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 = 6, placed for both diagonals, clean-up: no 4 in R1C2, no 3 in R12C5, no 3 in R1C8, no 1 in R2C1, no 2 in R2C9, no 4 in 10(2) cage at R3C3, no 5 in 11(2) cage at R3C7, no 5 in R4C3, no 2 in R4C7, no 1 in R5C12, no 4 in R6C3, no 7 in 13(2) cage at R6C6, no 4 in R7C4, no 8 in R7C6, no 1 in R8C9, no 4 in R9C8

2. Naked pair {89} in R89C1, locked for C1 and N7, clean-up: no 1,2 in R1C2, no 4,5 in R34C1, no 3,4 in R89C2

3. Naked pair {57} in R89C2, locked for C2 and N7, clean-up: no 3 in R1C1, no 2 in R2C1, no 4,6 in R34C2, no 2 in R5C1, no 1 in R6C1, no 2 in R67C2, no 1,3 in R8C4

4. Naked pair {67) in R34C1, locked for C1, clean-up: no 3 in R1C2, no 1 in R2C2

5. 1 in C2 only in R67C2 = {16}, locked for C2, clean-up: no 4 in R1C1

6. Naked pair {89} in R5C89, locked for R5 and N6, clean-up: no 1 in R3C9, no 2,3 in R4C3, no 1,2 in R6C3, no 6,7 in R7C8

7. R2C34 = {49/67} (cannot be {58} which clashes with R2C67}, no 5,8

8. 1 in R2 only in R2C589
8a. 45 rule on R2 3 innies R2C589 = 11 = {128/137} (cannot be {146} which clashes with R2C34, other combinations don’t contain 1), no 4,5,6, clean-up: no 4,5 in R1C5, no 4,5 in R1C8, no 2,3 in R1C9

9. 45 rule on R8 3 innies R8C125 = 22 = {589} -> R8C2 = 5, placed for D/, R8C15 = {89}, R9C2 = 7, clean-up: no 3 in R2C9, no 3 in R8C3, no 3 in R8C67, no 2 in R8C89, no 5,8,9 in R9C5, no 4 in R9C67, no 3 in R9C89

10. R8C89 = {34} (hidden pair in R8), locked for N9, clean-up: no 9 in R6C6, no 5 in R6C9, no 8 in R9C6, no 6 in R9C8

11. Naked pair {17} in R12C9, locked for C9 and N3, clean-up: no 6 in R1C6, no 2,8 in R12C8, no 2,8 in R3C9, no 4 in R4C6, no 6 in R4C8, no 2 in R4C9, no 9 in R9C8

12. R1C8 = 6, R2C8 = 3, placed for D/, R6C8 = 7 -> R7C8 = 8, R8C8 = 4, placed for D\, R8C9 = 3, R2C2 = 2, R1C1 = 1, both placed for D\, R1C2 = 9, R2C1 = 5 (both cage sums), R1C9 = 7, placed for D/, R2C9 = 1, R2C5 = 7 (step 8a) -> R1C5 = 2, R9C9 = 9, placed for D\ -> R9C8 = 1, R7C7 = 5 -> R6C6 = 8, placed for D\, R9C1 = 8, placed for D/

and the rest is naked singles without needing to use the diagonals; it’s slightly quicker if they are used.

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 3 in R12C5, no 4 in R3C3, no 5 in R3C7, no 5 in R4C3, no 2 in R4C7, no 1 in R5C12, no 4 in R6C3, no 4 in R7C4, no 8 in R7C6, no 7 in R7C7

2. Naked pair {89} in R89C1, locked for C1 and N7, clean-up: no 1,2 in R1C2, no 4,5 in R34C1, no 3,4 in R89C2

3. Naked pair {57} in R89C2, locked for C2 and N7, clean-up: no 3 in R1C1, no 2 in R2C1, no 4,6 in R34C2, no 2 in R5C1, no 1 in R6C1, no 2 in R67C2, no 1,3 in R8C4

4. Naked pair {67) in R34C1, locked for C1, clean-up: no 3,4 in R1C2, no 1 in R2C2

5. 1 in C2 only in R67C2 = {16}, locked for C2, clean-up: no 4 in R1C1, no 1 in R2C1

6. Naked pair {89} in R5C89, locked for R5 and N6, clean-up: no 1 in R3C9, no 2,3 in R4C3, no 1,2 in R6C3, no 6,7 in R7C8

7. R2C34 = {49/67} (cannot be {58} which clashes with R2C67}, no 5,8

8. 1 in R2 only in R2C589
8a. 45 rule on R2 3 innies R2C589 = 11 = {128/137} (cannot be {146} which clashes with R2C34, other combinations don’t contain 1), no 4,5,6, clean-up: no 4,5 in R1C5, no 3,4,5 in R1C8, no 2,3 in R1C9

