SudokuSolver Forum

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 8, clean-up: no 5 in R3C3, no 5 in R3C6, no 1 in R3C7, no 1 in R4C3, no 4 in R4C7, no 2 in R5C12, no 3 in R6C3, no 3 in R7C4, no 3 in R7C6, no 3 in R7C7

2. Naked pair {12} in R56C7, locked for C7 and N6 -> R9C7 = 3, R9C6 = 1, clean-up: no 6,7,8 in R2C6, no 8 in R2C7, no 8 in R3C7, no 4,5 in R3C8, no 8,9 in R3C9, no 6,7 in R4C6, no 9 in R5C6, no 5,6 in R5C89, no 9 in R6C6, no 8 in R8C1, no 8 in R8C2, no 4,6 in R8C5, no 8,9 in R8C6, no 4 in R8C89, no 6 in R9C5, no 4,6 in R9C89

3. Naked pair {34} in R5C89, locked for R5 and N6 -> R4C8 = 5, R9C8 = 2, R3C8 = 1, R9C9 = 5, R9C5 = 4 -> R8C5 = 3, R3C4 = 3, R4C5 = 1, R8C89 = [61], clean-up: no 2 in R1C3, no 4,8,9 in R12C8, no 8 in R12C9, no 4 in R2C3, no 6 in R2C7, no 6 in R3C2, no 8 in R3C3, no 9 in R3C6, no 4 in R3C7, no 6,7 in R3C9, no 8 in R4C2, no 6 in R4C3, no 8,9 in R4C7, no 7,9 in R4C9, no 6,7 in R5C12, no 7 in R5C6, no 7,8 in R6C3, no 7 in R6C5, no 5,6 in R6C6, no 7,8 in R6C9, no 2,4 in R7C3, no 7,8 in R7C4, no 7 in R7C5, no 7,8 in R7C6, no 8,9 in R7C9, no 7,9 in R8C1, no 7,9 in R8C2, no 9 in R8C34, no 5 in R8C6, no 7,8 in R8C7, no 8 in R9C1, no 8 in R9C2

4. R4C7 = 7, R5C6 = 5, clean-up: no 9 in R1C7, no 2 in R2C6, no 4 in R2C7, no 8 in R3C1, no 4 in R3C2, no 6 in R3C3, no 4 in R4C3, no 2 in R4C6, no 2 in R5C3, no 6 in R6C3, no 6 in R6C5, no 4 in R6C6, no 6 in R7C6

5. R2C67 = [45], R3C7 = 6, R4C6 = 3, R1C7 = 8 -> R1C6 = 6, clean-up: no 1 in R1C3, no 7,9 in R1C9, no 6 in R2C12, no 1,2,3 in R2C3, no 2 in R2C4, no 7 in R2C9, no 8 in R3C2, no 7,9 in R3C5, no 7 in R3C6, no 9 in R4C1, no 6 in R5C3

and the rest is naked singles.

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 9, clean-up: no 1 in R3C4, no 3 in R3C6, no 2 in R4C7, no 2 in R5C89, no 2 in R6C7, no 2 in R7C4, no 3 in R89C5

2. Naked pair {89} in R1C34, locked for R1, clean-up: no 2,3 in R2C8

3. Naked pair {89} in R2C67, locked for R1, clean-up: no 2,3 in R1C8, no 1,2 in R2C12

4. Naked pair {12} in R34C8, locked for C8, clean-up: no 8,9 in R67C8, no 8,9 in R8C9

[At this stage there’s a naked killer pair 6,7 in C8 but I think more progress can be made using the clash in C8, which some would call a blocking killer pair.]
5. R67C8 = {37} (cannot be {46} which clash with R12C8), locked for C8, clean-up: no 4 in R12C8, no 4,8 in R5C9, no 3,7 in R8C9

6. Naked pair {56} in R12C8, locked for C8 and N3, clean-up: no 1,2 in R1C6, no 2,3 in R12C9, no 3,4 in R4C6, no 5,6 in R4C9, no 5,6 in R5C9, no 4 in R8C9, no 8,9 in R9C9

