- r79c5 =7= r2c5 -7- r2c3 =7= r123c2 -7- r7c2 => r7c2<>7
Grouped Discontinuous Nice Loop: 9 r8c2 -9- r1c2 =9= r1c79 -9- r2c8 -6- r8c8 =6= r8c1 =5= r8c2 => r8c2<>9
Grouped Discontinuous Nice Loop: 7 r9c2 -7- r8c23 =7= r8c46 -7- r79c5 =7= r2c5 -7- r2c3 =7= r123c2 -7- r9c2 => r9c2<>7
Forcing Chain Contradiction in r9 => r9c9<>1
r9c9=1 r9c9<>6 r2c9=6 r2c8<>6 r2c8=9 r2c3<>9 r12c2=9 r9c2<>9
r9c9=1 r89c8<>1 r4c8=1 r4c5<>1 r4c5=9 r9c5<>9
r9c9=1 r9c9<>6 r2c9=6 r2c8<>6 r2c8=9 r9c8<>9
r9c9=1 r9c9<>9
Forcing Net Contradiction in r7c7 => r1c6<>2
r1c6=2 (r2c4<>2) r4c6<>2 r4c9=2 (r2c9<>2) r5c9<>2 r5c2=2 r2c2<>2 r2c1=2 (r2c1<>3) r2c1<>5 r2c2=5 (r2c2<>3) r8c2<>5 r8c1=5 r8c1<>6 r8c8=6 r2c8<>6 r2c9=6 r2c9<>3 r2c3=3 r4c3<>3 r4c4=3 r4c4<>5 r4c9=5 r4c9<>2 r4c6=2 r1c6<>2
Locked Candidates Type 1 (Pointing): 2 in b2 => r6c4<>2
Forcing Chain Contradiction in c3 => r8c4<>7
r8c4=7 r9c45<>7 r9c9=7 r9c9<>6 r2c9=6 r2c8<>6 r2c8=9 r2c3<>9
r8c4=7 r8c23<>7 r7c3=7 r7c3<>9
r8c4=7 r6c4<>7 r6c4=1 r4c5<>1 r4c5=9 r79c5<>9 r8c6=9 r8c3<>9
Forcing Net Contradiction in r9c9 => r1c6=8
r1c6<>8 (r1c6=7 r2c5<>7 r2c5=4 r2c4<>4 r9c4=4 r9c2<>4) r1c4=8 r8c4<>8 r8c4=1 (r8c8<>1) (r7c5<>1) r9c5<>1 r4c5=1 r4c8<>1 r9c8=1 r9c2<>1 r9c2=9 (r7c3<>9) r8c3<>9 r2c3=9 r2c8<>9 r2c8=6 r2c9<>6 r9c9=6
r1c6<>8 r1c4=8 (r9c4<>8) r8c4<>8 r8c4=1 (r8c8<>1) (r7c5<>1) r9c5<>1 r4c5=1 r4c8<>1 r9c8=1 r9c8<>8 r9c9=8
Grouped Discontinuous Nice Loop: 9 r4c8 -9- r4c5 =9= r79c5 -9- r8c6 -7- r9c45 =7= r9c9 =6= r2c9 -6- r2c8 -9- r4c8 => r4c8<>9
W-Wing: 8/1 in r4c8,r8c4 connected by 1 in r4c5,r6c4 => r8c8<>8
Grouped Discontinuous Nice Loop: 9 r8c8 -9- r8c6 -7- r9c45 =7= r9c9 =6= r2c9 -6- r2c8 -9- r8c8 => r8c8<>9
Empty Rectangle: 9 in b1 (r29c8) => r9c2<>9
Discontinuous Nice Loop: 1 r8c4 -1- r6c4 -7- r6c6 =7= r8c6 =9= r8c3 =8= r8c4 => r8c4<>1
Naked Single: r8c4=8
Locked Candidates Type 1 (Pointing): 8 in b7 => r7c9<>8
Sue de Coq: r8c123 - {15679} (r8c6 - {79}, r9c12 - {146}) => r7c123<>1, r7c12<>4
Hidden Single: r7c5=4
Naked Single: r2c5=7
Naked Single: r1c4=2
Full House: r2c4=4
Locked Candidates Type 1 (Pointing): 7 in b1 => r8c2<>7
Locked Candidates Type 1 (Pointing): 1 in b8 => r9c128<>1
Naked Single: r9c2=4
Naked Single: r9c1=6
Hidden Single: r6c1=4
Hidden Single: r8c8=6
Naked Single: r2c8=9
Naked Single: r2c3=3
Naked Single: r9c8=8
Full House: r4c8=1
Naked Single: r1c1=1
Naked Single: r5c3=1
Naked Single: r4c3=8
Naked Single: r4c5=9
Full House: r9c5=1
Naked Single: r1c7=7
Naked Single: r8c1=5
Naked Single: r6c2=2
Full House: r5c2=3
Naked Single: r4c6=2
Naked Single: r9c4=7
Full House: r8c6=9
Full House: r6c6=7
Full House: r9c9=9
Naked Single: r1c2=9
Full House: r1c9=3
Naked Single: r2c1=2
Naked Single: r8c2=1
Full House: r8c3=7
Full House: r7c3=9
Naked Single: r2c2=5
Full House: r2c9=6
Naked Single: r6c7=9
Naked Single: r5c4=5
Full House: r5c9=2
Naked Single: r4c9=5
Full House: r6c9=8
Full House: r6c4=1
Full House: r4c4=3
Naked Single: r7c7=1
Full House: r3c7=2
Full House: r3c9=1
Full House: r7c9=7
Naked Single: r7c2=8
Full House: r3c2=7
Full House: r3c1=8
Full House: r7c1=3
|
normal_sudoku_1440 | .5.89.7....7.4..8.2..6..4.....9.3..46..124....9.5........4...13..1..854.54..1...8 | 354891726167245389289637451815973264673124895492586137728459613931768542546312978 | normal_sudoku_1440 | 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 . 8 9 . 7 . .
. . 7 . 4 . . 8 .
2 . . 6 . . 4 . .
. . . 9 . 3 . . 4
6 . . 1 2 4 . . .
. 9 . 5 . . . . .
. . . 4 . . . 1 3
. . 1 . . 8 5 4 .
5 4 . . 1 . . . 8 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 354891726167245389289637451815973264673124895492586137728459613931768542546312978 #1 Extreme (4636)
Locked Candidates Type 2 (Claiming): 7 in c4 => r7c56,r8c5,r9c6<>7
Locked Candidates Type 2 (Claiming): 7 in r7 => r8c12<>7
2-String Kite: 3 in r3c5,r9c3 (connected by r8c5,r9c4) => r3c3<>3
Turbot Fish: 9 r3c3 =9= r2c1 -9- r8c1 =9= r8c9 => r3c9<>9
Discontinuous Nice Loop: 3 r3c2 -3- r3c5 =3= r8c5 -3- r8c1 -9- r2c1 =9= r3c3 =8= r3c2 => r3c2<>3
Almost Locked Set XZ-Rule: A=r2c12,r3c23 {13689}, B=r1c6,r2c4 {123}, X=3, Z=1 => r1c1<>1
Hidden Rectangle: 3/4 in r1c13,r6c13 => r6c3<>3
Discontinuous Nice Loop: 1 r2c6 -1- r1c6 =1= r1c9 -1- r3c9 -5- r2c9 =5= r2c6 => r2c6<>1
Almost Locked Set XY-Wing: A=r2c12,r3c23 {13689}, B=r8c45,r9c4 {2367}, C=r2c4 {23}, X,Y=2,3, Z=6 => r8c2<>6
Empty Rectangle: 6 in b5 (r8c59) => r6c9<>6
W-Wing: 2/3 in r2c4,r8c2 connected by 3 in r9c34 => r8c4<>2
Grouped AIC: 5 5- r2c6 -2- r2c4 -3- r9c4 =3= r9c3 =6= r7c23 -6- r7c5 -5 => r3c5,r7c6<>5
Hidden Single: r7c5=5
Grouped Discontinuous Nice Loop: 6 r7c6 -6- r8c5 -3- r9c4 =3= r9c3 =6= r7c23 -6- r7c6 => r7c6<>6
Uniqueness Test 5: 2/9 in r7c67,r9c67 => r9c8<>6
Forcing Chain Contradiction in r7c7 => r2c7<>2
r2c7=2 r7c7<>2
r2c7=2 r2c4<>2 r2c4=3 r9c4<>3 r9c3=3 r9c3<>6 r7c23=6 r7c7<>6
r2c7=2 r2c4<>2 r9c4=2 r7c6<>2 r7c6=9 r7c7<>9
Forcing Chain Contradiction in r6c9 => r1c6=1
r1c6<>1 r1c9=1 r6c9<>1
r1c6<>1 r1c6=2 r1c8<>2 r12c9=2 r6c9<>2
r1c6<>1 r3c6=1 r3c6<>7 r6c6=7 r6c9<>7
Locked Candidates Type 1 (Pointing): 2 in b2 => r2c9<>2
Forcing Chain Contradiction in r6c9 => r2c4=2
r2c4<>2 r2c6=2 r2c6<>5 r2c9=5 r3c9<>5 r3c9=1 r6c9<>1
r2c4<>2 r2c4=3 r3c5<>3 r8c5=3 r8c5<>6 r8c9=6 r1c9<>6 r1c9=2 r6c9<>2
r2c4<>2 r2c4=3 r3c5<>3 r3c5=7 r3c6<>7 r6c6=7 r6c9<>7
Naked Single: r2c6=5
Naked Single: r3c6=7
Full House: r3c5=3
Naked Single: r6c6=6
Naked Single: r8c5=6
Locked Candidates Type 1 (Pointing): 6 in b9 => r24c7<>6
Hidden Single: r4c8=6
Hidden Single: r4c3=5
Skyscraper: 2 in r4c7,r8c9 (connected by r48c2) => r6c9,r79c7<>2
Locked Pair: 6,9 in r79c7 => r25c7,r8c9,r9c8<>9
Hidden Single: r8c1=9
Hidden Single: r2c9=9
Naked Single: r3c8=5
Naked Single: r3c9=1
Naked Single: r2c7=3
Naked Single: r3c2=8
Full House: r3c3=9
Naked Single: r6c9=7
Naked Single: r1c8=2
Full House: r1c9=6
Naked Single: r2c1=1
Full House: r2c2=6
Naked Single: r5c7=8
Naked Single: r5c9=5
Full House: r8c9=2
Naked Single: r6c5=8
Full House: r4c5=7
Naked Single: r6c8=3
Naked Single: r9c8=7
Full House: r5c8=9
Naked Single: r5c3=3
Full House: r5c2=7
Naked Single: r8c2=3
Full House: r8c4=7
Full House: r9c4=3
Naked Single: r4c1=8
Naked Single: r6c1=4
Naked Single: r1c3=4
Full House: r1c1=3
Full House: r7c1=7
Naked Single: r7c2=2
Full House: r4c2=1
Full House: r6c3=2
Full House: r4c7=2
Full House: r6c7=1
Naked Single: r7c6=9
Full House: r9c6=2
Naked Single: r9c3=6
Full House: r7c3=8
Full House: r7c7=6
Full House: r9c7=9
|
normal_sudoku_1634 | ..9.4.8.3.7......13.8..1.7..235...9.8.7..935..9......793..6.....82....3.7.1..3..9 | 159742863276385941348691572623578194817429356594136287935264718482917635761853429 | normal_sudoku_1634 | 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 . 4 . 8 . 3
. 7 . . . . . . 1
3 . 8 . . 1 . 7 .
. 2 3 5 . . . 9 .
8 . 7 . . 9 3 5 .
. 9 . . . . . . 7
9 3 . . 6 . . . .
. 8 2 . . . . 3 .
7 . 1 . . 3 . . 9 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 159742863276385941348691572623578194817429356594136287935264718482917635761853429 #1 Extreme (10032)
Almost Locked Set XY-Wing: A=r235689c5 {1235789}, B=r4c79,r5c9,r6c7 {12468}, C=r8c1679 {14567}, X,Y=1,7, Z=8 => r4c5<>8
Forcing Net Contradiction in r6c8 => r1c1<>6
r1c1=6 (r8c1<>6) (r2c3<>6 r6c3=6 r6c3<>5) (r2c3<>6 r6c3=6 r5c2<>6 r9c2=6 r9c2<>5) r1c1<>1 r1c2=1 r1c2<>5 r3c2=5 (r3c9<>5) r2c3<>5 r7c3=5 r7c9<>5 r8c9=5 r8c9<>6 r8c7=6 (r8c7<>1) r8c7<>7 r7c7=7 r7c7<>1 r7c8=1 r6c8<>1
r1c1=6 r1c8<>6 r1c8=2 r6c8<>2
r1c1=6 (r1c1<>1 r1c2=1 r5c2<>1 r5c2=4 r4c1<>4 r4c1=1 r4c7<>1) (r1c6<>6) (r1c8<>6) (r1c2<>6) (r3c2<>6) r2c3<>6 r6c3=6 (r6c6<>6) (r6c8<>6) r5c2<>6 r9c2=6 r9c8<>6 r2c8=6 r2c6<>6 r4c6=6 r4c7<>6 r4c7=4 r6c8<>4
r1c1=6 r2c3<>6 r6c3=6 r6c8<>6
r1c1=6 (r1c1<>1 r1c2=1 r1c2<>5 r3c2=5 r3c9<>5 r3c9=4 r4c9<>4) (r1c6<>6) (r1c8<>6) (r1c2<>6) (r3c2<>6) r2c3<>6 r6c3=6 (r6c6<>6) (r6c8<>6) r5c2<>6 r9c2=6 r9c8<>6 r2c8=6 r2c6<>6 r4c6=6 r4c9<>6 r4c9=8 r6c8<>8
Forcing Net Contradiction in c6 => r1c2<>6
r1c2=6 r1c8<>6 r1c8=2 r1c6<>2
r1c2=6 r1c8<>6 r1c8=2 r1c1<>2 r2c1=2 r2c6<>2
r1c2=6 r1c2<>1 r5c2=1 r5c5<>1 r5c5=2 r6c6<>2
r1c2=6 (r1c8<>6 r1c8=2 r3c9<>2) r1c2<>1 r5c2=1 r5c5<>1 r5c5=2 r5c9<>2 r7c9=2 r7c6<>2
Almost Locked Set XZ-Rule: A=r1c128 {1256}, B=r2c138 {2456}, X=5, Z=6 => r2c7<>6
Forcing Net Contradiction in c4 => r2c1<>5
r2c1=5 (r3c2<>5 r9c2=5 r9c2<>6 r8c1=6 r8c9<>6 r8c9=4 r5c9<>4) (r3c2<>5) r6c1<>5 r6c3=5 r6c3<>6 r2c3=6 r3c2<>6 r3c2=4 r5c2<>4 r5c4=4
r2c1=5 (r1c2<>5) r3c2<>5 r9c2=5 (r9c2<>4) (r9c5<>5 r8c5=5 r8c9<>5) r9c2<>6 r8c1=6 r8c9<>6 r8c9=4 (r9c7<>4) r9c8<>4 r9c4=4
Forcing Net Contradiction in r6c8 => r2c1<>6
r2c1=6 (r2c3<>6 r6c3=6 r6c7<>6) (r2c3<>6 r6c3=6 r5c2<>6 r9c2=6 r9c7<>6) (r2c6<>6) (r2c3<>6 r6c3=6 r6c6<>6) r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 (r3c7<>6) r1c6<>6 r4c6=6 r4c7<>6 r8c7=6 (r8c7<>1) r8c7<>7 r7c7=7 r7c7<>1 r7c8=1 r6c8<>1