9. 45 rule on R8 3 innies R8C125 = 22 = {589} -> R8C2 = 5, R8C15 = {89}, R9C2 = 7, clean-up: no 3 in R8C3, no 3 in R8C67, no 2 in R8C89, no 5,8,9 in R9C5, no 4 in R9C67, no 3 in R9C89

10. R8C89 = {34} (hidden pair in R8), locked for N9, clean-up: no 9 in R6C6, no 5 in R6C9, no 8 in R9C6, no 6 in R9C89

11. R9C67 = {56} (hidden pair in R9)

12. 3 in R1 only in R1C67 = {34}, locked for R1, clean-up: no 9 in R1C34

13. R1C2 = 9 (hidden single in R1) -> R1C1 = 1, clean-up: no 4 in R2C4, no 8 in R2C5, no 8 in R2C8, no 7 in R2C9, no 2 in R34C2, no 1,9 in R4C4, no 5 in R6C1

14. R2C589 (step 8a) = {137} (only remaining combination), locked for R2, clean-up: no 7 in R1C5, no 7 in R1C8, no 6 in R1C9, no 4 in R2C12, no 6 in R2C34

15. R2C12 = [52], R2C34 = [49], R3C4 = 8, R4C5 = 9, R34C2 = [38], R5C12 = [34], R67C1 = [24], R1C5 = 2 -> R2C5 = 7, clean-up: no 2 in R3C7, no 7 in R45C3, no 2,7 in R4C4, no 3 in R4C6, no 5 in R4C7, no 4 in R4C8, no 1,6 in R4C9, no 2,7 in R5C4, no 6,7 in R6C3, no 1 in R6C4, no 1 in R6C7, no 3 in R7C3, no 1,3,6 in R7C4, no 1 in R7C5, no 5 in R7C6, no 6 in R7C9, no 1 in R9C4

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, placed for both diagonals, clean-up: no 2 in R1C2, no 9 in R12C5, no 8 in R2C9, no 5 in 9(2) cage at R3C3, no 5 in R3C4, no 7 in R3C6, no 9 in 13(2) cage at R2C7, no 7 in R4C3, no 6 in R4C7, no 8 in R5C89, no 6 in R6C3, no 9 in 13(2) cage at R6C6, no 2 in R6C7, no 5 in R7C4, no 2 in R7C6, no 8 in R8C1, no 6 in R89C5, no 5 in R8C9, no 5 in R9C2, no 5 in R9C8

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

3. R1C1 = 2, placed for D\, R1C2 = 4, clean-up: no 9 in R2C4, no 6 in R2C8, no 9 in R3C1, no 7 in 9(2) cage at R3C3, no 7,9 in R4C1, no 6 in R4C2, no 4 in R67C1, no 5 in R67C2, no 5 in R8C2, no 7 in R8C9, no 7 in R9C8

4. Naked pair {15} in R67C1, locked for C1, clean-up: no 6 in R34C1, no 9 in R5C2, no 7 in R89C1

5. R5C12 = {68} (cannot be [95] which clashes with R5C89), locked for R5 and N4, clean-up: no 3,5 in R45C3, no 2,4 in R4C7, no 2 in R5C4, no 2,4 in R6C3, no 1,3 in R7C2

6. R2C2 = 9 (hidden single on D\) -> R2C1 = 6, R5C12 = [86], clean-up: no 7 in R1C5, no 7 in R2C3, no 4,7 in R2C4, no 3 in R34C1, no 2 in R4C2, no 3 in R4C4, no 3 in R6C2, no 4 in R8C1, no 3 in R89C2
[Alternatively R2C2 was a hidden single in C2 but I spotted it on the diagonal first.]

7. R34C1 = [74], clean-up: no 4 in R3C6, no 6 in R3C9, no 1 in R4C2, no 2 in R4C5, no 6 in R4C6, no 1 in R4C8, no 3 in R4C9, no 7 in R5C3

8. Naked pair {58} in R2C34, locked for R2 -> R2C5 = 7 -> R1C5 = 6, clean-up: no 8 in R1C67, no 5,7 in R1C9, no 2 in R2C8, no 2,3 in R3C4, no 5 in R3C56, no 3 in R4C5, no 2,3 in R7C4, no 3 in R89C5