7. Naked pair {17} in R12C9, locked for C9 and N3 -> R3C8 = 2, R4C8 = 1, R5C9 = 3 -> R5C8 = 8, R9C8 = 9, R8C8 = 4 -> R8C9 = 6, R9C9 = 5, R7C9 = 8 -> R6C9 = 4, R34C9 = [92], R2C67 = [98], R1C34 = [98], R67C8 = [73], clean-up: no 5,6 in R1C6, no 5,6 in R3C3, no 3,4 in R3C5, no 4 in R3C6, no 5 in R4C1, no 3 in R4C2, no 6 in R4C3, no 5 in R4C4, no 8 in R4C5, no 7,8 in R4C6, no 5 in R5C12, no 7 in R5C3, no 2,5 in R5C4, no 4,7 in R5C6, no 6 in R6C2, no 1,6 in R6C3, no 5 in R6C4, no 1,6 in R6C5, no 1,3,5,6 in R6C6, no 9 in R6C7, no 2 in R7C1, no 1 in R7C3, no 2,5 in R7C6, no 2 in R7C7, no 1 in R8C1, no 1,3 in R8C34, no 7 in R8C5, no 2,3,5 in R8C6, no 2 in R8C7, no 4,6 in R9C1, no 3 in R9C2, no 6,7 in R9C3, no 6 in R9C4, no 8 in R9C5, no 1,2 in R9C6

8. R9C34 = [87], R9C5 = 4 -> R8C5 = 8, R8C67 = [17], R7C6 = 6, R4C6 = 5 -> R3C7 = 4, R1C67 = [43], R3C56 = [57], R5C6 = 2 -> R4C7 = 9

and the rest is naked singles.

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 4, clean-up: no 6 in R3C3, no 2 in R3C4, no 6 in R4C3, no 5 in R4C7, no 6 in R5C12, no 6 in R5C89, no 9 in R6C3, no 3 in R6C7, no 8 in R7C3, no 1 in R7C4, no 8 in R7C6, no 3 in R7C7, no 6 in R89C5

2. Naked pair {79} in R8C89, locked for R8 and N9, clean-up: no 3,5 in R6C8, no 2 in R6C9, no 1,3 in R8C34, no 2 in R8C67, no 1,3 in R9C1, no 1,3 in R9C5, no 3,5 in R9C6

3. 45 rule on C1234 2 outies R47C5 = 5 = {23} -> R4C5 = 2, R7C5 = 3 -> R3C4 = 4, R7C4 = 2, clean-up: no 5,7 in R1C3, no 8 in R1C7, no 5,7 in R2C3, no 6 in R2C7, no 8 in R3C1, no 6 in R3C2, no 8 in R3C3, no 5,6 in R3C6, no 9 in R3C9, no 6 in R4C1, no 6 in R4C4, no 8 in R4C8, no 7 in R4C9, no 8 in R5C3, no 9 in R6C1, no 9 in R6C4, no 9 in R6C5, no 5 in R6C6, no 9 in R6C8, no 6,7 in R6C9, no 9 in R7C6, no 5 in R7C7, no 6,8 in R8C3, no 8 in R8C5, no 6 in R8C7, no 7,8,9 in R9C3, no 7,8 in R9C5

4. R89C5 = [19], clean-up: no 6 in R12C5, no 7 in R3C6, no 8 in R8C67, no 6 in R9C2, no 2 in R9C3, no 3 in R9C7

5. Naked pair {78} in R12C5, locked for C5 and N2 -> R6C5 = 5 -> R7C6 = 7, R3C5 = 6 -> R3C6 = 2, clean-up: no 1,2,3 in R1C3, no 4,5 in R1C7, no 1,2,3 in R2C3, no 2,3,4,8 in R2C7, no 8 in R3C7, no 4,8 in R4C1, no 6 in R4C2, no 8 in R4C4, no 9 in R4C6, no 4,7 in R4C7, no 5,9 in R4C9, no 8 in R5C4, no 2 in R5C7, no 6 in R6C2, no 8 in R6C3, no 8 in R7C2, no 4 in R7C9, no 4 in R9C3, no 5 in R9C7

6. Naked pair {48} in R9C67, locked for R9, clean-up: no 2,6 in R8C1, no 3 in R8C2, no 3 in R9C3, no 1 in R9C89

7. Naked pair {56} in R9C34, locked for R9, clean-up: no 4 in R8C1, no 2 in R8C2

8. Naked pair {23} in R9C89, locked for R9 and N9 -> R9C1 = 7 -> R8C1 = 3, R9C2 = 1 -> R8C2 = 6, R9C34 = [56], R8C4 = 8, R9C67 = [48], R8C67 = [54], R8C3 = 2, R7C8 = 5 -> R6C8 = 7, R8C89 = [97], R6C4 = 3 -> R7C3 = 9, R7C2 = 4, R67C1 = [48], R6C3 = 6, R6C6 = 1, R7C7 = 6, R67C9 = [81], R6C2 = 9, R6C7 = 2 -> R5C7 = 5, clean-up: no 1,3 in R12C8 (other clean-ups aren’t needed at this stage)

9. Naked pair {26} in R12C8, locked for C8 and N3 -> R9C8 = 3

and the rest is naked singles.