r2c1=6 (r2c8<>6) (r2c3<>6 r6c3=6 r6c3<>5 r6c1=5 r8c1<>5 r7c3=5 r2c3<>5) (r2c3<>6 r6c3=6 r5c2<>6 r9c2=6 r9c2<>5) r2c1<>2 r1c1=2 (r1c1<>5) r1c1<>1 r1c2=1 (r5c2<>1 r5c2=4 r3c2<>4) r1c2<>5 r3c2=5 r1c2<>5 r1c6=5 (r2c5<>5) r2c6<>5 r2c7=5 r2c7<>9 r3c7=9 r3c7<>4 r3c9=4 r2c8<>4 r2c8=2 r6c8<>2
r2c1=6 (r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 r1c6<>6 r4c6=6 r4c7<>6) (r2c1<>2 r1c1=2 r1c1<>1) r2c3<>6 r6c3=6 r6c3<>5 r6c1=5 r6c1<>1 r4c1=1 r4c7<>1 r4c7=4 r6c8<>4
r2c1=6 r2c3<>6 r6c3=6 r6c8<>6
r2c1=6 (r2c6<>6) (r2c3<>6 r6c3=6 r6c6<>6) r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 r1c6<>6 r4c6=6 r4c6<>8 r4c9=8 r6c8<>8
XYZ-Wing: 2/4/6 in r12c8,r2c1 => r2c7<>2
Forcing Chain Contradiction in r2c8 => r2c4<>2
r2c4=2 r2c8<>2
r2c4=2 r2c1<>2 r2c1=4 r2c8<>4
r2c4=2 r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 r2c8<>6
Forcing Chain Contradiction in r2c8 => r2c5<>2
r2c5=2 r2c8<>2
r2c5=2 r2c1<>2 r2c1=4 r2c8<>4
r2c5=2 r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 r2c8<>6
Forcing Chain Contradiction in r2c8 => r2c6<>2
r2c6=2 r2c8<>2
r2c6=2 r2c1<>2 r2c1=4 r2c8<>4
r2c6=2 r2c1<>2 r1c1=2 r1c8<>2 r1c8=6 r2c8<>6
Forcing Chain Contradiction in r2c8 => r2c7<>4
r2c7=4 r2c1<>4 r2c1=2 r2c8<>2
r2c7=4 r2c8<>4
r2c7=4 r2c13<>4 r3c2=4 r3c2<>6 r2c3=6 r2c8<>6
Forcing Net Contradiction in r6c8 => r2c3<>5
r2c3=5 (r2c5<>5) (r1c2<>5 r1c6=5 r3c5<>5) (r1c2<>5) r3c2<>5 r9c2=5 r9c5<>5 r8c5=5 (r8c5<>1) r8c5<>9 r8c4=9 r8c4<>1 r8c7=1 r7c8<>1 r6c8=1
r2c3=5 (r7c3<>5 r7c3=4 r7c8<>4) (r2c3<>6 r6c3=6 r5c2<>6 r5c2=4 r4c1<>4 r2c1=4 r2c8<>4) (r2c5<>5) (r1c2<>5 r1c6=5 r3c5<>5) (r1c2<>5) r3c2<>5 r9c2=5 (r8c1<>5 r8c1=6 r8c9<>6) r9c5<>5 r8c5=5 r8c9<>5 r8c9=4 r9c8<>4 r6c8=4
Naked Triple: 2,4,6 in r2c138 => r2c46<>6
Forcing Net Contradiction in r3 => r2c3=6
r2c3<>6 (r2c8=6 r1c8<>6 r1c8=2 r9c8<>2) (r2c8=6 r9c8<>6) (r2c3=4 r7c3<>4 r7c3=5 r9c2<>5) r3c2=6 r9c2<>6 r9c2=4 (r9c4<>4) r9c8<>4 r9c8=8 r9c4<>8 r9c4=2 r3c4<>2
r2c3<>6 (r6c3=6 r5c2<>6) (r2c3=4 r7c3<>4 r7c3=5 r9c2<>5) r3c2=6 r9c2<>6 r9c2=4 r5c2<>4 r5c2=1 r5c5<>1 r5c5=2 r3c5<>2
r2c3<>6 r2c8=6 r1c8<>6 r1c8=2 r3c7<>2
r2c3<>6 r2c8=6 r1c8<>6 r1c8=2 r3c9<>2
Grouped Discontinuous Nice Loop: 4 r3c7 -4- r3c2 -5- r3c79 =5= r2c7 =9= r3c7 => r3c7<>4
Finned Swordfish: 4 r359 c249 fr9c7 fr9c8 => r78c9<>4
Forcing Chain Contradiction in c9 => r9c2<>4
r9c2=4 r3c2<>4 r3c9=4 r3c9<>6
r9c2=4 r3c2<>4 r3c2=5 r1c12<>5 r1c6=5 r2c6<>5 r2c6=8 r4c6<>8 r4c9=8 r4c9<>6
r9c2=4 r9c2<>6 r5c2=6 r5c9<>6
r9c2=4 r9c2<>6 r8c1=6 r8c9<>6
Turbot Fish: 4 r2c8 =4= r2c1 -4- r8c1 =4= r7c3 => r7c8<>4
Forcing Net Contradiction in r2c8 => r2c1=2
r2c1<>2 r2c1=4 (r8c1<>4) r3c2<>4 r5c2=4 (r5c2<>6) r5c2<>6 r9c2=6 r8c1<>6 r8c1=5 r8c9<>5 r8c9=6 r5c9<>6 r5c4=6 (r4c6<>6) r6c6<>6 r1c6=6 r1c8<>6 r1c8=2 r2c8<>2 r2c1=2
Naked Single: r2c8=4
Hidden Single: r3c2=4
Locked Candidates Type 1 (Pointing): 5 in b1 => r1c6<>5
Locked Candidates Type 1 (Pointing): 4 in b9 => r46c7<>4
Forcing Chain Contradiction in r7 => r5c9<>2
r5c9=2 r5c5<>2 r5c5=1 r5c2<>1 r5c2=6 r9c2<>6 r9c2=5 r7c3<>5
r5c9=2 r5c9<>4 r4c9=4 r4c9<>8 r4c6=8 r2c6<>8 r2c6=5 r7c6<>5
r5c9=2 r5c5<>2 r5c5=1 r5c2<>1 r5c2=6 r9c2<>6 r8c1=6 r8c9<>6 r8c9=5 r7c7<>5
r5c9=2 r5c9<>4 r4c9=4 r4c9<>8 r7c9=8 r7c9<>5
Locked Candidates Type 1 (Pointing): 2 in b6 => r6c456<>2
Skyscraper: 2 in r1c6,r3c9 (connected by r7c69) => r1c8,r3c45<>2
Naked Single: r1c8=6
Hidden Single: r3c4=6
Skyscraper: 6 in r5c9,r9c7 (connected by r59c2) => r46c7,r8c9<>6
Naked Single: r4c7=1
Naked Single: r8c9=5
Naked Single: r4c5=7
Naked Single: r6c7=2
Naked Single: r3c9=2
Naked Single: r6c8=8
Naked Single: r7c9=8
Naked Single: r9c8=2
Full House: r7c8=1
Hidden Single: r4c6=8
Naked Single: r2c6=5
Naked Single: r2c7=9
Full House: r3c7=5
Full House: r3c5=9
Naked Single: r8c5=1
Naked Single: r5c5=2
Naked Single: r6c5=3
Naked Single: r2c5=8
Full House: r2c4=3
Full House: r9c5=5
Naked Single: r9c2=6
Naked Single: r5c2=1
Full House: r1c2=5
Full House: r1c1=1
Naked Single: r8c1=4
Full House: r7c3=5
Full House: r6c3=4
Naked Single: r9c7=4
Full House: r9c4=8
Naked Single: r5c4=4
Full House: r5c9=6
Full House: r4c9=4
Full House: r4c1=6
Full House: r6c1=5
Naked Single: r8c6=7
Naked Single: r6c4=1
Full House: r6c6=6
Naked Single: r7c7=7
Full House: r8c7=6
Full House: r8c4=9
Naked Single: r1c6=2
Full House: r1c4=7
Full House: r7c4=2
Full House: r7c6=4
|
normal_sudoku_2767 | ..7..62...62..8.73.9....16.571843629623..1.4.849562731.3.1..4.7.8..3..1.7........ | 457316298162498573398257164571843629623971845849562731936125487285734916714689352 | normal_sudoku_2767 | 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 2 . .
. 6 2 . . 8 . 7 3
. 9 . . . . 1 6 .
5 7 1 8 4 3 6 2 9
6 2 3 . . 1 . 4 .
8 4 9 5 6 2 7 3 1
. 3 . 1 . . 4 . 7
. 8 . . 3 . . 1 .
7 . . . . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 457316298162498573398257164571843629623971845849562731936125487285734916714689352 #1 Easy (206)
Hidden Single: r7c3=6
Hidden Single: r3c3=8
Hidden Single: r9c7=3
Hidden Single: r9c2=1
Full House: r1c2=5
Hidden Single: r5c7=8
Full House: r5c9=5
Naked Single: r3c9=4
Naked Single: r1c9=8
Naked Single: r3c1=3
Naked Single: r1c8=9
Full House: r2c7=5
Full House: r8c7=9
Naked Single: r1c5=1
Naked Single: r1c1=4
Full House: r1c4=3
Full House: r2c1=1
Naked Single: r2c5=9
Full House: r2c4=4
Naked Single: r8c1=2
Full House: r7c1=9
Naked Single: r5c5=7
Full House: r5c4=9
Naked Single: r8c9=6
Full House: r9c9=2
Naked Single: r7c6=5
Naked Single: r8c4=7
Naked Single: r9c4=6
Full House: r3c4=2
Naked Single: r3c6=7
Full House: r3c5=5
Naked Single: r7c8=8
Full House: r7c5=2
Full House: r9c5=8
Full House: r9c8=5
Naked Single: r8c6=4
Full House: r8c3=5
Full House: r9c3=4
Full House: r9c6=9
|
normal_sudoku_375 | ..98...54.4...5.......943...7.5..4....4.8..25......6.719.2..54.42.95..6...5..8.92 | 769832154843165279251794386976521438314687925582349617198276543427953861635418792 | normal_sudoku_375 | 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 4
. 4 . . . 5 . . .
. . . . 9 4 3 . .
. 7 . 5 . . 4 . .
. . 4 . 8 . . 2 5
. . . . . . 6 . 7
1 9 . 2 . . 5 4 .
4 2 . 9 5 . . 6 .
. . 5 . . 8 . 9 2 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 769832154843165279251794386976521438314687925582349617198276543427953861635418792 #1 Extreme (3016)
Locked Candidates Type 1 (Pointing): 8 in b7 => r2346c3<>8
Locked Candidates Type 1 (Pointing): 3 in b9 => r4c9<>3
Locked Candidates Type 1 (Pointing): 7 in b9 => r12c7<>7
Locked Candidates Type 2 (Claiming): 2 in r3 => r12c1,r2c3<>2
Naked Triple: 1,3,6 in r159c2 => r36c2<>1, r3c2<>6, r6c2<>3
Uniqueness Test 4: 5/8 in r3c12,r6c12 => r36c1<>8
2-String Kite: 8 in r2c1,r6c8 (connected by r4c1,r6c2) => r2c8<>8
Discontinuous Nice Loop: 7 r2c5 -7- r2c8 -1- r1c7 -2- r2c7 =2= r2c5 => r2c5<>7
Grouped Discontinuous Nice Loop: 1 r2c9 -1- r8c9 =1= r89c7 -1- r5c7 -9- r2c7 =9= r2c9 => r2c9<>1
Grouped Discontinuous Nice Loop: 1 r3c9 -1- r8c9 =1= r89c7 -1- r5c7 -9- r2c7 =9= r2c9 =6= r3c9 => r3c9<>1
Grouped Discontinuous Nice Loop: 7 r3c3 =2= r3c1 =5= r3c2 =8= r2c1 -8- r2c7 =8= r8c7 =7= r9c7 -7- r9c1 =7= r123c1 -7- r3c3 => r3c3<>7
Almost Locked Set XZ-Rule: A=r12459c1 {236789}, B=r46c3,r5c2 {1236}, X=2, Z=3 => r6c1<>3
Almost Locked Set XZ-Rule: A=r1259c1 {36789}, B=r1589c7 {12789}, X=9, Z=8 => r2c7<>8
Hidden Single: r8c7=8
Naked Single: r7c9=3
Naked Single: r8c9=1
Full House: r9c7=7
Hidden Single: r7c3=8
Hidden Single: r8c3=7
Full House: r8c6=3
Locked Candidates Type 1 (Pointing): 6 in b7 => r9c45<>6
Uniqueness Test 3: 3/6 in r5c12,r9c12 => r5c46<>1, r5c6<>9
Naked Pair: 6,7 in r57c6 => r14c6<>6, r1c6<>7
Naked Pair: 1,2 in r1c67 => r1c25<>1, r1c5<>2
Hidden Single: r5c2=1
Naked Single: r5c7=9
Naked Single: r4c9=8
Naked Single: r3c9=6
Full House: r2c9=9
Hidden Single: r2c1=8
Naked Single: r3c2=5
Naked Single: r6c2=8
Hidden Single: r3c8=8
Hidden Single: r6c1=5
Hidden Single: r2c8=7
Hidden Single: r6c6=9
Hidden Single: r4c1=9
Hidden Single: r3c1=2
Naked Single: r3c3=1
Full House: r3c4=7
Hidden Single: r1c1=7
Hidden Single: r7c5=7
Full House: r7c6=6
Naked Single: r5c6=7
Remote Pair: 3/6 r1c5 -6- r1c2 -3- r9c2 -6- r9c1 -3- r5c1 -6- r5c4 => r2c4,r46c5<>3, r2c4,r4c5<>6
Naked Single: r2c4=1
Naked Single: r1c6=2
Full House: r4c6=1
Naked Single: r2c7=2
Full House: r1c7=1
Naked Single: r9c4=4
Full House: r9c5=1
Naked Single: r4c5=2
Naked Single: r4c8=3
Full House: r4c3=6
Full House: r6c8=1
Naked Single: r6c4=3
Full House: r5c4=6
Full House: r6c5=4
Full House: r5c1=3
Full House: r6c3=2
Full House: r2c3=3
Full House: r9c1=6
Full House: r1c2=6
Full House: r2c5=6
Full House: r9c2=3
Full House: r1c5=3
|
normal_sudoku_1781 | .48..1..7.7...491....7...4..8.9....421.4...594.9.32.......6.....9.8....18.....5.. | 948651237675324918123798645386975124217486359459132876731569482592843761864217593 | normal_sudoku_1781 | 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 . . 1 . . 7
. 7 . . . 4 9 1 .
. . . 7 . . . 4 .
. 8 . 9 . . . . 4
2 1 . 4 . . . 5 9
4 . 9 . 3 2 . . .
. . . . 6 . . . .
