SudokuSolver Forum

1. Starting off

24/3@r3c8 = {789}
4/2@r4c9 = {13}
-> 3/2@r2c8 = [12]
-> {12} in n1 in r3c123
Innies r12 -> r2c16 = +9 = {36} or {45}
Whatever goes in r2c6 (from 3456) must go in n3 in r1 and therefore in r3c123 in n1.

19/3@r3c3 contains at least one of (89).
35/7@r2c6 must contain at least one of (89) - in rows 3 or 4 since r2c6 from (3456).
-> 19/3@r3c3 cannot be {289}
-> r3c12 = {12}


2. Columns 1 & 2

3/2@r8c1 = {12} and r3c12 = {12}
-> r56c3 = {12}

12/4@r3c2 has {12} at r3c2 and r5c3
-> r45c2 = {36} or {45}

Putting r3c1 = 1 -> r24c1 and r45c2 = {3456} which prevents any solution for 12/2@r5c1

-> r3c1 = 2
-> r3c2 = 1, r5c3 = 2, r6c3 = 1, 3/2@r8c1 = [12]
-> 10/3@r2c1 = {235}
-> 12/2@r5c1 = {48}
-> r45c2 = {36}
-> 10/2@r2c1 = [325]
-> r2c6 = 6
-> r3c3 = 6
-> r4c34 = [94]
-> r6c2 = 7
-> r7c12 = [64]

Also r2c23 = +13 = {58} or [94]
-> 20/3@r1c1 from [794] or [7{58}]
-> r19c1 = [79]


3. Middle bit

4s in n4, r4c4, and r7c2 prevent 4 from being in 34/7@r6c3
-> 7 not in 34/7@r6c3 (thanks Andrew)
-> 7 in n7 in r89c3
-> 7 in n8 in r89c6
-> 7 in n9 in r7c789

Innies r1234 (given r3c2 = 1) -> r4c259 = +10
-> r4c259 either [361] or [613]
-> r4c678 = {278}

Innies n5 (given r4c4 = 4) -> r4c6+r6c46 = +17
r6c6 cannot be a 9 (would put 1 or 3 in r6c7)
-> r6c46 cannot be +15 since 7 already in r6 and r6c6 cannot be 6 or 9
-> r4c6 cannot be 2
-> r4c678 = [827]
-> r6c46 = [63] (Innies n5)
-> r4c259 = [613]
-> r5c29 = [31]
Also r6c5 = 2
-> r5c456 = {579}
-> 6 in r5c78


4. Finishing off
r67c7 = +10 can only be [91]
-> 10/3@r9c7 = [325]
-> r78c3 = {35}
Also -> 2 not in 39/7@r8c3
-> 4 not in 39/7@r8c3
-> r9c6 = 4 (HS in r9)
-> r8c6 = 7, r9c3 = 7

Also in n6 two of the remaining cells in 24/4@r5c7 (to go with 6) are from (458) - must be {45}
-> r7c8 = 9, r6c9 = 8
-> r78c9 = [74]
Also r3c89 = [89]
-> r8c78 = [86]
-> r5c78 = [64], r6c8 = 5
-> r1c89 = [36]

Innies r89 -> r8c4 = 9
r3c4567 = {3457}
-> r12c4 = +10 must be [28]
-> 20/3@r1c1 = [758]
-> r2c23 = [94]
-> r1c56 = [91] and r3c5 = 4
Also r9c4 = 1
Also 3 in c5 only in r78
-> r3c4 = 3
-> HS 7 in n2 -> r2c5 = 7
-> r3c67 = [57]
-> r5c456 = [759]

etc., etc.

Prelims

a) R2C89 = {12}
b) R45C9 = {13}
c) R56C1 = {39/48/57}, no 1,2,6
d) R8C12 = {12}
e) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
f) 10(3) cage at R2C1 = {127/136/145/235}, no 8,9
g) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
h) 24(3) cage at R3C8 = {789}
i) 19(3) cage at R6C9 = {289/379/469/478/568}, no 1
j) 10(3) cage at R9C7 = {127/136/145/235}, no 8,9
k) 12(4) cage at R3C2 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1a. Naked pair {13} in R45C9, locked for C9 -> R2C89 = [12]
1b. Naked pair {12} in R8C12, locked for R8 and N7
1c. Naked pair {789} in 24(3) cage at R3C8, CPE no 7,8,9 in R1C8
1d. 1,2 in R1 only in R1C456, locked for N2
1e. 1 in C3 only in R56C3, locked for N4

2. Killer pair 1,2 in 12(4) cage at R3C2 and R8C2, locked for C2
2a. Hidden killer pair 1,2 in 12(4) cage at R3C2 and R8C2 for C2, R8C2 = {12} -> 12(4) cage must contain one of 1,2 in C2 -> R5C3 = {12}

3. 10(3) cage at R2C1 = {136/145/235} (cannot be {127} which clashes with R8C1), no 7