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 4, clean-up: no 7 in R12C5, no 5 in R3C3, no 9 in R3C7, no 2 in R4C3, no 6 in R4C7, no 7 in R5C12, no 6 in R5C89, no 5 in R6C3, no 3 in R6C7, no 5 in R7C3, no 2 in R7C6, no 6 in R7C7, no 8 in R89C5

2. Naked pair {79} in R34C1, locked for C1, clean-up: no 3,5 in R1C2, no 2 in R2C2, no 2 in R5C2

3. Naked pair {89} in R8C34, locked for R8, clean-up: no 1 in R8C89, no 1 in R9C2, no 3 in R9C5

4. 45 rule on C6789 2 outies R36C5 = 3 = {12}, locked for C5, clean-up: no 9 in R12C5, no 1,2,3,5 in R3C6, no 1 in R7C6

5. 45 rule on R1234 2 outies R5C36 = 13 = {58} (only possible combination), R5C3 = 5 -> R4C3 = 1, R5C6 = 8 -> R4C7 = 2, clean-up: no 1,5 in R1C4, no 7 in R1C6, no 1 in R1C7, no 9 in R2C4, no 6 in R2C7, no 3,4 in R3C2, no 7,8 in R3C3, no 6 in R3C4, no 5 in R3C7, no 8,9 in R3C9, no 3,6 in R5C12, no 4 in R6C3, no 5 in R6C7, no 2,6 in R7C1, no 9 in R7C2, no 4 in R7C9, no 4 in R8C6, no 9 in R9C4

6. R5C12 = [29], clean-up: no 3 in R1C1, no 7 in R2C2, no 7 in R5C4, no 1 in R5C89, no 7 in R6C3, no 5 in R7C1, no 5 in R7C2, no 5 in R89C1

7. Naked pair {24} in R1C34, locked for R1, clean-up: no 8 in R1C12, no 5 in R1C6, no 5,7 in R1C7, no 6 in R2C8, no 7,9 in R2C9

8. R1C12 = [57], R34C1 = [97], clean-up: no 4 in R2C12, no 1,3 in R2C4, no 1,3 in R2C8, no 4,6 in R2C9, no 2 in R3C3, no 6 in R3C7, no 5 in R3C8, no 3 in R3C9, no 3 in R4C8

9. Naked pair {37} in R5C89, locked for R5 and N6, clean-up: no 7 in R3C9, no 6 in R6C3, no 4 in R6C7

10. Naked pair {16} in R56C7, locked for C7 and N6, clean-up: no 3 in R1C6, no 4 in R3C9, no 9 in R6C6, no 8 in R7C8, no 5 in R7C9, no 5 in R8C6, no 4,9 in R9C6

11. Naked pair {12} in R3C25, locked for R3 -> R3C9 = 6 -> R4C9 = 4, R3C6 = 7 -> R3C5 = 1, R34C2 = [23], R1C34 = [42], R3C3 = 3 -> R4C4 = 6, R5C4 = 1, R6C3 = 8, R67C2 = [68], R2C2 = 1, R2C3 = 6, R2C1 = 8, R2C4 = 4, R8C34 = [98], R3C4 = 5, R4C5 = 9, R1C6 = 6, R12C5 = [83], R1C7 = 3, R1C89 = [19], R2C67 = [95], R2C89 = [72], R5C89 = [37], R67C9 = [51], R8C9 = 3 -> R8C8 = 6

and the rest is naked singles.

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 6, clean-up: no 4 in R12C5, no 5 in R3C3, no 2 in R3C4, no 4 in R3C6, no 7 in R3C7, no 4 in R4C3, no 5 in R4C7, no 5 in R5C12, no 2 in R5C89, no 7 in R6C3, no 1 in R6C7, no 9 in R7C4, no 2 in R7C7

2. Naked pair {13} in R1C34, locked for R1, clean-up: no 6,8 in R1C12, no 7,9 in R2C5, no 8 in R2C8, no 5 in R2C9

3. Killer pair 1,2 in R7C3 and R89C1, locked for N7, clean-up: no 5,6 in R6C2, no 9 in R9C4

4. R67C9 = {18/27/36} (cannot be {45} which clashes with R12C9), no 4,5

5. 45 rule on C9 3 innies R589C9 = 20 = {389/479/569/578}, no 1,2, clean-up: no 7 in R5C8, no 7,8 in R8C8
5a. 3 of {389} must be in R5C9 -> no 3 in R8C9, clean-up: no 6 in R8C8
5b. 9 of {569} must be in R9C9 -> no 6 in R9C9, clean-up: no 9 in R9C8