. 9 . 8 . . . . 1
8 . . . . . 5 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 948651237675324918123798645386975124217486359459132876731569482592843761864217593 #1 Extreme (10420)
Locked Candidates Type 1 (Pointing): 8 in b5 => r5c7<>8
Locked Candidates Type 2 (Claiming): 7 in r6 => r4c78,r5c7<>7
Discontinuous Nice Loop: 2 r7c8 -2- r4c8 =2= r4c7 =1= r6c7 =7= r6c8 =8= r7c8 => r7c8<>2
Discontinuous Nice Loop: 8 r7c7 -8- r7c8 =8= r6c8 =7= r6c7 =1= r6c4 -1- r4c5 =1= r9c5 =4= r9c3 -4- r7c3 =4= r7c7 => r7c7<>8
Discontinuous Nice Loop: 3 r3c7 -3- r5c7 -6- r6c9 -8- r6c7 =8= r3c7 => r3c7<>3
Discontinuous Nice Loop: 7 r8c5 -7- r5c5 -8- r5c6 =8= r3c6 -8- r3c7 =8= r6c7 =1= r6c4 -1- r4c5 =1= r9c5 =4= r8c5 => r8c5<>7
Discontinuous Nice Loop: 2 r9c8 -2- r4c8 =2= r4c7 =1= r6c7 =7= r6c8 =8= r7c8 =9= r9c8 => r9c8<>2
Discontinuous Nice Loop: 7 r9c5 -7- r5c5 -8- r5c6 =8= r3c6 -8- r3c7 =8= r6c7 =1= r6c4 -1- r4c5 =1= r9c5 => r9c5<>7
Locked Candidates Type 1 (Pointing): 7 in b8 => r45c6<>7
Discontinuous Nice Loop: 9 r9c5 -9- r9c8 =9= r7c8 =8= r6c8 =7= r6c7 =1= r6c4 -1- r4c5 =1= r9c5 => r9c5<>9
Locked Candidates Type 1 (Pointing): 9 in b8 => r3c6<>9
Almost Locked Set XZ-Rule: A=r5c7,r6c89 {3678}, B=r7c89,r89c8,r9c9 {236789}, X=7, Z=3 => r78c7<>3
Almost Locked Set XY-Wing: A=r9c249 {1236}, B=r148c8 {2367}, C=r6c2489 {15678}, X,Y=1,7, Z=3,6 => r9c8<>3, r9c8<>6
Hidden Rectangle: 7/9 in r7c68,r9c68 => r7c6<>7
Almost Locked Set XY-Wing: A=r1345c7 {12368}, B=r7c89,r8c78,r9c89 {2346789}, C=r123458c5 {1245789}, X,Y=1,4, Z=2 => r7c7<>2
Forcing Chain Contradiction in r8 => r3c5<>2
r3c5=2 r3c2<>2 r79c2=2 r8c3<>2
r3c5=2 r8c5<>2
r3c5=2 r1c45<>2 r1c78=2 r23c9<>2 r79c9=2 r8c7<>2
r3c5=2 r1c45<>2 r1c78=2 r23c9<>2 r79c9=2 r8c8<>2
Forcing Chain Verity => r2c5<>5
r1c5=2 r1c5<>9 r1c1=9 r1c1<>5 r1c45=5 r2c5<>5
r2c5=2 r2c5<>5
r8c5=2 r8c5<>4 r9c5=4 r9c5<>1 r4c5=1 r4c7<>1 r6c7=1 r6c7<>8 r3c7=8 r2c9<>8 r2c5=8 r2c5<>5
r9c5=2 r9c5<>1 r4c5=1 r4c7<>1 r6c7=1 r6c7<>8 r3c7=8 r2c9<>8 r2c5=8 r2c5<>5
Forcing Chain Contradiction in r3c5 => r3c6<>5
r3c6=5 r3c5<>5
r3c6=5 r3c9<>5 r2c9=5 r2c9<>8 r2c5=8 r3c5<>8
r3c6=5 r1c45<>5 r1c1=5 r1c1<>9 r1c5=9 r3c5<>9
Forcing Chain Contradiction in r8 => r3c7<>2
r3c7=2 r3c2<>2 r79c2=2 r8c3<>2
r3c7=2 r3c7<>8 r6c7=8 r6c7<>1 r6c4=1 r4c5<>1 r9c5=1 r9c5<>4 r8c5=4 r8c5<>2
r3c7=2 r8c7<>2
r3c7=2 r4c7<>2 r4c8=2 r8c8<>2
Forcing Chain Contradiction in r3c6 => r7c6<>3
r7c6=3 r3c6<>3
r7c6=3 r7c6<>9 r7c8=9 r7c8<>8 r7c9=8 r6c9<>8 r6c9=6 r6c4<>6 r12c4=6 r3c6<>6
r7c6=3 r7c6<>9 r7c8=9 r7c8<>8 r7c9=8 r2c9<>8 r2c5=8 r3c6<>8
Forcing Net Verity => r6c2=5
r7c4=3 (r1c4<>3) (r7c9<>3) (r7c2<>3) (r8c6<>3) r9c6<>3 r3c6=3 (r3c9<>3) r3c2<>3 r9c2=3 (r8c3<>3 r8c8=3 r1c8<>3) r9c9<>3 r2c9=3 r1c7<>3 r1c1=3 (r1c1<>5) r1c1<>9 r1c5=9 r1c5<>5 r1c4=5 r6c4<>5 r6c2=5
r8c6=3 (r8c6<>5) r8c6<>7 r9c6=7 r9c8<>7 r9c8=9 r7c8<>9 r7c6=9 r7c6<>5 r4c6=5 r6c4<>5 r6c2=5
r9c4=3 (r1c4<>3) (r9c9<>3) (r9c2<>3) (r8c6<>3) r9c6<>3 r3c6=3 (r3c9<>3) r3c2<>3 r7c2=3 r7c9<>3 r2c9=3 (r1c7<>3) r1c8<>3 r1c1=3 (r1c1<>5) r1c1<>9 r1c5=9 r1c5<>5 r1c4=5 r6c4<>5 r6c2=5
r9c6=3 (r9c6<>7 r8c6=7 r8c6<>5) r9c6<>9 r9c8=9 r7c8<>9 r7c6=9 r7c6<>5 r4c6=5 r6c4<>5 r6c2=5
Grouped Discontinuous Nice Loop: 6 r9c3 -6- r9c2 =6= r3c2 -6- r3c6 =6= r12c4 -6- r6c4 -1- r4c5 =1= r9c5 =4= r9c3 => r9c3<>6
Forcing Chain Contradiction in c6 => r3c3<>6
r3c3=6 r3c6<>6
r3c3=6 r5c3<>6 r4c13=6 r4c6<>6
r3c3=6 r3c7<>6 r3c7=8 r3c6<>8 r5c6=8 r5c6<>6
Forcing Chain Contradiction in c6 => r8c3<>6
r8c3=6 r9c2<>6 r3c2=6 r3c6<>6
r8c3=6 r5c3<>6 r4c13=6 r4c6<>6
r8c3=6 r9c2<>6 r3c2=6 r3c7<>6 r3c7=8 r3c6<>8 r5c6=8 r5c6<>6
Forcing Net Verity => r1c1=9
r3c5=5 (r3c5<>8) (r4c5<>5 r4c6=5 r4c6<>6) (r2c4<>5) (r1c4<>5) r1c5<>5 r1c1=5 (r2c1<>5) r2c3<>5 r2c9=5 r2c9<>8 r2c5=8 r5c5<>8 r5c6=8 r5c6<>6 r3c6=6 (r3c9<>6) (r2c4<>6 r6c4=6 r6c9<>6) r3c2<>6 r9c2=6 r9c9<>6 r2c9=6 r2c9<>5 r3c9=5 r3c5<>5 r3c5=9 r1c5<>9 r1c1=9
r3c5=8 (r3c5<>5) r2c5<>8 r2c9=8 r6c9<>8 r6c9=6 r9c9<>6 r9c2=6 (r9c2<>3) r9c2<>3 r7c2=3 r7c4<>3 r9c4=3 (r9c9<>3) r9c6<>3 r3c6=3 (r3c9<>3) (r8c6<>3) (r1c4<>3) (r2c4<>3) (r3c2<>3) r3c2<>3 r7c2=3 r7c9<>3 r2c9=3 r2c9<>8 r2c5=8 r3c5<>8 r3c5=9 r1c5<>9 r1c1=9
r3c5=9 r1c5<>9 r1c1=9
Hidden Single: r3c5=9
Locked Candidates Type 2 (Claiming): 5 in r1 => r2c4<>5
Forcing Chain Contradiction in c9 => r4c7=1
r4c7<>1 r4c5=1 r6c4<>1 r6c4=6 r1c4<>6 r1c78=6 r2c9<>6
r4c7<>1 r4c5=1 r6c4<>1 r6c4=6 r1c4<>6 r1c78=6 r3c9<>6
r4c7<>1 r4c5=1 r6c4<>1 r6c4=6 r6c9<>6
r4c7<>1 r4c5=1 r6c4<>1 r6c4=6 r12c4<>6 r3c6=6 r3c2<>6 r9c2=6 r9c9<>6
Hidden Single: r9c5=1
Hidden Single: r6c4=1
Hidden Single: r4c8=2
Hidden Single: r9c3=4
Hidden Single: r8c5=4
Hidden Single: r5c7=3
Hidden Single: r7c7=4
Locked Candidates Type 1 (Pointing): 6 in b5 => r3c6<>6
Locked Candidates Type 1 (Pointing): 2 in b8 => r12c4<>2
Naked Triple: 2,3,6 in r9c249 => r9c6<>3
2-String Kite: 3 in r1c8,r8c6 (connected by r1c4,r3c6) => r8c8<>3
XY-Wing: 6/8/3 in r1c8,r3c67 => r1c4,r3c9<>3
Hidden Single: r1c8=3
W-Wing: 2/3 in r7c2,r9c4 connected by 3 in r79c9 => r7c4,r9c2<>2
Hidden Single: r9c4=2
XY-Wing: 3/8/6 in r2c4,r3c67 => r2c9<>6
Uniqueness Test 3: 7/9 in r7c68,r9c68 => r7c13<>3, r7c13<>5, r7c3<>2
Locked Pair: 1,7 in r7c13 => r7c8,r8c13<>7
Locked Candidates Type 1 (Pointing): 5 in b7 => r8c6<>5
Empty Rectangle: 3 in b7 (r38c6) => r3c2<>3
Locked Candidates Type 2 (Claiming): 3 in c2 => r8c13<>3
Hidden Single: r8c6=3
Naked Single: r3c6=8
Naked Single: r7c4=5
Naked Single: r2c5=2
Naked Single: r3c7=6
Naked Single: r5c6=6
Naked Single: r1c4=6
Full House: r2c4=3
Full House: r1c5=5
Full House: r1c7=2
Naked Single: r7c6=9
Full House: r9c6=7
Full House: r4c6=5
Naked Single: r3c2=2
Naked Single: r5c3=7
Full House: r5c5=8
Full House: r4c5=7
Naked Single: r3c9=5
Full House: r2c9=8
Naked Single: r8c7=7
Full House: r6c7=8
Naked Single: r7c8=8
Naked Single: r9c8=9
Naked Single: r7c2=3
Full House: r9c2=6
Full House: r9c9=3
Naked Single: r7c3=1
Naked Single: r6c9=6
Full House: r7c9=2
Full House: r8c8=6
Full House: r7c1=7
Full House: r6c8=7
Naked Single: r8c1=5
Full House: r8c3=2
Naked Single: r3c3=3
Full House: r3c1=1
Naked Single: r2c1=6
Full House: r2c3=5
Full House: r4c3=6
Full House: r4c1=3
|
normal_sudoku_2398 | ..856.4.2...2....12...1.5......56.28..517264..2.84...5...78..5.9.362581....4....6 | 318567492459238761276914583794356128835172649621849375162783954943625817587491236 | normal_sudoku_2398 | 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 6 . 4 . 2
. . . 2 . . . . 1
2 . . . 1 . 5 . .
. . . . 5 6 . 2 8
. . 5 1 7 2 6 4 .
. 2 . 8 4 . . . 5
. . . 7 8 . . 5 .
9 . 3 6 2 5 8 1 .
. . . 4 . . . . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 318567492459238761276914583794356128835172649621849375162783954943625817587491236 #1 Hard (1160)
Naked Pair: 3,9 in r2c5,r3c4 => r123c6<>3, r123c6<>9
Naked Single: r1c6=7
Naked Triple: 3,7,9 in r1c8,r2c7,r3c9 => r23c8<>3, r23c8<>7, r23c8<>9
Hidden Pair: 5,8 in r9c12 => r9c12<>1, r9c12<>7
Skyscraper: 9 in r1c8,r5c9 (connected by r15c2) => r3c9,r6c8<>9
Skyscraper: 9 in r1c8,r2c5 (connected by r9c58) => r2c7<>9
Hidden Single: r1c8=9
Locked Candidates Type 2 (Claiming): 3 in r1 => r2c12,r3c2<>3
2-String Kite: 3 in r2c7,r4c4 (connected by r2c5,r3c4) => r4c7<>3
Jellyfish: 3 r1345 c1249 => r6c1,r7c9<>3
Skyscraper: 3 in r2c5,r7c6 (connected by r27c7) => r9c5<>3
Naked Single: r9c5=9
Full House: r2c5=3
Naked Single: r2c7=7
Naked Single: r3c4=9
Full House: r4c4=3
Full House: r6c6=9
Naked Single: r3c9=3
Naked Single: r5c9=9
Naked Single: r4c7=1
Naked Single: r7c9=4
Full House: r8c9=7
Full House: r8c2=4
Naked Single: r6c7=3
Full House: r6c8=7
Naked Single: r9c8=3
Naked Single: r9c7=2
Full House: r7c7=9
Naked Single: r9c6=1
Full House: r7c6=3
Naked Single: r9c3=7
Hidden Single: r4c1=7
Naked Single: r4c2=9
Full House: r4c3=4
Naked Single: r3c3=6
Naked Single: r2c2=5
Naked Single: r2c3=9
Naked Single: r3c2=7
Naked Single: r3c8=8
Full House: r2c8=6
Full House: r3c6=4
Full House: r2c6=8
Full House: r2c1=4
Naked Single: r6c3=1
Full House: r6c1=6
Full House: r7c3=2
Naked Single: r9c2=8
Full House: r9c1=5
Naked Single: r7c1=1
Full House: r7c2=6
Naked Single: r5c2=3
Full House: r1c2=1
Full House: r1c1=3
Full House: r5c1=8
|
normal_sudoku_223 | 237.4..5.689.5.3.1451..6..279318.....2869...7.4672.89..14.....6..5......8.2419... | 237841659689257341451936782793185264528694137146723895314578926975362418862419573 | normal_sudoku_223 | 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 3 7 . 4 . . 5 .
6 8 9 . 5 . 3 . 1
4 5 1 . . 6 . . 2
7 9 3 1 8 . . . .
. 2 8 6 9 . . . 7
. 4 6 7 2 . 8 9 .
. 1 4 . . . . . 6
. . 5 . . . . . .
8 . 2 4 1 9 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 237841659689257341451936782793185264528694137146723895314578926975362418862419573 #1 Easy (220)
Naked Single: r2c4=2
Naked Single: r2c6=7
Full House: r2c8=4
Naked Single: r3c5=3
Naked Single: r7c5=7
Full House: r8c5=6
Naked Single: r8c2=7
Full House: r9c2=6
Hidden Single: r1c6=1
Hidden Single: r6c1=1
Full House: r5c1=5
Hidden Single: r1c7=6
Hidden Single: r4c8=6
Hidden Single: r7c4=5
Hidden Single: r4c7=2
Naked Single: r7c7=9
Naked Single: r3c7=7
Naked Single: r7c1=3
Full House: r8c1=9
Naked Single: r3c8=8
Full House: r1c9=9
Full House: r3c4=9
Full House: r1c4=8
Full House: r8c4=3
Naked Single: r9c7=5
Naked Single: r7c8=2
Full House: r7c6=8
Full House: r8c6=2
Naked Single: r9c9=3
Full House: r9c8=7
Naked Single: r8c8=1
Full House: r5c8=3
Naked Single: r6c9=5
Full House: r6c6=3
Naked Single: r8c7=4
Full House: r5c7=1
Full House: r5c6=4
Full House: r4c9=4
Full House: r8c9=8
Full House: r4c6=5
|
normal_sudoku_160 | 5231.4.698...3.1.2..1.......345.1.98.1...8...6583....1.75913..61..856...386427915 | 523184769869735142741692583234571698917268354658349271475913826192856437386427915 | normal_sudoku_160 | 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 3 1 . 4 . 6 9
8 . . . 3 . 1 . 2
. . 1 . . . . . .
. 3 4 5 . 1 . 9 8
. 1 . . . 8 . . .
6 5 8 3 . . . . 1
. 7 5 9 1 3 . . 6
1 . . 8 5 6 . . .
3 8 6 4 2 7 9 1 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 523184769869735142741692583234571698917268354658349271475913826192856437386427915 #1 Extreme (3658)
Locked Candidates Type 1 (Pointing): 9 in b4 => r5c5<>9
2-String Kite: 2 in r4c7,r8c3 (connected by r4c1,r5c3) => r8c7<>2
2-String Kite: 4 in r2c8,r7c1 (connected by r2c2,r3c1) => r7c8<>4
Empty Rectangle: 7 in b5 (r1c57) => r5c7<>7
Finned X-Wing: 7 r16 c57 fr6c8 => r4c7<>7
X-Chain: 7 r1c7 =7= r1c5 -7- r4c5 =7= r4c1 -7- r3c1 =7= r2c3 => r2c8<>7
Discontinuous Nice Loop: 9 r3c2 -9- r2c3 -7- r2c4 -6- r2c2 =6= r3c2 => r3c2<>9
Discontinuous Nice Loop: 7 r3c7 -7- r1c7 =7= r1c5 -7- r4c5 -6- r4c7 =6= r5c7 =5= r3c7 => r3c7<>7
Discontinuous Nice Loop: 4 r5c8 -4- r5c5 =4= r6c5 =9= r6c6 -9- r2c6 -5- r2c8 -4- r5c8 => r5c8<>4
Grouped Discontinuous Nice Loop: 2 r5c1 -2- r4c1 =2= r4c7 =6= r5c7 =5= r5c8 -5- r2c8 =5= r2c6 =9= r2c23 -9- r3c1 =9= r5c1 => r5c1<>2
Discontinuous Nice Loop: 7 r5c5 -7- r4c5 =7= r4c1 =2= r5c3 -2- r5c4 =2= r6c6 =9= r6c5 =4= r5c5 => r5c5<>7
Discontinuous Nice Loop: 7 r6c5 -7- r4c5 =7= r4c1 =2= r5c3 -2- r5c4 =2= r6c6 =9= r6c5 => r6c5<>7
Locked Candidates Type 2 (Claiming): 7 in r6 => r5c89<>7
AIC: 2/7 7- r6c8 =7= r6c7 -7- r1c7 =7= r1c5 -7- r4c5 =7= r4c1 =2= r7c1 -2- r8c3 =2= r8c8 -2 => r6c8<>2, r8c8<>7
AIC: 7 7- r1c7 =7= r1c5 -7- r4c5 -6- r4c7 =6= r5c7 =5= r5c8 -5- r2c8 -4- r6c8 -7 => r3c8,r6c7<>7
Hidden Single: r6c8=7
W-Wing: 4/2 in r6c7,r7c1 connected by 2 in r4c17 => r7c7<>4
Hidden Single: r7c1=4
Naked Single: r8c2=9
Full House: r8c3=2
Hidden Single: r4c1=2
Naked Single: r4c7=6
Full House: r4c5=7
Naked Single: r1c5=8
Full House: r1c7=7
Hidden Single: r8c9=7
W-Wing: 6/4 in r3c2,r5c5 connected by 4 in r35c9 => r3c5<>6
Naked Single: r3c5=9
Naked Single: r2c6=5
Naked Single: r3c1=7
Full House: r5c1=9
Full House: r5c3=7
Full House: r2c3=9
Naked Single: r6c5=4
Full House: r5c5=6
Naked Single: r2c8=4
Naked Single: r3c6=2
Full House: r6c6=9
Full House: r6c7=2
Full House: r5c4=2
Naked Single: r2c2=6
Full House: r2c4=7
Full House: r3c4=6
Full House: r3c2=4
Naked Single: r3c9=3
Full House: r5c9=4
Naked Single: r8c8=3
Full House: r8c7=4
Naked Single: r7c7=8
Full House: r7c8=2
Naked Single: r5c8=5
Full House: r3c8=8
Full House: r3c7=5
Full House: r5c7=3
|
normal_sudoku_6626 | 3....65.8..67.8139..1..367.2....59...542..7...9...4.5......2495..56....7..2547.61 | 379416528546728139821953674218375946654289713793164852167832495435691287982547361 | normal_sudoku_6626 | 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 5 . 8
. . 6 7 . 8 1 3 9
. . 1 . . 3 6 7 .