9. Naked pair {59} in R1C67, locked for R1 -> R1C8 = 7 -> R2C8 = 1, placed for D/, R1C9 = 8, placed for D/ -> R2C9 = 4, clean-up: no 5 in 13(2) cage at R3C7, no 2 in R3C9, no 2,6,9 in R4C9, no 5 in R5C9, no 6 in 14(2) cage at R6C4, no 1 in R67C9, no 5 in R8C8, no 2 in R8C9, no 1,8 in R9C2

10. R3C7 = 6, R4C6 = 7, placed for D/ -> R89C2 = [27], R67C2 = [18], R67C1 = [51], R6C4 = 9, placed for D/, R7C3 = 5, R89C1 = [93], R9C3 = 6 -> R9C4 = 2, R2C34 = [85], R1C67 = [95], R7C7 = 7 -> R6C6 = 6, placed for D\, clean-up: no 3 in R3C3, no 1 in R4C4 (other clean-ups omitted)

11. R3C3 = 1, R4C4 = 8, both placed for D\

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 9 in R12C5, no 5 in R3C3, no 5 in R3C4, no 7 in R3C6, no 9 in R3C7, no 7 in R4C3, no 6 in R4C7, no 8 in R5C89, no 6 in R6C3, no 2 in R6C7, no 5 in R7C4, no 2 in R7C6, no 9 in R7C7, no 6 in R89C5

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

3. Naked pair {24} in R1C12, locked for R1 and N1, clean-up: no 9 in R2C4, no 6 in R2C8, no 8 in R2C9, no 7,9 in R4C1, no 6 in R4C2, no 5,7 in R4C4

4. 1 in C1 only in R67C1 = {15}, locked for C1, clean-up: no 6 in R34C1, no 9 in R5C2, no 7 in R89C1
[Alternatively R67C1 = {15} (cannot be {24} which clashes with R1C1), ...]

5. R2C34 = [58/85/94] (cannot be {67} which clashes with R2C12), no 6,7

6. 45 rule on C2 3 innies R125C2 = 19 = {289/469/478} (cannot be {568} because R1C2 only contains 2,4), no 5, clean-up: no 9 in R5C1
6a. R5C2 = {68} -> no 6,8 in R2C2, clean-up: no 7,9 in R2C1

7. Naked pair {68} in R25C1, locked for C1, clean-up: no 3 in R34C1, no 4 in R89C1

8. Naked pair {39} in R89C1, locked for C1 and N7 -> R3C1 = 7 -> R4C1 = 4, R1C12 = [24], R2C2 = 9 -> R2C1 = 6, R5C12 = [86], clean-up: no 7 in R1C5, no 4 in R2C4, no 4 in R3C6, no 6 in R3C9, no 1,2 in R4C2, no 3,5 in R4C3, no 2,3 in R4C4, no 2 in R4C5, no 6 in R4C6, no 2 in R4C7, no 1 in R4C8, no 3 in R4C9, no 3,5,7 in R5C3, no 2 in 10(2) cage at R5C4, no 3,5 in R6C2, no 1,5 in R7C2, no 5 in R89C2, no 2,8 in R8C4, no 5 in R9C4

9. Naked pair {29} in R45C3, locked for C3 and N4, clean-up: no 1 in R5C4, no 5 in R6C4, no 7 in R7C2, no 9 in R8C4, no 6 in R9C4

10. Naked quad {1278} in R6789C2, locked for C2

11. Naked pair {58} in R2C34, locked for R2 -> R2C5 = 7 -> R1C5 = 6, clean-up: no 8 in R1C67, no 5,7 in R1C9, no 2 in R2C8, no 2,3 in R3C4, no 5 in R3C56, no 3 in R4C5, no 2,3 in R7C4, no 3 in R89C5

12. Naked pair {59} in R1C67, locked for R1 -> R1C8 = 7 -> R2C8 = 1, R1C9 = 8 -> R2C9 = 4, clean-up: no 2 in R3C9, no 5,9 in R4C6, no 2,6,9 in R4C9, no 5 in R5C9, no 1 in R67C9, no 5 in R8C8, no 2 in R8C9, no 5 in R9C8, no 2 in R9C9

13. Naked pair {23} in R67C9, locked for C9 -> R3C9 = 9, R5C9 = 7 -> R5C8 = 5, R4C9 = 1, R56C7 = [24], R1C67 = [95], R2C67 = [23], R3C7 = 6 -> R4C6 = 7, R45C3 = [29], R67C9 = [32], R34C8 = [26], R4C4 = 8 -> R3C3 = 1, R1C34 = [31], R2C34 = [85], R3C4 = 4, R4C5 = 5, R34C2 = [53], R4C7 = 9, R5C6 = 1, R6C6 = 6 -> R7C7 = 7

and the rest is naked singles.