6. 45 rule on C1234 2 outies R47C5 = 12 = {39/57}
6a. 3,5 only in R4C5 -> R4C5 = {35}, R7C5 = {79}, clean-up: no 1,6,7 in R3C4, no 7 in R7C4

7. Naked pair {35} in 8(2) cage at R3C4, CPE no 3 in R3C5, no 3,5 in R4C4, clean-up: no 6,8 in R3C3, no 7 in R3C6

8. R12C5 = [28/82/91] (cannot be [73] which clashes with R47C5), no 3,7

9. 1 in N5 only in R6C46, locked for R6, clean-up: no 6 in R7C2, no 8 in R7C9

10. 7 in N7 only in R89C3, locked for C3, clean-up: no 8 in R2C4, no 3 in R45C3, no 4 in R4C4

11. 45 rule in R1234 2 outies R5C36 = 11 = [29/47/83/92], no 1 in R5C3, no 4,5,8 in R5C6, clean-up: no 9 in R4C3, no 3,6,7 in R4C7

12. 45 rule on R6789 2 outies R5C47 = 9 = [45/54/72/81], no 9 in R5C4, no 3 in R5C7, clean-up: no 4 in R6C3, no 4 in R6C7

13. 45 rule on C6789 2 outies R36C5 = 11 = [29/47/74/83], no 1,9 in R3C5, no 5,8 in R6C5, clean-up: no 1,9 in R3C6, no 4,7 in R7C6

14. 8 in C5 only in R123C5, locked for N2, clean-up: no 7 in R1C7, no 2 in R3C5, no 9 in R6C5 (step 13), no 3 in R7C6
[There’s also 8 in N2 only in one of the two 10(2) cages so 2 must be in the same cage but that’s a more advanced technique “locking cages” so I won’t use it here.]

15. 3 in C5 only in R46C5, locked for N5, clean-up: no 8 in R4C7, no 8 in R5C3 (step 11), no 2 in R4C3, no 5 in R7C7

16. X-Wing for 1 in R1C34 and 3(2) cage at R6C4, no other 1 in C34, clean-up: no 9 in R5C3, no 2 in R5C6 (step 11), no 9 in R4C7

17. 1 in C8 only in R58C8
17a. 45 rule on C8 3 innies R589C8 = 12 = {138/147/156}, no 2, clean-up: no 7 in R8C9
[Alternatively there’s the advanced technique “locking cages” 9 only in one of the 11(2) cages in C8 so 2 must be in the same 11(2) cage.]

18. 45 rule on R2 3 innies R2C589 = 10 = {127/145} (cannot be {136/235} because 3,5,6 only in R2C8), no 3,6,8,9, 1 locked for R2, clean-up: no 2 in R1C5, no 2,5,8 in R1C8, no 6 in R2C67
18a. 5,7 only in R2C8 -> R2C8 = {57}, clean-up: no 7,9 in R1C8

19. 3 in R2 only in R2C67 -> R2C67 = {34}, locked for R2, clean-up: no 2 in R1C9, no 9 in R2C12

20. R2C589 (step 18) = {127} (only remaining combination) -> R2C8 = 7 -> R1C8 = 4, R1C9 = 5 -> R2C9 = 1, R2C5 = 2 -> R1C5 = 8, R2C67 = [43], clean-up: no 7 in R1C6, no 6 in R2C12, no 8 in R2C3, no 6 in R3C6, no 9 in R3C7, no 9 in R3C9, no 8,9 in R4C6, no 6,8 in R4C8, no 3,6,7,9 in R4C9, no 4 in R5C7, no 3 in R5C8, no 5 in R6C6, no 8 in R6C9, no 8 in R9C9

[Now it’s cracked. Lots of naked singles and cage sums follow.]
21. R3C56 = [73], R1C34 = [31], R3C4 = 5, R4C5 = 3, R6C4 = 2, R7C3 = 1, R6C5 = 4 -> R7C6 = 8, R7C45 = [69], R7C7 = 7, R6C6 = 1, R2C34 = [69], R1C67 = [69], R4C3 = 8 -> R5C3 = 2, R4C4 = 7 -> R3C3 = 4, R4C6 = 5 -> R3C7 = 8, R5C4 = 8 -> R6C3 = 5, R5C6 = 9 -> R4C7 = 2, R4C8 = 9 -> R3C8 = 2, R34C9 = [64], R8C9 = 8 -> R8C8 = 1

and the rest is naked singles.