2 . . . . 5 9 . .
. 5 4 2 . . 7 . .
. 9 . . . 4 . 5 .
. . . . . 2 4 9 5
. . 5 6 . . . . 7
. . 2 5 4 7 . 6 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 379416528546728139821953674218375946654289713793164852167832495435691287982547361 #1 Easy (226)
Hidden Single: r1c3=9
Hidden Single: r9c1=9
Hidden Single: r3c4=9
Hidden Single: r1c2=7
Hidden Single: r1c4=4
Naked Single: r1c8=2
Full House: r1c5=1
Full House: r3c9=4
Naked Single: r8c8=8
Naked Single: r5c8=1
Full House: r4c8=4
Naked Single: r9c7=3
Full House: r8c7=2
Full House: r9c2=8
Full House: r6c7=8
Naked Single: r5c6=9
Full House: r8c6=1
Naked Single: r3c2=2
Naked Single: r8c1=4
Naked Single: r2c2=4
Naked Single: r3c5=5
Full House: r2c5=2
Full House: r2c1=5
Full House: r3c1=8
Naked Single: r8c2=3
Full House: r8c5=9
Naked Single: r5c1=6
Naked Single: r7c3=7
Naked Single: r4c2=1
Full House: r7c2=6
Full House: r7c1=1
Full House: r6c1=7
Naked Single: r5c9=3
Full House: r5c5=8
Naked Single: r6c3=3
Full House: r4c3=8
Naked Single: r4c9=6
Full House: r6c9=2
Naked Single: r4c4=3
Full House: r4c5=7
Naked Single: r7c5=3
Full House: r6c5=6
Full House: r6c4=1
Full House: r7c4=8
|
normal_sudoku_1815 | .32.1..7.71...9.839.837.2.137..4.....8195374....7.183..2318..971.7.9.3.889..37... | 632518974714269583958374261379846125281953746546721839423185697167492358895637412 | normal_sudoku_1815 | 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 . 1 . . 7 .
7 1 . . . 9 . 8 3
9 . 8 3 7 . 2 . 1
3 7 . . 4 . . . .
. 8 1 9 5 3 7 4 .
. . . 7 . 1 8 3 .
. 2 3 1 8 . . 9 7
1 . 7 . 9 . 3 . 8
8 9 . . 3 7 . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 632518974714269583958374261379846125281953746546721839423185697167492358895637412 #1 Extreme (6368)
W-Wing: 6/2 in r5c9,r6c5 connected by 2 in r56c1 => r6c9<>6
Finned X-Wing: 4 r38 c26 fr8c4 => r7c6<>4
2-String Kite: 4 in r1c9,r7c1 (connected by r7c7,r9c9) => r1c1<>4
Forcing Net Verity => r1c4<>4
r1c9=4 r1c4<>4
r1c9=5 (r1c1<>5 r1c1=6 r3c2<>6) (r1c9<>4 r9c9=4 r7c7<>4 r7c1=4 r6c1<>4 r6c1=5 r6c2<>5) (r1c9<>4 r9c9=4 r9c3<>4) (r2c7<>5) r3c8<>5 r3c8=6 r2c7<>6 r2c7=4 r2c3<>4 r6c3=4 r6c2<>4 r6c2=6 r6c5<>6 (r6c5=2 r4c6<>2 r8c6=2 r8c8<>2) r2c5=6 r3c6<>6 r3c8=6 r8c8<>6 r8c8=5 r7c7<>5 r7c1=5 r7c1<>4 r7c7=4 r9c9<>4 r1c9=4 r1c4<>4
r1c9=6 (r3c8<>6) (r1c1<>6 r1c1=5 r2c3<>5) (r2c7<>6) r3c8<>6 r3c8=5 (r8c8<>5) r2c7<>5 (r2c4=5 r2c4<>2) (r2c4=5 r2c4<>6) (r2c4=5 r8c4<>5) r2c7=4 r2c3<>4 (r6c3=4 r6c3<>5) r2c3=6 (r9c3<>6 r9c3=5 r4c3<>5) r3c2<>6 r3c6=6 r7c6<>6 r7c6=5 r8c6<>5 r8c2=5 r9c3<>5 r2c3=5 r2c4<>5 r2c4=4 r1c4<>4
r1c9=9 (r6c9<>9 r6c3=9 r6c3<>4) r1c9<>4 r9c9=4 (r7c7<>4) (r9c7<>4) r9c3<>4 r2c3=4 r2c7<>4 r1c7=4 r1c4<>4
Forcing Net Verity => r1c6<>4
r1c9=4 r1c6<>4
r1c9=5 (r1c1<>5 r1c1=6 r1c4<>6 r1c4=8 r4c4<>8 r4c6=8 r4c6<>2 r8c6=2 r8c8<>2) (r1c1<>5 r1c1=6 r3c2<>6) (r1c9<>4 r9c9=4 r7c7<>4 r7c1=4 r6c1<>4 r6c1=5 r6c2<>5) (r1c9<>4 r9c9=4 r9c3<>4) (r2c7<>5) r3c8<>5 r3c8=6 r2c7<>6 r2c7=4 r2c3<>4 r6c3=4 r6c2<>4 r6c2=6 r6c5<>6 r2c5=6 r3c6<>6 r3c8=6 r8c8<>6 r8c8=5 r7c7<>5 r7c1=5 r7c1<>4 r7c7=4 r9c9<>4 r1c9=4 r1c6<>4
r1c9=6 (r3c8<>6 r3c8=5 r2c7<>5 r2c4=5 r2c4<>2) (r3c8<>6 r3c8=5 r2c7<>5 r2c4=5 r2c4<>6) (r3c8<>6 r3c8=5 r2c7<>5 r2c7=4 r2c3<>4 r2c3=6 r9c3<>6 r9c3=5 r4c3<>5) (r3c8<>6 r3c8=5 r2c7<>5 r2c7=4 r2c3<>4 r6c3=4 r6c3<>5) (r3c8<>6 r3c8=5 r2c7<>5 r2c4=5 r8c4<>5) (r3c8<>6 r3c8=5 r8c8<>5) (r3c8<>6 r3c8=5 r3c6<>5) (r1c9<>4) r1c9<>9 r1c7=9 r1c7<>4 r1c6=4 r3c6<>4 r3c6=6 r7c6<>6 r7c6=5 r8c6<>5 r8c2=5 r9c3<>5 r2c3=5 r2c4<>5 r2c4=4 r1c6<>4
r1c9=9 (r6c9<>9 r6c3=9 r6c3<>4) r1c9<>4 r9c9=4 (r7c7<>4) (r9c7<>4) r9c3<>4 r2c3=4 r2c7<>4 r1c7=4 r1c6<>4
Locked Candidates Type 2 (Claiming): 4 in r1 => r2c7<>4
Naked Pair: 5,6 in r2c7,r3c8 => r1c79<>5, r1c79<>6
Grouped Discontinuous Nice Loop: 6 r6c1 -6- r6c5 =6= r2c5 -6- r1c46 =6= r1c1 -6- r6c1 => r6c1<>6
Almost Locked Set XY-Wing: A=r5c9 {26}, B=r27c7 {456}, C=r157c1 {2456}, X,Y=2,4, Z=6 => r4c7<>6
Finned Franken Swordfish: 5 r17b3 c167 fr1c4 fr3c8 => r3c6<>5
W-Wing: 6/5 in r1c1,r2c7 connected by 5 in r3c28 => r2c3<>6
Sashimi Swordfish: 6 r127 c167 fr1c4 fr2c4 fr2c5 => r3c6<>6
Naked Single: r3c6=4
Hidden Single: r2c3=4
Grouped Discontinuous Nice Loop: 6 r4c8 -6- r5c9 =6= r5c1 -6- r46c3 =6= r9c3 -6- r9c9 =6= r45c9 -6- r4c8 => r4c8<>6
Locked Candidates Type 1 (Pointing): 6 in b6 => r9c9<>6
Forcing Chain Verity => r6c2<>5
r2c7=5 r3c8<>5 r3c2=5 r6c2<>5
r4c7=5 r46c9<>5 r9c9=5 r9c3<>5 r46c3=5 r6c2<>5
r7c7=5 r7c7<>4 r7c1=4 r6c1<>4 r6c2=4 r6c2<>5
r9c7=5 r9c3<>5 r46c3=5 r6c2<>5
W-Wing: 6/5 in r1c1,r9c3 connected by 5 in r38c2 => r7c1<>6
Turbot Fish: 6 r3c8 =6= r3c2 -6- r8c2 =6= r9c3 => r9c8<>6
Sashimi X-Wing: 6 r27 c67 fr2c4 fr2c5 => r1c6<>6
Discontinuous Nice Loop: 2 r8c4 -2- r8c6 =2= r4c6 -2- r6c5 -6- r6c2 -4- r8c2 =4= r8c4 => r8c4<>2
Discontinuous Nice Loop: 6 r8c4 -6- r7c6 -5- r7c1 -4- r8c2 =4= r8c4 => r8c4<>6
Almost Locked Set XZ-Rule: A=r27c7 {456}, B=r7c1,r9c3 {456}, X=4, Z=6 => r9c7<>6
AIC: 5 5- r7c6 -6- r7c7 =6= r2c7 =5= r3c8 -5- r3c2 =5= r8c2 -5 => r7c1,r8c46<>5
Naked Single: r7c1=4
Naked Single: r8c4=4
Hidden Single: r6c2=4
Naked Pair: 5,6 in r27c7 => r49c7<>5
X-Wing: 5 r38 c28 => r49c8<>5
Locked Candidates Type 1 (Pointing): 5 in b6 => r9c9<>5
Locked Triple: 1,2,4 in r9c789 => r8c8,r9c4<>2
Hidden Single: r8c6=2
Remote Pair: 5/6 r1c1 -6- r3c2 -5- r3c8 -6- r2c7 -5- r7c7 -6- r8c8 -5- r8c2 -6- r9c3 -5- r9c4 -6- r7c6 => r1c6,r2c4<>5, r2c4<>6
Naked Single: r1c6=8
Naked Single: r2c4=2
Naked Single: r4c6=6
Full House: r7c6=5
Full House: r7c7=6
Full House: r9c4=6
Naked Single: r2c5=6
Full House: r6c5=2
Full House: r4c4=8
Full House: r2c7=5
Full House: r1c4=5
Naked Single: r8c8=5
Full House: r8c2=6
Full House: r9c3=5
Full House: r3c2=5
Full House: r3c8=6
Full House: r1c1=6
Naked Single: r6c1=5
Full House: r5c1=2
Full House: r5c9=6
Naked Single: r4c3=9
Full House: r6c3=6
Full House: r6c9=9
Naked Single: r4c7=1
Naked Single: r1c9=4
Full House: r1c7=9
Full House: r9c7=4
Naked Single: r4c8=2
Full House: r4c9=5
Full House: r9c9=2
Full House: r9c8=1
|
normal_sudoku_626 | ........73.......1..2.4..6..1..24....385...4.4..186..9..6.32.5.573...9......5.6.3 | 851263497364795281792841365915324876638579142427186539146932758573618924289457613 | normal_sudoku_626 | 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 . . . . . . . 1
. . 2 . 4 . . 6 .
. 1 . . 2 4 . . .
. 3 8 5 . . . 4 .
4 . . 1 8 6 . . 9
. . 6 . 3 2 . 5 .
5 7 3 . . . 9 . .
. . . . 5 . 6 . 3 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 851263497364795281792841365915324876638579142427186539146932758573618924289457613 #1 Easy (278)
Hidden Single: r5c7=1
Hidden Single: r4c4=3
Hidden Single: r7c1=1
Hidden Single: r3c6=1
Naked Single: r8c6=8
Hidden Single: r1c3=1
Hidden Single: r8c5=1
Naked Single: r8c8=2
Naked Single: r8c9=4
Full House: r8c4=6
Naked Single: r7c9=8
Naked Single: r3c9=5
Naked Single: r7c7=7
Full House: r9c8=1
Naked Single: r4c9=6
Full House: r5c9=2
Hidden Single: r3c7=3
Naked Single: r6c7=5
Naked Single: r4c7=8
Naked Single: r6c2=2
Naked Single: r6c3=7
Full House: r6c8=3
Full House: r4c8=7
Naked Single: r4c1=9
Full House: r4c3=5
Full House: r5c1=6
Naked Single: r1c1=8
Naked Single: r1c8=9
Full House: r2c8=8
Naked Single: r3c1=7
Full House: r9c1=2
Naked Single: r3c2=9
Full House: r3c4=8
Naked Single: r1c4=2
Naked Single: r1c5=6
Naked Single: r2c3=4
Full House: r9c3=9
Naked Single: r7c2=4
Full House: r7c4=9
Full House: r9c2=8
Naked Single: r1c7=4
Full House: r2c7=2
Naked Single: r1c2=5
Full House: r1c6=3
Full House: r2c2=6
Naked Single: r9c6=7
Full House: r9c4=4
Full House: r2c4=7
Naked Single: r5c6=9
Full House: r2c6=5
Full House: r2c5=9
Full House: r5c5=7
|
normal_sudoku_3020 | .......5...2..3...6.8......5.374916...963..75467...9.37.651..39.9.3.75.6..5..671. | 371498652952163847648275391523749168819632475467851923786514239194327586235986714 | normal_sudoku_3020 | 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 . . 3 . . .
6 . 8 . . . . . .
5 . 3 7 4 9 1 6 .
. . 9 6 3 . . 7 5
4 6 7 . . . 9 . 3
7 . 6 5 1 . . 3 9
. 9 . 3 . 7 5 . 6
. . 5 . . 6 7 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 371498652952163847648275391523749168819632475467851923786514239194327586235986714 #1 Extreme (3172)
Hidden Single: r5c7=4
Locked Candidates Type 1 (Pointing): 1 in b4 => r5c6<>1
2-String Kite: 4 in r1c3,r7c6 (connected by r7c2,r8c3) => r1c6<>4
Turbot Fish: 4 r1c3 =4= r8c3 -4- r8c8 =4= r9c9 => r1c9<>4
Hidden Rectangle: 6/8 in r1c57,r2c57 => r1c5<>8
Discontinuous Nice Loop: 4 r3c8 -4- r8c8 =4= r8c3 =1= r8c1 -1- r2c1 -9- r2c8 =9= r3c8 => r3c8<>4
Skyscraper: 4 in r1c3,r2c8 (connected by r8c38) => r2c2<>4
Almost Locked Set XZ-Rule: A=r457c2 {1248}, B=r157c6 {1248}, X=4, Z=1 => r1c2<>1
Forcing Chain Contradiction in r7 => r3c8=9
r3c8<>9 r3c8=2 r6c8<>2 r6c8=8 r4c9<>8 r4c2=8 r7c2<>8
r3c8<>9 r3c8=2 r6c8<>2 r6c8=8 r6c456<>8 r5c6=8 r7c6<>8
r3c8<>9 r3c8=2 r13c7<>2 r7c7=2 r7c7<>8
W-Wing: 8/2 in r4c9,r7c7 connected by 2 in r68c8 => r9c9<>8
Discontinuous Nice Loop: 2 r1c5 -2- r8c5 -8- r8c8 =8= r7c7 -8- r2c7 -6- r2c5 =6= r1c5 => r1c5<>2
Discontinuous Nice Loop: 2 r5c2 -2- r4c2 =2= r4c9 -2- r9c9 -4- r8c8 =4= r8c3 =1= r8c1 -1- r5c1 =1= r5c2 => r5c2<>2
Discontinuous Nice Loop: 2 r7c6 -2- r5c6 =2= r5c1 -2- r4c2 =2= r4c9 -2- r9c9 -4- r9c4 =4= r7c6 => r7c6<>2
Skyscraper: 2 in r4c9,r7c7 (connected by r47c2) => r9c9<>2
Naked Single: r9c9=4
Hidden Single: r2c8=4
Hidden Single: r8c3=4
Full House: r1c3=1
Naked Single: r2c1=9
Naked Single: r1c1=3
Hidden Single: r7c6=4
Hidden Single: r8c1=1
Hidden Single: r5c2=1
Hidden Single: r3c7=3
Hidden Single: r9c2=3
Naked Pair: 2,8 in r15c6 => r36c6<>2, r6c6<>8
Remote Pair: 2/8 r1c6 -8- r5c6 -2- r5c1 -8- r9c1 -2- r7c2 -8- r7c7 -2- r8c8 -8- r8c5 => r1c7,r3c5<>2, r1c7,r2c5<>8
Naked Single: r1c7=6
Naked Single: r2c7=8
Full House: r7c7=2
Full House: r7c2=8
Full House: r8c8=8
Full House: r9c1=2
Full House: r6c8=2
Full House: r8c5=2
Full House: r5c1=8
Full House: r4c2=2
Full House: r4c9=8
Full House: r5c6=2
Naked Single: r2c4=1
Naked Single: r1c6=8
Naked Single: r2c9=7
Naked Single: r3c6=5
Full House: r6c6=1
Naked Single: r6c4=8
Full House: r6c5=5
Naked Single: r1c9=2
Full House: r3c9=1
Naked Single: r2c2=5
Full House: r2c5=6
Naked Single: r3c5=7
Naked Single: r9c4=9
Full House: r9c5=8
Full House: r1c5=9
Naked Single: r3c2=4
Full House: r1c2=7
Full House: r1c4=4
Full House: r3c4=2
|
normal_sudoku_550 | ..9.8.6.......94...6352...9.....3.6...6.5.3..381.7.295175.4.9..234..58..69813.5.. | 429781653517369428863524179952813764746952381381476295175248936234695817698137542 | normal_sudoku_550 | 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 . 6 . .
. . . . . 9 4 . .
. 6 3 5 2 . . . 9
. . . . . 3 . 6 .
. . 6 . 5 . 3 . .
3 8 1 . 7 . 2 9 5
1 7 5 . 4 . 9 . .
2 3 4 . . 5 8 . .
6 9 8 1 3 . 5 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 429781653517369428863524179952813764746952381381476295175248936234695817698137542 #1 Extreme (2312)
Locked Candidates Type 2 (Claiming): 4 in r6 => r45c4,r5c6<>4
Skyscraper: 1 in r2c5,r3c7 (connected by r4c57) => r2c89,r3c6<>1
Locked Candidates Type 2 (Claiming): 1 in r3 => r1c89<>1
Skyscraper: 7 in r2c3,r3c7 (connected by r4c37) => r2c89,r3c1<>7
W-Wing: 7/1 in r4c7,r8c8 connected by 1 in r3c78 => r5c8<>7
Sue de Coq: r4c123 - {24579} (r4c57 - {179}, r5c2 - {24}) => r5c1<>4, r4c4<>9, r4c9<>1, r4c9<>7
AIC: 4 4- r3c6 -7- r3c7 =7= r4c7 -7- r4c3 -2- r4c4 -8- r7c4 =8= r7c6 =6= r6c6 =4= r6c4 -4 => r1c4,r6c6<>4
Naked Single: r6c6=6
Full House: r6c4=4
AIC: 8 8- r4c4 -2- r4c3 -7- r4c7 -1- r4c5 =1= r5c6 =8= r7c6 -8 => r5c6,r7c4<>8
Hidden Single: r7c6=8
XY-Chain: 4 4- r4c9 -8- r4c4 -2- r7c4 -6- r8c5 -9- r4c5 -1- r5c6 -2- r5c2 -4 => r4c12,r5c89<>4
Hidden Single: r4c9=4
Hidden Single: r5c2=4
Hidden Single: r9c8=4
Hidden Single: r4c4=8
Naked Triple: 1,7,8 in r358c8 => r1c8<>7, r2c8<>8
2-String Kite: 7 in r3c8,r9c6 (connected by r8c8,r9c9) => r3c6<>7
Naked Single: r3c6=4
Naked Single: r3c1=8
Hidden Single: r1c1=4
Hidden Single: r2c9=8
Hidden Single: r5c8=8
Locked Candidates Type 1 (Pointing): 7 in b1 => r2c4<>7
Locked Candidates Type 1 (Pointing): 7 in b2 => r1c9<>7
W-Wing: 1/7 in r1c6,r5c9 connected by 7 in r9c69 => r5c6<>1
Naked Single: r5c6=2
Naked Single: r5c4=9
Full House: r4c5=1
Naked Single: r9c6=7
Full House: r1c6=1
Full House: r9c9=2
Naked Single: r5c1=7
Full House: r5c9=1
Full House: r4c7=7
Full House: r3c7=1
Full House: r3c8=7
Naked Single: r2c5=6
Full House: r8c5=9
Naked Single: r8c4=6
Full House: r7c4=2
Naked Single: r1c9=3
Naked Single: r7c8=3
Full House: r7c9=6
Full House: r8c9=7
Full House: r8c8=1
Naked Single: r2c1=5
Full House: r4c1=9
Naked Single: r4c3=2
Full House: r2c3=7
Full House: r4c2=5
Naked Single: r2c4=3
Full House: r1c4=7
Naked Single: r1c2=2
Full House: r1c8=5
Full House: r2c8=2
Full House: r2c2=1
|
normal_sudoku_621 | ...3.....1....7..3.3..6.9.73.869.172...12.34..21..36.9.1........9.2..7.62.5.....1 | 752319864169847523834562917348695172976128345521473689617954238493281756285736491 | normal_sudoku_621 | 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 . . . . 7 . . 3
. 3 . . 6 . 9 . 7
3 . 8 6 9 . 1 7 2
. . . 1 2 . 3 4 .
. 2 1 . . 3 6 . 9
. 1 . . . . . . .
. 9 . 2 . . 7 . 6
2 . 5 . . . . . 1 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 752319864169847523834562917348695172976128345521473689617954238493281756285736491 #1 Extreme (4312)
Locked Candidates Type 1 (Pointing): 7 in b5 => r6c1<>7
Naked Pair: 4,5 in r4c2,r6c1 => r5c12<>5
Naked Triple: 4,5,8 in r368c1 => r17c1<>4, r1c1<>5, r17c1<>8
2-String Kite: 5 in r3c1,r4c6 (connected by r4c2,r6c1) => r3c6<>5
XY-Wing: 4/5/8 in r6c18,r8c1 => r8c8<>8
XY-Chain: 8 8- r5c6 -5- r5c9 -8- r6c8 -5- r6c1 -4- r8c1 -8 => r8c6<>8
Discontinuous Nice Loop: 8 r1c6 -8- r5c6 -5- r5c9 =5= r6c8 -5- r8c8 -3- r8c3 -4- r3c3 -2- r3c6 =2= r1c6 => r1c6<>8
Almost Locked Set Chain: 8- r5c6 {58} -5- r5c9 {58} -8- r6c8 {58} -5- r8c8 {35} -3- r38c3 {234} -2- r3458c6 {12458} -8 => r79c6<>8
Turbot Fish: 8 r3c6 =8= r5c6 -8- r5c9 =8= r6c8 => r3c8<>8
Sashimi X-Wing: 8 r38 c15 fr3c4 fr3c6 => r12c5<>8
Forcing Chain Contradiction in c4 => r5c6=8
r5c6<>8 r3c6=8 r3c6<>2 r1c6=2 r1c6<>9 r2c4=9 r2c4<>5
r5c6<>8 r5c6=5 r5c9<>5 r6c8=5 r6c1<>5 r3c1=5 r3c4<>5
r5c6<>8 r5c6=5 r6c4<>5
r5c6<>8 r5c6=5 r5c9<>5 r6c8=5 r8c8<>5 r7c789=5 r7c4<>5
Naked Single: r5c9=5
Full House: r6c8=8
Locked Candidates Type 1 (Pointing): 8 in b2 => r79c4<>8
Naked Pair: 4,8 in r7c9,r9c7 => r7c7<>4, r7c7<>8
Discontinuous Nice Loop: 2 r1c7 -2- r1c6 =2= r3c6 -2- r3c3 -4- r8c3 -3- r8c8 -5- r7c7 -2- r1c7 => r1c7<>2
Discontinuous Nice Loop: 4 r3c4 -4- r3c3 -2- r3c6 =2= r1c6 =9= r2c4 =8= r3c4 => r3c4<>4
Sashimi X-Wing: 4 r34 c26 fr3c1 fr3c3 => r12c2<>4
Discontinuous Nice Loop: 5 r8c6 -5- r8c8 -3- r8c3 -4- r9c2 =4= r4c2 =5= r4c6 -5- r8c6 => r8c6<>5
Discontinuous Nice Loop: 5 r3c8 -5- r8c8 =5= r8c5 =1= r8c6 -1- r3c6 =1= r3c8 => r3c8<>5
Naked Triple: 1,2,4 in r3c368 => r3c1<>4
Locked Candidates Type 1 (Pointing): 4 in b1 => r78c3<>4
Naked Single: r8c3=3
Naked Single: r8c8=5
Naked Single: r7c7=2
Locked Pair: 6,7 in r7c13 => r7c45,r9c2<>7, r7c6,r9c2<>6
Hidden Single: r9c6=6
Naked Pair: 4,8 in r9c27 => r9c45<>4, r9c5<>8
Remote Pair: 8/4 r1c9 -4- r7c9 -8- r9c7 -4- r9c2 => r1c2<>8
Locked Candidates Type 2 (Claiming): 8 in r1 => r2c7<>8
Naked Pair: 4,5 in r2c57 => r2c24<>5, r2c34<>4
Skyscraper: 4 in r7c4,r8c1 (connected by r6c14) => r8c56<>4
Naked Single: r8c6=1
Naked Single: r8c5=8
Full House: r8c1=4
Naked Single: r6c1=5
Naked Single: r9c2=8
Naked Single: r3c1=8
Naked Single: r4c2=4
Full House: r4c6=5
Naked Single: r2c2=6
Naked Single: r9c7=4
Naked Single: r3c4=5
Naked Single: r2c8=2
Naked Single: r5c2=7
Full House: r1c2=5
Naked Single: r2c7=5
Full House: r1c7=8
Naked Single: r7c9=8
Full House: r1c9=4
Naked Single: r2c5=4
Naked Single: r2c3=9
Full House: r2c4=8
Naked Single: r3c8=1
Full House: r1c8=6
Naked Single: r1c5=1
Naked Single: r3c6=2
Full House: r1c6=9
Full House: r3c3=4
Full House: r7c6=4
Naked Single: r6c5=7
Full House: r6c4=4
Naked Single: r1c1=7
Full House: r1c3=2
Naked Single: r5c3=6
Full House: r5c1=9
Full House: r7c1=6
Full House: r7c3=7
Naked Single: r7c4=9
Full House: r9c4=7
Naked Single: r9c5=3
Full House: r7c5=5
Full House: r7c8=3
Full House: r9c8=9
|
normal_sudoku_3001 | ..4.68..7.....38.....1...9...78.9.4..4.7125.99...467.8..16...8.3....1..6.6...52.. | 234968157196573824578124693617859342843712569952346718421637985385291476769485231 | normal_sudoku_3001 | 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 8 . . 7
. . . . . 3 8 . .
. . . 1 . . . 9 .
. . 7 8 . 9 . 4 .
. 4 . 7 1 2 5 . 9
9 . . . 4 6 7 . 8
. . 1 6 . . . 8 .
3 . . . . 1 . . 6
. 6 . . . 5 2 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 234968157196573824578124693617859342843712569952346718421637985385291476769485231 #1 Extreme (6648)
Skyscraper: 4 in r2c9,r8c7 (connected by r28c4) => r3c7,r79c9<>4
Naked Triple: 1,3,6 in r134c7 => r7c7<>3
2-String Kite: 1 in r1c7,r6c2 (connected by r4c7,r6c8) => r1c2<>1
2-String Kite: 6 in r2c8,r4c1 (connected by r4c7,r5c8) => r2c1<>6
Discontinuous Nice Loop: 3 r3c3 -3- r3c7 -6- r4c7 =6= r5c8 =3= r5c3 -3- r3c3 => r3c3<>3
Locked Candidates Type 1 (Pointing): 3 in b1 => r46c2<>3
Discontinuous Nice Loop: 8 r9c1 -8- r5c1 =8= r5c3 =3= r6c3 -3- r6c4 =3= r9c4 =4= r9c1 => r9c1<>8
Discontinuous Nice Loop: 9 r9c4 -9- r9c3 -8- r8c2 =8= r3c2 =3= r1c2 =9= r1c4 -9- r9c4 => r9c4<>9
Hidden Pair: 8,9 in r9c35 => r9c5<>3, r9c5<>7
Discontinuous Nice Loop: 1 r2c9 -1- r9c9 -3- r9c4 -4- r2c4 =4= r2c9 => r2c9<>1
Forcing Chain Contradiction in r1 => r2c3<>5
r2c3=5 r1c1<>5
r2c3=5 r1c2<>5
r2c3=5 r2c3<>6 r2c8=6 r5c8<>6 r5c8=3 r5c3<>3 r6c3=3 r6c4<>3 r6c4=5 r1c4<>5
r2c3=5 r2c3<>6 r2c8=6 r5c8<>6 r5c8=3 r4c79<>3 r4c5=3 r7c5<>3 r7c9=3 r7c9<>5 r8c8=5 r1c8<>5
Forcing Chain Contradiction in c9 => r2c9<>2
r2c9=2 r2c9<>5
r2c9=2 r2c9<>4 r3c9=4 r3c9<>5
r2c9=2 r2c9<>4 r2c4=4 r9c4<>4 r9c4=3 r7c5<>3 r7c9=3 r7c9<>5
Forcing Chain Contradiction in c3 => r9c9=1
r9c9<>1 r9c9=3 r9c4<>3 r6c4=3 r6c3<>3 r5c3=3 r5c8<>3 r5c8=6 r2c8<>6 r2c3=6 r2c3<>2
r9c9<>1 r4c9=1 r4c9<>2 r3c9=2 r3c3<>2
r9c9<>1 r4c9=1 r4c9<>2 r6c8=2 r6c3<>2
r9c9<>1 r9c9=3 r9c4<>3 r7c5=3 r7c5<>2 r7c12=2 r8c3<>2
Swordfish: 3 r569 c348 => r1c8<>3
Discontinuous Nice Loop: 2 r4c1 -2- r4c9 -3- r5c8 -6- r4c7 =6= r4c1 => r4c1<>2
Forcing Chain Contradiction in r7 => r4c9=2
r4c9<>2 r4c9=3 r4c5<>3 r7c5=3 r9c4<>3 r9c4=4 r9c1<>4 r7c1=4 r7c1<>2
r4c9<>2 r4c2=2 r7c2<>2
r4c9<>2 r4c9=3 r4c5<>3 r7c5=3 r7c5<>2
Discontinuous Nice Loop: 5 r1c2 -5- r4c2 -1- r4c7 =1= r1c7 =3= r1c2 => r1c2<>5
Discontinuous Nice Loop: 5 r1c4 -5- r6c4 -3- r4c5 =3= r4c7 -3- r1c7 =3= r1c2 =9= r1c4 => r1c4<>5
Turbot Fish: 5 r1c1 =5= r1c8 -5- r8c8 =5= r7c9 => r7c1<>5
AIC: 1 1- r1c7 -3- r3c9 =3= r7c9 =5= r7c2 -5- r4c2 -1- r4c7 =1= r6c8 -1 => r12c8,r4c7<>1
Hidden Single: r6c8=1
Hidden Single: r1c7=1
Hidden Single: r1c2=3
Hidden Single: r1c4=9
Hidden Rectangle: 1/5 in r2c12,r4c12 => r2c1<>5
XY-Chain: 5 5- r1c1 -2- r1c8 -5- r8c8 -7- r9c8 -3- r5c8 -6- r4c7 -3- r4c5 -5 => r4c1<>5
Locked Candidates Type 2 (Claiming): 5 in c1 => r23c2,r3c3<>5
Finned Swordfish: 5 c348 r268 fr1c8 => r2c9<>5
Naked Single: r2c9=4
Hidden Single: r3c6=4
Full House: r7c6=7
W-Wing: 5/3 in r3c9,r4c5 connected by 3 in r7c59 => r3c5<>5
Locked Candidates Type 1 (Pointing): 5 in b2 => r2c8<>5
W-Wing: 2/4 in r7c1,r8c4 connected by 4 in r9c14 => r7c5,r8c23<>2
Sue de Coq: r8c23 - {5789} (r8c8 - {57}, r9c3 - {89}) => r7c2<>9
Naked Pair: 2,5 in r67c2 => r23c2<>2, r48c2<>5
Naked Single: r4c2=1
Naked Single: r4c1=6
Naked Single: r4c7=3
Full House: r4c5=5
Full House: r5c8=6
Full House: r6c4=3
Naked Single: r5c1=8
Full House: r5c3=3
Naked Single: r3c7=6
Naked Single: r2c8=2
Naked Single: r9c4=4
Naked Single: r1c8=5
Full House: r1c1=2
Full House: r3c9=3
Full House: r7c9=5
Naked Single: r2c4=5
Full House: r8c4=2
Naked Single: r2c5=7
Full House: r3c5=2
Naked Single: r9c1=7
Naked Single: r8c8=7
Full House: r9c8=3
Naked Single: r3c3=8
Naked Single: r7c1=4
Naked Single: r7c2=2
Naked Single: r2c1=1
Full House: r3c1=5
Full House: r3c2=7
Naked Single: r2c2=9
Full House: r2c3=6
Naked Single: r9c3=9
Full House: r9c5=8
Naked Single: r7c7=9
Full House: r7c5=3
Full House: r8c5=9
Full House: r8c7=4
Naked Single: r6c2=5
Full House: r8c2=8
Full House: r8c3=5
Full House: r6c3=2
|
normal_sudoku_3899 | ..3..268.4.6...5...28..6..38..6...7..6547.....3...1456.8136...969.12...53....9.6. | 953712684476938521128546793814695372265473918739281456581367249697124835342859167 | normal_sudoku_3899 | 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 6 8 .