Prelims

There would be 40 prelims but since they are all for 2-cell cages I’ll leave you to do them yourself, eliminating 1, 3, 5 or 7 candidates depending whether the cage has 4, 3, 2 or 1 possible combinations.

1. 45 rule on whole grid 1 remaining innie R5C5 = 3, clean-up: no 9 in R3C3, no 6 in R3C4, no 8 in R3C6, no 7 in R4C3, no 7 in R4C7, no 4 in R5C89, no 6 in R6C3, no 7 in R7C3, no 6 in R7C6, no 8 in R7C7, no 4 in R89C5

2. Naked pair {79} in R8C34, locked for R8, clean-up: no 2,4 in R8C89, no 2 in R9C1

3. Naked pair {79} in R9C89, locked for R9 and N9, clean-up: no 2,4 in R6C6, no 2 in R8C1, no 1 in R9C34, no 1,3 in R9C67

4. 45 rule on R1 3 innies R1C589 = 22 = {589/679}, clean-up: no 9 in R2C5, no 6,7,8,9 in R2C8, no 7,8,9 in R2C9

5. 4 in R1 only in R1C67 = {34}, locked for R1, clean-up: no 5 in R1C12, no 5 in R1C34

6. 5 in R1 only in R1C59 -> R1C589 (step 4) = {589} (only remaining combination), clean-up: no 6,7 in R2C5, no 3,4 in R2C8, no 4,5 in R2C9

7. 45 rule in R2 3 innies R2C589 = 12 = {138/156/246} (cannot be {345} because R2C8 only contains 1,2)
7a. 3,6 only in R2C9 -> R2C9 = {36}, clean-up: no 9 in R1C9

8. 1 in R9 only in R9C126
8a. 45 rule on R9 3 innies R9C126 = 11 = {128/146}, no 3,5, clean-up: no 4,6 in R8C1, no 1 in R8C2, no 2 in R8C5

9. R9C34 = {35} (hidden pair in R9)

10. 45 rule on R8 3 innies R8C125 = 11 = {128/146/236/245}
10a. 5 of {245} must be in R8C1 -> no 5 in R8C25, clean-up: no 1 in R9C2, no 2 in R9C5

11. Naked pair {24} in R89C2, locked for C2 and N7, clean-up: no 6 in R1C1, no 8 in R2C1, no 5,7 in R34C2, no 9 in R5C1, no 6,8 in R67C2, no 6,8 in R6C4, no 5 in R8C1

12. Killer pair 1,3 in R34C2 and R67C2, locked for C2, clean-up: no 7 in R1C1, no 9 in R2C1

13. R67C1 = {59} (cannot be {68} which clashes with R89C1), locked for C1, clean-up: no 7 in R2C2, no 4 in R34C1, no 8 in R5C2

14. Naked pair {16} in R89C5, locked for C5 and N8, clean-up: no 3,8 in R3C4, no 5 in R3C6, no 8 in R6C5, no 7 in R7C45, no 3,8 in R7C6, no 1,6 in R8C7, no 4 in R9C7

15. Killer pair 3,5 in R8C67 and R8C89, locked for R8, clean-up: no 6 in R9C1

16. Naked pair {18} in R89C1, locked for C1 and N7 -> R1C1 = 2 -> R1C2 = 6, clean-up: no 4,8 in R2C4, no 7 in R3C1, no 3 in R34C2, no 3,7 in R4C1, no 7 in R5C1, no 5 in R5C2

17. R34C1 = [36], R5C1 = 4 -> R5C2 = 9, R67C1 = [59], R8C34 = [79], R1C34 = [17], R34C2 = [81], R2C12 = [75], R67C2 = [73], R9C34 = [53], R3C3 = 4 -> R4C4 = 8, R2C3 = 9 -> R2C4 = 1, R2C8 = 2 -> R1C8 = 8, R1C9 = 5 -> R2C9 = 6, R1C5 = 9 -> R2C5 = 4, R1C67 = [34], R2C67 = [83], R6C5 = 2, R3C5 = 5, R3C4 = 2, R3C6 = 6, R4C5 = 7, R7C5 = 8, R6C4 = 4, R7C34 = [65], R7C7 = 2, R8C7 = 5 -> R8C6 = 2, R4C67 = [59], R4C8 = 4 -> R3C8 = 9

and the rest is naked singles.