4 . 6 . . . 5 . .
. 2 8 . . 6 . . 3
8 . . 6 . . . 7 .
. 6 5 4 7 . . . .
. 3 . . . 1 4 5 6
. 8 1 3 6 . . . 9
6 9 . 1 2 . . . 5
3 . . . . 9 . 6 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 953712684476938521128546793814695372265473918739281456581367249697124835342859167 #1 Easy (270)
Hidden Single: r6c4=2
Hidden Single: r6c5=8
Naked Single: r5c6=3
Naked Single: r4c6=5
Full House: r4c5=9
Hidden Single: r2c5=3
Hidden Single: r4c7=3
Hidden Single: r8c8=3
Hidden Single: r7c1=5
Hidden Single: r6c3=9
Full House: r6c1=7
Hidden Single: r1c2=5
Hidden Single: r5c1=2
Naked Single: r4c3=4
Full House: r4c2=1
Full House: r4c9=2
Naked Single: r8c3=7
Full House: r9c3=2
Full House: r9c2=4
Full House: r2c2=7
Naked Single: r8c7=8
Full House: r8c6=4
Naked Single: r9c5=5
Naked Single: r2c6=8
Full House: r7c6=7
Full House: r9c4=8
Naked Single: r2c9=1
Naked Single: r2c4=9
Full House: r2c8=2
Naked Single: r7c7=2
Full House: r7c8=4
Naked Single: r5c9=8
Naked Single: r9c9=7
Full House: r1c9=4
Full House: r9c7=1
Naked Single: r1c4=7
Full House: r3c4=5
Naked Single: r3c8=9
Full House: r3c7=7
Full House: r5c7=9
Full House: r5c8=1
Naked Single: r1c5=1
Full House: r1c1=9
Full House: r3c1=1
Full House: r3c5=4
|
normal_sudoku_5011 | ..4756319165..34..9734216....8....6.6....874.45.6378.....17..36..6..51...17.6...4 | 824756319165983427973421685738249561692518743451637892589174236246395178317862954 | normal_sudoku_5011 | 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 5 6 3 1 9
1 6 5 . . 3 4 . .
9 7 3 4 2 1 6 . .
. . 8 . . . . 6 .
6 . . . . 8 7 4 .
4 5 . 6 3 7 8 . .
. . . 1 7 . . 3 6
. . 6 . . 5 1 . .
. 1 7 . 6 . . . 4 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 824756319165983427973421685738249561692518743451637892589174236246395178317862954 #1 Extreme (1876)
Hidden Single: r4c1=7
Locked Candidates Type 1 (Pointing): 8 in b2 => r2c89<>8
Locked Candidates Type 1 (Pointing): 3 in b4 => r8c2<>3
Locked Candidates Type 2 (Claiming): 8 in r7 => r8c12,r9c1<>8
Uniqueness Test 4: 2/8 in r1c12,r7c12 => r7c12<>2
Uniqueness Test 4: 2/7 in r2c89,r8c89 => r8c89<>2
Hidden Rectangle: 2/3 in r8c14,r9c14 => r9c4<>2
Sashimi Swordfish: 2 c367 r479 fr5c3 fr6c3 => r4c2<>2
Sashimi Swordfish: 9 c367 r479 fr5c3 fr6c3 => r4c2<>9
Naked Single: r4c2=3
Hidden Single: r5c9=3
Hidden Single: r5c4=5
Locked Candidates Type 1 (Pointing): 2 in b5 => r4c79<>2
Locked Candidates Type 1 (Pointing): 2 in b6 => r6c3<>2
Locked Candidates Type 2 (Claiming): 2 in c7 => r9c8<>2
W-Wing: 9/2 in r7c3,r9c6 connected by 2 in r79c7 => r7c6<>9
Turbot Fish: 9 r6c8 =9= r4c7 -9- r4c6 =9= r9c6 => r9c8<>9
Naked Pair: 5,8 in r39c8 => r8c8<>8
AIC: 9 9- r5c2 -2- r1c2 -8- r1c1 =8= r7c1 =5= r7c7 -5- r4c7 =5= r4c9 =1= r4c5 =4= r4c6 -4- r7c6 -2- r7c3 -9 => r56c3,r78c2<>9
Naked Single: r6c3=1
Naked Single: r5c3=2
Full House: r5c2=9
Full House: r7c3=9
Full House: r5c5=1
Naked Single: r6c9=2
Full House: r6c8=9
Naked Single: r2c9=7
Naked Single: r4c7=5
Full House: r4c9=1
Naked Single: r8c8=7
Naked Single: r2c8=2
Naked Single: r8c9=8
Full House: r3c9=5
Full House: r3c8=8
Full House: r9c8=5
Naked Single: r7c7=2
Full House: r9c7=9
Naked Single: r7c6=4
Naked Single: r9c6=2
Full House: r4c6=9
Naked Single: r7c2=8
Full House: r7c1=5
Naked Single: r8c5=9
Naked Single: r9c1=3
Full House: r9c4=8
Full House: r8c4=3
Naked Single: r4c4=2
Full House: r4c5=4
Full House: r2c5=8
Full House: r2c4=9
Naked Single: r1c2=2
Full House: r1c1=8
Full House: r8c1=2
Full House: r8c2=4
|
normal_sudoku_5912 | 13.4.6...9.6.513.4.5493..6..43.....759..24638...3..4...69....4331.64.9.54.5.93..6 | 132476859986251374754938162643189527591724638278365491869517243317642985425893716 | normal_sudoku_5912 | 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 . 4 . 6 . . .
9 . 6 . 5 1 3 . 4
. 5 4 9 3 . . 6 .
. 4 3 . . . . . 7
5 9 . . 2 4 6 3 8
. . . 3 . . 4 . .
. 6 9 . . . . 4 3
3 1 . 6 4 . 9 . 5
4 . 5 . 9 3 . . 6 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 132476859986251374754938162643189527591724638278365491869517243317642985425893716 #1 Extreme (7302)
Finned Franken Swordfish: 2 r18b2 c368 fr1c7 fr1c9 fr2c4 => r2c8<>2
Forcing Chain Contradiction in r1c3 => r2c4<>7
r2c4=7 r2c4<>2 r2c2=2 r1c3<>2
r2c4=7 r5c4<>7 r5c3=7 r1c3<>7
r2c4=7 r1c5<>7 r1c5=8 r1c3<>8
Finned Franken Swordfish: 7 r28b2 c368 fr1c5 fr2c2 => r1c3<>7
Forcing Net Contradiction in c6 => r1c7<>2
r1c7=2 (r3c7<>2) (r3c9<>2) (r4c7<>2) (r1c9<>2) r3c9<>2 r6c9=2 r4c8<>2 r4c1=2 r3c1<>2 r3c6=2
r1c7=2 (r3c9<>2 r6c9=2 r4c8<>2 r4c1=2 r7c1<>2) (r7c7<>2) r1c7<>5 r1c8=5 r6c8<>5 r6c6=5 r7c6<>5 r7c4=5 r7c4<>2 r7c6=2
Forcing Net Verity => r1c7<>7
r1c5=7 r1c7<>7
r6c5=7 (r6c5<>6 r6c1=6 r6c1<>2) (r6c5<>6 r6c1=6 r6c1<>2) (r6c1<>7) r1c5<>7 (r1c5=8 r1c3<>8 r1c3=2 r6c3<>2) (r1c5=8 r1c3<>8 r1c3=2 r3c1<>2) r3c6=7 r3c1<>7 r7c1=7 r7c1<>2 r4c1=2 r6c2<>2 r6c8=2 r2c2=2 r2c2<>7 r2c8=7 r1c7<>7
r7c5=7 (r7c1<>7) r1c5<>7 r3c6=7 r3c1<>7 r6c1=7 (r6c1<>6 r6c5=6 r4c5<>6 r4c1=6 r4c1<>2) (r6c3<>7 r8c3=7 r8c8<>7) r3c1<>7 r2c2=7 r2c8<>7 r2c8=8 r8c8<>8 r8c8=2 r4c8<>2 r4c7=2 r4c7<>5 r1c7=5 r1c7<>7
Forcing Chain Contradiction in r8 => r6c5<>7
r6c5=7 r5c4<>7 r5c3=7 r8c3<>7
r6c5=7 r1c5<>7 r3c6=7 r8c6<>7
r6c5=7 r1c5<>7 r1c8=7 r8c8<>7
Forcing Net Contradiction in r7 => r1c5=7
r1c5<>7 (r7c5=7 r7c1<>7) (r1c5=8 r1c3<>8 r1c3=2 r3c1<>2) r3c6=7 r3c1<>7 r3c1=8 r7c1<>8 r7c1=2
r1c5<>7 (r1c5=8 r2c4<>8 r2c4=2 r7c4<>2) r1c8=7 (r8c8<>7) r2c8<>7 r2c8=8 r8c8<>8 r8c8=2 r7c7<>2 r7c6=2
W-Wing: 8/2 in r1c3,r3c6 connected by 2 in r2c24 => r3c1<>8
Sashimi Swordfish: 8 r138 c368 fr1c7 fr3c7 => r2c8<>8
Naked Single: r2c8=7
Hidden Single: r3c1=7
Skyscraper: 7 in r5c4,r8c6 (connected by r58c3) => r6c6,r79c4<>7
Hidden Single: r5c4=7
Full House: r5c3=1
XYZ-Wing: 1/2/8 in r29c4,r7c5 => r7c4<>8
Grouped Discontinuous Nice Loop: 2 r7c4 -2- r7c1 -8- r7c5 -1- r79c4 =1= r4c4 =5= r7c4 => r7c4<>2
Almost Locked Set XZ-Rule: A=r6c1235 {12678}, B=r7c15 {128}, X=1, Z=2 => r4c1<>2
Locked Candidates Type 1 (Pointing): 2 in b4 => r6c89<>2
Locked Candidates Type 2 (Claiming): 2 in c9 => r1c8,r3c7<>2
Hidden Rectangle: 6/8 in r4c15,r6c15 => r6c5<>8
Discontinuous Nice Loop: 8 r4c6 -8- r3c6 -2- r3c9 -1- r6c9 -9- r6c6 =9= r4c6 => r4c6<>8
Grouped AIC: 1/2 2- r9c4 =2= r2c4 =8= r3c6 -8- r3c7 -1- r79c7 =1= r9c8 -1 => r9c4<>1, r9c8<>2
Locked Candidates Type 1 (Pointing): 1 in b8 => r7c7<>1
Naked Pair: 2,8 in r29c4 => r4c4<>8
Hidden Pair: 6,8 in r4c15 => r4c5<>1
2-String Kite: 8 in r3c7,r9c4 (connected by r2c4,r3c6) => r9c7<>8
Uniqueness Test 4: 6/8 in r4c15,r6c15 => r6c1<>8
X-Wing: 8 c15 r47 => r7c67<>8
Locked Candidates Type 1 (Pointing): 8 in b9 => r1c8<>8
W-Wing: 9/5 in r1c8,r4c6 connected by 5 in r6c68 => r4c8<>9
Hidden Single: r4c6=9
Multi Colors 1: 8 (r1c3,r2c4,r3c7) / (r1c7,r2c2,r3c6,r9c4), (r4c1,r6c6,r7c5) / (r4c5,r7c1) => r8c3<>8
W-Wing: 2/7 in r7c7,r8c3 connected by 7 in r9c27 => r7c1,r8c8<>2
Naked Single: r7c1=8
Naked Single: r8c8=8
Naked Single: r4c1=6
Full House: r6c1=2
Naked Single: r7c5=1
Naked Single: r9c8=1
Naked Single: r4c5=8
Full House: r6c5=6
Naked Single: r7c4=5
Naked Single: r6c6=5
Full House: r4c4=1
Naked Single: r6c8=9
Naked Single: r1c8=5
Full House: r4c8=2
Full House: r4c7=5
Full House: r6c9=1
Naked Single: r1c7=8
Naked Single: r3c9=2
Full House: r1c9=9
Full House: r1c3=2
Full House: r3c7=1
Full House: r3c6=8
Full House: r2c2=8
Full House: r2c4=2
Full House: r9c4=8
Naked Single: r8c3=7
Full House: r6c3=8
Full House: r6c2=7
Full House: r8c6=2
Full House: r9c2=2
Full House: r7c6=7
Full House: r9c7=7
Full House: r7c7=2
|
normal_sudoku_907 | 65....2.3..4..3..1132.8.7..3.18...7..6.39.12.4....1.36.1..38.9.5.3.7.....4...53.7 | 657149283984723651132586749321864975865397124479251836716438592593672418248915367 | normal_sudoku_907 | 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 5 . . . . 2 . 3
. . 4 . . 3 . . 1
1 3 2 . 8 . 7 . .
3 . 1 8 . . . 7 .
. 6 . 3 9 . 1 2 .
4 . . . . 1 . 3 6
. 1 . . 3 8 . 9 .
5 . 3 . 7 . . . .
. 4 . . . 5 3 . 7 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 657149283984723651132586749321864975865397124479251836716438592593672418248915367 #1 Extreme (2230)
Locked Candidates Type 1 (Pointing): 2 in b4 => r8c2<>2
Locked Candidates Type 2 (Claiming): 5 in c8 => r2c7,r3c9<>5
Continuous Nice Loop: 2/4/7/8 8= r8c9 =2= r7c9 -2- r7c1 -7- r5c1 -8- r5c9 =8= r8c9 =2 => r7c4<>2, r8c9<>4, r2c1<>7, r5c3<>8
AIC: 4 4- r1c5 =4= r4c5 -4- r5c6 -7- r5c1 =7= r7c1 -7- r7c3 -6- r7c4 -4 => r13c4<>4
Locked Candidates Type 2 (Claiming): 4 in c4 => r8c6<>4
AIC: 9 9- r4c2 -2- r4c6 =2= r8c6 -2- r8c9 -8- r8c2 -9 => r26c2<>9
Turbot Fish: 9 r2c1 =9= r1c3 -9- r6c3 =9= r6c7 => r2c7<>9
Hidden Single: r3c9=9
Locked Candidates Type 1 (Pointing): 4 in b3 => r8c8<>4
Sue de Coq: r45c6 - {2467} (r3c6 - {46}, r6c45 - {257}) => r4c5<>2, r4c5<>5, r1c6<>4, r8c6<>6
Locked Candidates Type 1 (Pointing): 5 in b5 => r6c37<>5
Hidden Single: r5c3=5
Naked Triple: 2,8,9 in r8c269 => r8c4<>2, r8c4<>9, r8c78<>8
Skyscraper: 8 in r5c1,r8c2 (connected by r58c9) => r6c2,r9c1<>8
Naked Triple: 2,5,7 in r6c245 => r6c3<>7
X-Wing: 7 r26 c24 => r1c4<>7
X-Wing: 8 r19 c38 => r2c8,r6c3<>8
Naked Single: r6c3=9
Naked Single: r4c2=2
Naked Single: r6c7=8
Naked Single: r6c2=7
Full House: r5c1=8
Naked Single: r2c7=6
Naked Single: r5c9=4
Full House: r5c6=7
Naked Single: r2c2=8
Full House: r8c2=9
Naked Single: r2c1=9
Full House: r1c3=7
Naked Single: r2c8=5
Naked Single: r8c7=4
Naked Single: r4c9=5
Full House: r4c7=9
Full House: r7c7=5
Naked Single: r1c6=9
Naked Single: r8c6=2
Naked Single: r9c1=2
Full House: r7c1=7
Naked Single: r7c3=6
Full House: r9c3=8
Naked Single: r2c5=2
Full House: r2c4=7
Naked Single: r3c8=4
Full House: r1c8=8
Naked Single: r7c9=2
Full House: r8c9=8
Full House: r7c4=4
Naked Single: r1c4=1
Full House: r1c5=4
Naked Single: r6c5=5
Full House: r6c4=2
Naked Single: r3c6=6
Full House: r3c4=5
Full House: r4c6=4
Full House: r4c5=6
Full House: r9c5=1
Naked Single: r8c4=6
Full House: r8c8=1
Full House: r9c8=6
Full House: r9c4=9
|
normal_sudoku_3434 | .7.....4.5.......99.8.4.7..6....14...8.496..74..2...6.75..1...41.35.42..8....3..5 | 372189546546327819918645723695731482281496357437258961759812634163574298824963175 | normal_sudoku_3434 | 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 .
5 . . . . . . . 9
9 . 8 . 4 . 7 . .
6 . . . . 1 4 . .
. 8 . 4 9 6 . . 7
4 . . 2 . . . 6 .
7 5 . . 1 . . . 4
1 . 3 5 . 4 2 . .
8 . . . . 3 . . 5 | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 372189546546327819918645723695731482281496357437258961759812634163574298824963175 #1 Extreme (7630)
Turbot Fish: 9 r6c7 =9= r4c8 -9- r8c8 =9= r8c2 => r6c2<>9
Almost Locked Set XZ-Rule: A=r46c2,r5c1 {1239}, B=r4c89,r5c78,r6c9 {123589}, X=9, Z=1 => r6c7<>1
Almost Locked Set XY-Wing: A=r6c29 {138}, B=r12579c3 {124569}, C=r8c29 {689}, X,Y=8,9, Z=1 => r6c3<>1
Almost Locked Set XY-Wing: A=r8c29 {689}, B=r46c9,r5c78 {12358}, C=r12579c3 {124569}, X,Y=5,9, Z=8 => r1c9<>8
Almost Locked Set XY-Wing: A=r8c29 {689}, B=r12579c3 {124569}, C=r46c9,r5c78 {12358}, X,Y=5,8, Z=9 => r9c2<>9
Almost Locked Set Chain: 3- r6c29 {138} -8- r8c29 {689} -9- r46c2,r5c13 {12359} -5- r46c9,r5c78 {12358} -3 => r6c7<>3
Forcing Chain Contradiction in r4c2 => r1c7<>1
r1c7=1 r13c9<>1 r6c9=1 r6c2<>1 r6c2=3 r5c1<>3 r5c1=2 r4c2<>2
r1c7=1 r13c9<>1 r6c9=1 r6c2<>1 r6c2=3 r4c2<>3
r1c7=1 r9c7<>1 r9c8=1 r9c8<>7 r8c8=7 r8c8<>9 r8c2=9 r4c2<>9
Forcing Chain Contradiction in r4c2 => r2c7<>1
r2c7=1 r13c9<>1 r6c9=1 r6c2<>1 r6c2=3 r5c1<>3 r5c1=2 r4c2<>2
r2c7=1 r13c9<>1 r6c9=1 r6c2<>1 r6c2=3 r4c2<>3
r2c7=1 r9c7<>1 r9c8=1 r9c8<>7 r8c8=7 r8c8<>9 r8c2=9 r4c2<>9
Forcing Net Verity => r1c4<>3
r5c1=2 r1c1<>2 r1c1=3 r1c4<>3
r5c3=2 (r5c1<>2 r5c1=3 r4c2<>3 r4c2=9 r4c3<>9) (r5c1<>2 r5c1=3 r4c2<>3 r4c2=9 r6c3<>9) (r9c3<>2) r7c3<>2 r7c6=2 (r3c6<>2 r3c6=5 r1c6<>5 r1c7=5 r5c7<>5) r9c5<>2 r9c2=2 r9c2<>4 r9c3=4 r9c3<>9 r7c3=9 r8c2<>9 r8c8=9 (r9c8<>9 r9c4=9 r9c4<>7) r8c8<>7 r8c5=7 r9c5<>7 r9c8=7 r9c8<>1 r9c7=1 r5c7<>1 r5c7=3 r5c1<>3 r1c1=3 r1c4<>3
r5c8=2 (r5c8<>3) (r3c8<>2) (r4c9<>2) r5c1<>2 r1c1=2 r1c9<>2 r3c9=2 (r3c6<>2 r3c6=5 r3c8<>5) r3c9<>1 r1c9=1 r3c8<>1 (r3c4=1 r3c4<>6) r3c8=3 (r3c2<>3) r7c8<>3 r7c7=3 r5c7<>3 r5c1=3 (r4c2<>3) r6c2<>3 (r6c2=1 r6c9<>1) (r6c2=1 r5c3<>1) (r6c2=1 r6c9<>1) r2c2=3 r2c2<>4 r2c3=4 r2c3<>1 r1c3=1 r1c9<>1 r3c9=1 r3c4<>1 r3c4=3 r1c4<>3
Forcing Net Verity => r1c5<>2
r4c3=9 (r6c3<>9 r6c7=9 r6c7<>5) (r4c3<>5) r4c3<>7 r6c3=7 r6c3<>5 r5c3=5 (r5c7<>5) (r5c8<>5) r5c7<>5 r1c7=5 r3c8<>5 (r3c6=5 r6c6<>5 r6c5=5 r6c5<>3) r4c8=5 r5c8<>5 r5c3=5 (r5c7<>5) (r5c8<>5) r5c3<>1 r6c2=1 r6c2<>3 r6c9=3 (r5c7<>3) r5c8<>3 r5c1=3 r1c1<>3 r1c1=2 r1c5<>2
r6c3=9 (r4c3<>9 r4c8=9 r4c8<>5) (r6c3<>5) r6c3<>7 r4c3=7 r4c3<>5 r5c3=5 r5c8<>5 r3c8=5 r3c6<>5 r3c6=2 r1c5<>2
r7c3=9 (r7c6<>9 r1c6=9 r1c6<>8) (r8c2<>9 r8c2=6 r8c9<>6 r8c9=8 r7c8<>8 r7c4=8 r1c4<>8) (r7c6<>9 r1c6=9 r1c6<>5) r7c3<>2 r7c6=2 r3c6<>2 r3c6=5 r1c5<>5 r1c7=5 r1c7<>8 r1c5=8 r1c5<>2
r9c3=9 (r9c3<>2) r9c3<>4 r9c2=4 r9c2<>2 r9c5=2 r1c5<>2
2-String Kite: 2 in r2c5,r7c3 (connected by r7c6,r9c5) => r2c3<>2
Forcing Net Verity => r1c5<>3
r5c1=2 r1c1<>2 r1c1=3 r1c5<>3
r5c3=2 (r5c1<>2 r5c1=3 r4c2<>3 r4c2=9 r4c3<>9) (r5c1<>2 r5c1=3 r4c2<>3 r4c2=9 r6c3<>9) (r9c3<>2) r7c3<>2 r7c6=2 (r7c6<>9 r1c6=9 r1c6<>8) r9c5<>2 r9c2=2 r9c2<>4 r9c3=4 r9c3<>9 r7c3=9 (r8c2<>9 r8c2=6 r8c9<>6 r8c9=8 r7c8<>8 r7c4=8 r1c4<>8) r7c3<>2 r7c6=2 (r7c6<>9 r1c6=9 r1c6<>8) r3c6<>2 r3c6=5 (r1c6<>5) r1c5<>5 r1c7=5 r1c7<>8 r1c5=8 r1c5<>3
r5c8=2 (r5c8<>3) (r3c8<>2) (r4c9<>2) r5c1<>2 r1c1=2 r1c9<>2 r3c9=2 (r3c6<>2 r3c6=5 r3c8<>5) r3c9<>1 r1c9=1 (r1c9<>3) r3c8<>1 (r3c4=1 r3c4<>6) r3c8=3 (r2c7<>3) (r2c8<>3) (r1c7<>3) r7c8<>3 r7c7=3 r5c7<>3 r5c1=3 (r6c2<>3 r6c2=1 r6c9<>1) (r6c2<>3 r6c2=1 r5c3<>1) (r6c2<>3 r6c2=1 r6c9<>1) r1c1<>3 r1c5=3 (r2c4<>3) r2c5<>3 r2c2=3 r2c2<>4 r2c3=4 r2c3<>1 r1c3=1 r1c9<>1 r3c9=1 r3c4<>1 r3c4=3 r1c5<>3
Finned Swordfish: 3 r157 c178 fr1c9 => r2c78,r3c8<>3
Grouped Discontinuous Nice Loop: 8 r6c7 -8- r2c7 -6- r79c7 =6= r8c9 =8= r46c9 -8- r6c7 => r6c7<>8
Forcing Chain Contradiction in r3c8 => r3c9<>2
r3c9=2 r3c9<>3 r1c79=3 r1c1<>3 r5c1=3 r6c2<>3 r6c2=1 r6c9<>1 r13c9=1 r3c8<>1
r3c9=2 r3c8<>2
r3c9=2 r3c6<>2 r3c6=5 r3c8<>5
Skyscraper: 2 in r4c9,r5c1 (connected by r1c19) => r4c23,r5c8<>2
Discontinuous Nice Loop: 3 r1c7 -3- r1c1 -2- r5c1 =2= r5c3 -2- r7c3 =2= r7c6 -2- r3c6 -5- r3c8 =5= r1c7 => r1c7<>3
Locked Candidates Type 1 (Pointing): 3 in b3 => r46c9<>3
XY-Chain: 3 3- r4c2 -9- r8c2 -6- r8c9 -8- r6c9 -1- r6c2 -3 => r23c2,r5c1<>3
Naked Single: r5c1=2
Full House: r1c1=3
Hidden Single: r3c9=3
Locked Candidates Type 2 (Claiming): 3 in r5 => r4c8<>3
Turbot Fish: 1 r1c9 =1= r6c9 -1- r6c2 =1= r5c3 => r1c3<>1
XYZ-Wing: 2/6/9 in r17c3,r8c2 => r9c3<>6
Empty Rectangle: 6 in b7 (r3c24) => r7c4<>6
2-String Kite: 6 in r1c9,r7c3 (connected by r7c7,r8c9) => r1c3<>6
Naked Single: r1c3=2
Hidden Single: r4c9=2
Hidden Single: r9c2=2
Hidden Single: r7c6=2
Naked Single: r3c6=5
Hidden Single: r2c5=2
Hidden Single: r9c3=4
Hidden Single: r2c2=4
Hidden Single: r3c8=2
Hidden Single: r1c6=9
Hidden Single: r1c7=5
Naked Single: r6c7=9
Hidden Single: r2c4=3
Hidden Single: r2c6=7
Full House: r6c6=8
Naked Single: r4c4=7
Naked Single: r6c9=1
Naked Single: r1c9=6
Full House: r8c9=8
Naked Single: r5c7=3
Naked Single: r6c2=3
Naked Single: r1c5=8
Full House: r1c4=1
Full House: r3c4=6
Full House: r3c2=1
Full House: r2c3=6
Naked Single: r2c7=8
Full House: r2c8=1
Naked Single: r5c8=5
Full House: r4c8=8
Full House: r5c3=1
Naked Single: r7c7=6
Full House: r9c7=1
Naked Single: r4c2=9
Full House: r8c2=6
Full House: r7c3=9
Naked Single: r6c5=5
Full House: r4c5=3
Full House: r4c3=5
Full House: r6c3=7
Naked Single: r9c4=9
Full House: r7c4=8
Full House: r7c8=3
Naked Single: r8c5=7
Full House: r8c8=9
Full House: r9c8=7
Full House: r9c5=6
|
normal_sudoku_4298 | .9..8......82..9..6...95.7886..127933198..452..29..8...8..496....6.28..99..6...8. | 295487136178263945643195278864512793319876452752934861581349627436728519927651384 | normal_sudoku_4298 | 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 . . . .
. . 8 2 . . 9 . .
6 . . . 9 5 . 7 8
8 6 . . 1 2 7 9 3
3 1 9 8 . . 4 5 2
. . 2 9 . . 8 . .
. 8 . . 4 9 6 . .
. . 6 . 2 8 . . 9
9 . . 6 . . . 8 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 295487136178263945643195278864512793319876452752934861581349627436728519927651384 #1 Extreme (11798)
Locked Candidates Type 1 (Pointing): 7 in b4 => r6c56<>7
Locked Candidates Type 1 (Pointing): 6 in b6 => r6c56<>6
X-Wing: 2 r39 c27 => r1c7<>2
2-String Kite: 5 in r4c3,r9c5 (connected by r4c4,r6c5) => r9c3<>5
Finned X-Wing: 4 r34 c34 fr3c2 => r1c3<>4
Finned Swordfish: 7 r268 c124 fr2c5 fr2c6 => r1c4<>7
Locked Candidates Type 2 (Claiming): 7 in c4 => r9c56<>7
Naked Pair: 3,5 in r69c5 => r2c5<>3
Uniqueness Test 1: 6/7 in r2c56,r5c56 => r2c6<>6, r2c6<>7
Naked Triple: 1,3,4 in r13c4,r2c6 => r1c6<>1, r1c6<>3, r1c6<>4
Forcing Net Contradiction in c9 => r7c1<>7
r7c1=7 r7c9<>7
r7c1=7 (r9c3<>7 r1c3=7 r1c3<>5) (r9c3<>7 r9c9=7 r9c9<>4) r7c1<>2 r7c8=2 r9c7<>2 r9c2=2 r9c2<>4 r9c3=4 (r3c3<>4) r4c3<>4 r4c4=4 (r1c4<>4 r1c9=4 r2c9<>4) (r6c6<>4 r6c1=4 r6c6<>4 r6c6=3 r9c6<>3 r9c6=1 r9c7<>1) (r6c6<>4 r6c1=4 r6c6<>4 r6c6=3 r6c5<>3 r9c5=3 r9c7<>3) r3c4<>4 r3c2=4 r3c2<>2 r3c7=2 r9c7<>2 r9c7=5 (r1c7<>5) r9c7<>2 r9c2=2 r3c2<>2 r3c7=2 r1c8<>2 r1c1=2 r1c1<>5 r1c9=5 r1c9<>4 r9c9=4 r9c9<>7
Forcing Net Contradiction in r9c9 => r7c9<>5
r7c9=5 (r9c7<>5) (r9c9<>5) (r7c4<>5) (r7c3<>5) (r8c7<>5) r9c7<>5 r1c7=5 r1c3<>5 r4c3=5 r4c4<>5 r8c4=5 r9c5<>5 r9c2=5 (r9c2<>4) (r9c2<>2 r9c7=2 r3c7<>2 r3c2=2 r3c2<>4) r9c5<>5 r6c5=5 r4c4<>5 r4c4=4 r3c4<>4 r3c3=4 r9c3<>4 r9c9=4 r9c9<>7 r7c9=7 r7c9<>5
Forcing Net Contradiction in r2 => r7c3<>7
r7c3=7 (r7c9<>7 r7c9=1 r8c7<>1) (r7c9<>7 r7c9=1 r8c8<>1) (r8c1<>7) r8c2<>7 r8c4=7 r8c4<>1 r8c1=1 r2c1<>1
r7c3=7 (r7c9<>7 r7c9=1 r9c7<>1) (r7c9<>7 r7c9=1 r9c9<>1) (r7c9<>7 r7c9=1 r8c7<>1) (r7c9<>7 r7c9=1 r8c8<>1) (r8c1<>7) r8c2<>7 r8c4=7 r8c4<>1 r8c1=1 r9c3<>1 r9c6=1 r2c6<>1
r7c3=7 r7c9<>7 r7c9=1 r6c9<>1 r6c8=1 r2c8<>1
r7c3=7 r7c9<>7 r7c9=1 r2c9<>1
Forcing Net Contradiction in r8 => r1c8<>6
r1c8=6 (r1c8<>4) (r1c6<>6 r1c6=7 r1c3<>7 r9c3=7 r9c3<>4) r1c8<>2 r1c1=2 (r1c1<>4) (r1c1<>4) r7c1<>2 r7c8=2 r9c7<>2 r9c2=2 r9c2<>4 r9c9=4 (r8c8<>4 r2c8=4 r2c6<>4 r6c6=4 r6c1<>4) r1c9<>4 r1c4=4 (r3c4<>4) r4c4<>4 r4c3=4 r3c3<>4 r3c2=4 r2c1<>4 r8c1=4 r8c1<>1
r1c8=6 r1c6<>6 r1c6=7 r1c3<>7 r9c3=7 (r8c1<>7) r8c2<>7 r8c4=7 r8c4<>1
r1c8=6 (r1c8<>4) (r1c6<>6 r1c6=7 r1c3<>7 r9c3=7 r9c3<>4) r1c8<>2 r1c1=2 (r1c1<>4) r7c1<>2 r7c8=2 r9c7<>2 r9c2=2 r9c2<>4 r9c9=4 r1c9<>4 r1c4=4 r4c4<>4 r4c4=5 r6c5<>5 r9c5=5 (r9c7<>5) r9c9<>5 r8c7=5 r8c7<>1
r1c8=6 r6c8<>6 r6c8=1 r8c8<>1
Forcing Net Verity => r1c9<>1
r1c8=4 (r2c9<>4 r9c9=4 r9c9<>7) r1c8<>2 r1c1=2 (r1c1<>7) r7c1<>2 r7c8=2 r9c7<>2 r9c2=2 r9c2<>7 r9c3=7 r1c3<>7 r1c6=7 r1c6<>6 r1c9=6 r1c9<>1
r1c9=4 r1c9<>1
r2c8=4 r2c8<>6 r6c8=6 r6c9<>6 r6c9=1 r1c9<>1
r2c9=4 (r2c9<>5) r2c6<>4 r6c6=4 r6c6<>3 r6c5=3 r9c5<>3 r9c5=5 r9c9<>5 r1c9=5 r1c9<>1
Forcing Net Contradiction in r1 => r6c2<>4
r6c2=4 (r9c2<>4) (r3c2<>4) r4c3<>4 r4c4=4 (r1c4<>4) r3c4<>4 r3c3=4 (r1c1<>4) r9c3<>4 r9c9=4 r1c9<>4 r1c8=4 r1c8<>2 r1c1=2 r1c1<>5
r6c2=4 r4c3<>4 r4c3=5 r1c3<>5
r6c2=4 (r9c2<>4) (r3c2<>4) r4c3<>4 r4c4=4 r3c4<>4 r3c3=4 r9c3<>4 r9c9=4 r9c9<>5 r89c7=5 r1c7<>5
r6c2=4 (r6c2<>7 r6c1=7 r1c1<>7) (r6c6<>4 r6c6=3 r9c6<>3 r9c6=1 r9c3<>1) (r6c6<>4 r6c6=3 r6c5<>3 r9c5=3 r9c3<>3) (r3c2<>4) r4c3<>4 r4c4=4 r3c4<>4 r3c3=4 r9c3<>4 r9c3=7 r1c3<>7 r1c6=7 r1c6<>6 r1c9=6 r1c9<>5
Forcing Net Contradiction in r2 => r7c8<>1
r7c8=1 (r8c7<>1) (r8c8<>1) r7c9<>1 r7c9=7 r7c4<>7 r8c4=7 r8c4<>1 r8c1=1 r2c1<>1
r7c8=1 (r9c7<>1) (r9c9<>1) (r8c7<>1) (r8c8<>1) r7c9<>1 r7c9=7 r7c4<>7 r8c4=7 r8c4<>1 r8c1=1 r9c3<>1 r9c6=1 r2c6<>1
r7c8=1 r2c8<>1
r7c8=1 r6c8<>1 r6c9=1 r2c9<>1
Forcing Net Contradiction in c4 => r1c1<>7
r1c1=7 (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r2c8<>3) (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r8c7<>3) (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r8c8<>3) (r8c1<>7) r1c3<>7 r9c3=7 r8c2<>7 r8c4=7 r8c4<>3 r8c2=3 r2c2<>3 r2c6=3 r1c4<>3
r1c1=7 (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r2c8<>3) (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r8c7<>3) (r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r8c8<>3) (r8c1<>7) r1c3<>7 r9c3=7 r8c2<>7 r8c4=7 r8c4<>3 r8c2=3 r2c2<>3 r2c6=3 r3c4<>3
r1c1=7 r1c1<>2 r1c8=2 r7c8<>2 r7c8=3 r7c4<>3
r1c1=7 (r8c1<>7) r1c3<>7 r9c3=7 r8c2<>7 r8c4=7 r8c4<>3
Forcing Chain Contradiction in r9c3 => r9c9<>1
r9c9=1 r9c3<>1
r9c9=1 r9c6<>1 r9c6=3 r9c3<>3
r9c9=1 r9c6<>1 r9c6=3 r6c6<>3 r6c6=4 r6c1<>4 r4c3=4 r9c3<>4
r9c9=1 r6c9<>1 r6c9=6 r1c9<>6 r1c6=6 r1c6<>7 r1c3=7 r9c3<>7
Forcing Net Contradiction in r1c9 => r1c7<>5
r1c7=5 (r1c9<>5) r2c9<>5 r9c9=5 (r9c9<>4 r8c8=4 r1c8<>4) r9c5<>5 r6c5=5 (r4c4<>5 r4c4=4 r1c4<>4) (r6c1<>5) r6c2<>5 r6c2=7 r6c1<>7 r6c1=4 r1c1<>4 r1c9=4
r1c7=5 (r1c9<>5) r2c9<>5 r9c9=5 (r9c9<>7) r9c5<>5 r6c5=5 r6c2<>5 r6c2=7 r9c2<>7 r9c3=7 r1c3<>7 r1c6=7 r1c6<>6 r1c9=6
Locked Candidates Type 1 (Pointing): 5 in b3 => r9c9<>5
Forcing Chain Contradiction in r8 => r8c2<>5
r8c2=5 r7c13<>5 r7c4=5 r4c4<>5 r4c4=4 r4c3<>4 r6c1=4 r8c1<>4
r8c2=5 r8c2<>4
r8c2=5 r7c13<>5 r7c4=5 r7c4<>7 r7c9=7 r9c9<>7 r9c9=4 r8c8<>4
Forcing Chain Contradiction in c8 => r9c2<>5
r9c2=5 r9c2<>2 r9c7=2 r3c7<>2 r1c8=2 r1c8<>4
r9c2=5 r9c5<>5 r9c5=3 r6c5<>3 r6c6=3 r6c6<>4 r2c6=4 r2c8<>4
r9c2=5 r7c13<>5 r7c4=5 r7c4<>7 r7c9=7 r9c9<>7 r9c9=4 r8c8<>4
Discontinuous Nice Loop: 7 r2c1 -7- r2c5 -6- r1c6 =6= r1c9 =5= r2c9 -5- r2c2 =5= r6c2 =7= r6c1 -7- r2c1 => r2c1<>7
Discontinuous Nice Loop: 5 r7c4 -5- r4c4 -4- r4c3 =4= r6c1 =7= r8c1 -7- r8c4 =7= r7c4 => r7c4<>5
Locked Candidates Type 2 (Claiming): 5 in r7 => r8c1<>5
Discontinuous Nice Loop: 1 r8c7 -1- r7c9 -7- r7c4 =7= r8c4 =5= r8c7 => r8c7<>1
Sashimi X-Wing: 1 c67 r29 fr1c7 fr3c7 => r2c89<>1
Finned Franken Swordfish: 1 r29b3 c367 fr1c8 fr2c1 => r1c3<>1
Forcing Chain Contradiction in c9 => r4c3=4
r4c3<>4 r4c3=5 r6c2<>5 r2c2=5 r2c9<>5 r1c9=5 r1c9<>4
r4c3<>4 r4c4=4 r6c6<>4 r2c6=4 r2c9<>4
r4c3<>4 r6c1=4 r6c1<>7 r8c1=7 r9c23<>7 r9c9=7 r9c9<>4
Full House: r4c4=5
Naked Single: r6c5=3
Naked Single: r6c6=4
Naked Single: r9c5=5
Hidden Single: r8c7=5
Empty Rectangle: 3 in b9 (r29c6) => r2c8<>3
Naked Triple: 4,5,6 in r12c9,r2c8 => r1c8<>4
2-String Kite: 4 in r2c8,r9c2 (connected by r8c8,r9c9) => r2c2<>4
W-Wing: 1/3 in r3c3,r9c6 connected by 3 in r2c26 => r9c3<>1
W-Wing: 3/1 in r1c7,r2c6 connected by 1 in r9c67 => r1c4<>3
W-Wing: 3/1 in r3c3,r9c6 connected by 1 in r2c16 => r9c3<>3
Naked Single: r9c3=7
Naked Single: r9c9=4
Hidden Single: r1c6=7
Naked Single: r2c5=6
Full House: r5c5=7
Full House: r5c6=6
Naked Single: r2c8=4
Naked Single: r2c9=5
Naked Single: r1c9=6
Naked Single: r2c1=1
Naked Single: r6c9=1
Full House: r6c8=6
Full House: r7c9=7
Naked Single: r2c6=3
Full House: r2c2=7
Full House: r9c6=1
Naked Single: r3c3=3
Naked Single: r8c1=4
Naked Single: r6c2=5
Full House: r6c1=7
Naked Single: r7c4=3
Full House: r8c4=7
Naked Single: r1c3=5
Full House: r7c3=1
Naked Single: r8c2=3
Full House: r8c8=1
Naked Single: r7c8=2
Full House: r1c8=3
Full House: r7c1=5
Full House: r1c1=2
Full House: r9c2=2
Full House: r9c7=3
Full House: r3c2=4
Naked Single: r1c7=1
Full House: r1c4=4
Full House: r3c4=1
Full House: r3c7=2
|
normal_sudoku_3659 | .8314..6515....8.46.4.581374.....5......2.74....47...186.51.4.3...764.58745..361. | 983147265157236894624958137471389526538621749296475381869512473312764958745893612 | normal_sudoku_3659 | 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 1 4 . . 6 5
1 5 . . . . 8 . 4
6 . 4 . 5 8 1 3 7
4 . . . . . 5 . .
. . . . 2 . 7 4 .
. . . 4 7 . . . 1
8 6 . 5 1 . 4 . 3
. . . 7 6 4 . 5 8
7 4 5 . . 3 6 1 . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 983147265157236894624958137471389526538621749296475381869512473312764958745893612 #1 Hard (426)
Hidden Single: r6c7=3
Hidden Single: r1c6=7
Hidden Single: r2c3=7
Hidden Single: r7c8=7
Hidden Single: r4c2=7
Locked Candidates Type 1 (Pointing): 3 in b4 => r5c4<>3
Naked Pair: 2,9 in r36c2 => r58c2<>9, r8c2<>2
Remote Pair: 2/9 r3c4 -9- r3c2 -2- r1c1 -9- r1c7 -2- r8c7 -9- r9c9 => r9c4<>2, r9c4<>9
Naked Single: r9c4=8
Naked Single: r9c5=9
Full House: r7c6=2
Full House: r9c9=2
Full House: r7c3=9
Full House: r8c7=9
Full House: r1c7=2
Full House: r1c1=9
Full House: r2c8=9
Full House: r3c2=2
Full House: r3c4=9
Naked Single: r2c5=3
Full House: r4c5=8
Naked Single: r2c6=6
Full House: r2c4=2
Naked Single: r6c2=9
Naked Single: r5c4=6
Full House: r4c4=3
Naked Single: r4c8=2
Full House: r6c8=8
Naked Single: r6c6=5
Naked Single: r5c9=9
Full House: r4c9=6
Naked Single: r6c1=2
Full House: r6c3=6
Naked Single: r5c6=1
Full House: r4c6=9
Full House: r4c3=1
Naked Single: r8c1=3
Full House: r5c1=5
Naked Single: r5c2=3
Full House: r5c3=8
Full House: r8c3=2
Full House: r8c2=1
|
normal_sudoku_1720 | .7...413.1.37..9.44...3.27.34..1...7.1.87...38.74.3519..4....9..31.4...27.6...... | 572984136163725984498136275349512867615879423827463519284357691931648752756291348 | normal_sudoku_1720 | 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 3 .
1 . 3 7 . . 9 . 4
4 . . . 3 . 2 7 .
3 4 . . 1 . . . 7
. 1 . 8 7 . . . 3
8 . 7 4 . 3 5 1 9
. . 4 . . . . 9 .
. 3 1 . 4 . . . 2
7 . 6 . . . . . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 572984136163725984498136275349512867615879423827463519284357691931648752756291348 #1 Extreme (3300)
Locked Candidates Type 1 (Pointing): 8 in b7 => r23c2<>8
Skyscraper: 9 in r1c5,r3c2 (connected by r9c25) => r1c13,r3c46<>9
2-String Kite: 6 in r1c1,r6c5 (connected by r5c1,r6c2) => r1c5<>6
Empty Rectangle: 2 in b1 (r6c25) => r1c5<>2
Empty Rectangle: 2 in b7 (r6c25) => r7c5<>2
Finned Swordfish: 2 r269 c256 fr9c4 => r7c6<>2
Finned Swordfish: 8 r248 c678 fr2c5 => r3c6<>8
Discontinuous Nice Loop: 6 r3c2 -6- r6c2 =6= r5c1 =9= r8c1 -9- r9c2 =9= r3c2 => r3c2<>6
Sashimi Swordfish: 6 c259 r267 fr1c9 fr3c9 => r2c8<>6
Locked Candidates Type 1 (Pointing): 6 in b3 => r7c9<>6
Discontinuous Nice Loop: 5 r3c2 =9= r3c3 =8= r3c9 =6= r1c9 -6- r1c1 =6= r5c1 =9= r8c1 -9- r9c2 =9= r3c2 => r3c2<>5
Naked Single: r3c2=9
Hidden Single: r8c1=9
Grouped Discontinuous Nice Loop: 2 r1c1 -2- r1c3 =2= r45c3 -2- r6c2 -6- r2c2 =6= r1c1 => r1c1<>2
Discontinuous Nice Loop: 8 r1c3 -8- r3c3 =8= r3c9 =6= r1c9 -6- r1c1 =6= r2c2 =2= r1c3 => r1c3<>8
Hidden Single: r3c3=8
Grouped AIC: 5 5- r3c9 =5= r3c46 -5- r12c5 =5= r79c5 -5- r8c46 =5= r8c8 -5 => r2c8,r79c9<>5
Naked Single: r2c8=8
Hidden Single: r1c5=8
Hidden Single: r4c7=8
Hidden Single: r1c4=9
Hidden Single: r9c5=9
Hidden Single: r8c6=8
Hidden Single: r1c3=2
Hidden Single: r8c7=7
Hidden Single: r7c6=7
Locked Candidates Type 2 (Claiming): 5 in c3 => r5c1<>5
Naked Pair: 5,6 in r7c5,r8c4 => r79c4,r9c6<>5, r7c4<>6
Naked Triple: 2,4,6 in r5c178 => r5c6<>2, r5c6<>6
Skyscraper: 5 in r1c1,r2c5 (connected by r7c15) => r2c2<>5
Naked Single: r2c2=6
Full House: r1c1=5
Full House: r1c9=6
Full House: r3c9=5
Naked Single: r6c2=2
Full House: r6c5=6
Naked Single: r7c1=2
Full House: r5c1=6
Naked Single: r7c5=5
Full House: r2c5=2
Full House: r2c6=5
Naked Single: r5c7=4
Naked Single: r7c2=8
Full House: r9c2=5
Naked Single: r8c4=6
Full House: r8c8=5
Naked Single: r5c6=9
Naked Single: r5c8=2
Full House: r5c3=5
Full House: r4c8=6
Full House: r9c8=4
Full House: r4c3=9
Naked Single: r9c7=3
Full House: r7c7=6
Naked Single: r7c9=1
Full House: r7c4=3
Full House: r9c9=8
Naked Single: r3c4=1
Full House: r3c6=6
Naked Single: r4c6=2
Full House: r4c4=5
Full House: r9c4=2
Full House: r9c6=1
|
normal_sudoku_2432 | ....36.2.2...9461..56278.499246.5.3...1.29..4...34129.6.....4.....962.81.1.4..9.. | 489136725237594618156278349924685137361729854578341296695813472743962581812457963 | normal_sudoku_2432 | 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 .
2 . . . 9 4 6 1 .
. 5 6 2 7 8 . 4 9
9 2 4 6 . 5 . 3 .
. . 1 . 2 9 . . 4
. . . 3 4 1 2 9 .
6 . . . . . 4 . .
. . . 9 6 2 . 8 1
. 1 . 4 . . 9 . . | Complete the sudoku board based on the rules and visual elements. | sudoku | sudoku_benchmark | hard | 489136725237594618156278349924685137361729854578341296695813472743962581812457963 #1 Easy (164)
Naked Single: r2c4=5
Full House: r1c4=1
Naked Single: r3c7=3
Full House: r3c1=1
Naked Single: r4c5=8
Full House: r5c4=7
Full House: r7c4=8
Naked Single: r4c9=7
Full House: r4c7=1
Naked Single: r9c5=5
Full House: r7c5=1
Naked Single: r2c9=8
Naked Single: r1c9=5
Full House: r1c7=7
Naked Single: r6c9=6
Naked Single: r8c7=5
Full House: r5c7=8
Full House: r5c8=5
Naked Single: r7c8=7
Full House: r9c8=6
Naked Single: r5c1=3
Full House: r5c2=6
Naked Single: r7c6=3
Full House: r9c6=7
Naked Single: r7c2=9
Naked Single: r7c9=2
Full House: r7c3=5
Full House: r9c9=3
Naked Single: r9c1=8
Full House: r9c3=2
Naked Single: r1c1=4
Naked Single: r1c2=8
Full House: r1c3=9
Naked Single: r8c1=7
Full House: r6c1=5
Naked Single: r6c2=7
Full House: r6c3=8
Naked Single: r8c3=3
Full House: r2c3=7
Full House: r2c2=3
Full House: r8c2=4
|
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