4. 39(7) cage at R8C3 = {1356789/2346789}
4a. 10(3) cage at R9C7 = {136/145/235} (cannot be {127} which clashes with 39(7) cage), no 7
4b. Killer pair 1,2 in 39(7) cage and 10(3) cage, locked for R9

5. 45 rule on R12 2 innies R2C16 = 9 = {36/45}, no 7,8,9

6. 45 rule on R89 2 innies R8C49 = 13 = {49/58/67}, no 3

7. 45 rule on R1 2 outies R2C57 = 1 innie R1C4 + 10
7a. Max R2C57 = 17 -> max R1C4 = 7

8. 45 rule on R8 2 outies R8C35 = 1 innie R9C6 + 4, IOU no 4 in R8C3

9. 24(3) cage + 24(4) cage at R6C7 total 48, max R34567C8 = 35 -> min R3C9 + R5C7 = 13, no 2 in R5C7

10. 45 rule on R1234 2 outies R5C23 = 2 innies R4C59 + 1
10a. Max R5C23 = 8 -> max R4C59 = 7, no 7,8,9 in R4C5

11. 39(7) cage at R8C3 = {1356789/2346789}
11a. 5 of {1356789} must be in R8C35 (both of 1,5 in R9C12345 would clash with 10(3) cage at R9C7), no 5 in R9C12345
11b. 5 in R9 only in R9C6789, CPE no 5 in R8C78

12. 45 rule on C9 3 innies R139C9 = 20 = {479/569/578}
12a. 4 of R9C9 must be in R9C9 -> no 4 in R1C9

13. R139C9 (step 12) = {479/569/578}
13a. R139C9 = {479/578} => R1C9 + R3C89 = {789} or R139C9 = {569}, 9 in R13C9
-> 9 in R1C9 + R3C89 (locking cages), locked for N3

14. 45 rule on R6789 3 outies R5C178 = 1 innie R6C5 + 16
14a. Max R5C178 = 24 -> max R6C5 = 8

15. 45 rule on C1 4 innies R1789C1 = 23 = {1679/2489/2579/2678} (cannot be {1589} which clashes with R56C1, cannot be {3479/3569/3578/4568} because R8C1 only contains one of 1,2), no 3
[Alternatively, which I spotted first, combined cage 10(3) cage at R2C1 + R56C1 must contain 3, locked for C1.]

16. Double hidden killer triple 7,8,9 in 35(7) cage at R2C6, 19(3) cage at R3C3 and 24(3) cage at R3C8 for R34, 24(3) cage contains 7,8,9, 35(7) cage must contain at least two of 7,8,9, 19(3) cage must contain at least one of 7,8,9
-> 35(7) cage must contain two of 7,8,9 = {1245689/1345679/2345678} (cannot be {1235789} which contains all of 7,8,9) and 19(3) cage = {469/568} (cannot be {289/379/478} which contain two of 7,8,9), no 2,3,7
16a. Double hidden killer pair 8,9 in 35(7) cage at R2C6, 19(3) cage at R3C3 and 24(3) cage at R3C8 for R34, 19(3) cage contains one of 8,9, 24(3) cage contains both of 8,9 -> 35(7) cage must contain one of 8,9
-> 35(7) cage = {1345679/2345678} (cannot be {1245689} which contains both of 8,9)
[Alternatively 35(7) cage and 24(3) cage must both contain 7 for R34.]

17. R3C12 = {12} (hidden pair in N1)
17a. R56C3 = {12} (hidden pair in C3), locked for N4

18. Hidden killer triple 7,8,9 in R4C3, R56C1 and R6C2 for N4, R56C1 contains one of 7,8,9 -> R4C3 = {89}, R6C2 = {789}

19. 19(3) cage at R3C3 (step 16) = {469/568}
19a. R4C3 = {89} -> no 8,9 in R3C3 + R4C4
19b. 19(3) cage = {469/568}, CPE no 6 in R3C4

20. 10(3) cage at R2C1 (step 3) = {136/145/235}
20a. 12(4) cage at R3C2 = {1236/1245} -> R45C2 = {36/45}
Consider combinations for R45C2
R45C2 = {36}, locked for N4
or R45C2 = {45}, locked for N4, R4C1 = 6 (hidden single in N4) -> 10(3) cage = {136}, locked for C1
-> R56C1 = {48/57}, no 3,9
20b. R45C2 = {36} (only remaining combination, cannot be {45} which clashes with R56C1), locked for C2 and N4
[Cracked. The rest is fairly straightforward.]

21. 10(3) cage at R2C1 (step 3) = {145/235} (cannot be {136} because 3,6 only in R2C1), no 6, 5 locked for C1, clean-up: no 7 in R56C1
21a. Naked pair {48} in R56C1, locked for C1 and N4 -> R4C1 = 5, R2C1 = 3, R3C1 = 2 (cage sum), R3C2 = 1, R5C3 = 2, R6C3 = 1, R8C12 = [12], R2C6 = 6 (step 5)

22. R4C3 = 9
22a. 24(3) cage at R3C8 = {789}, 9 locked for R3 and N3
22b. 35(7) cage at R2C6 (step 16b) = {2345678} (only remaining combination), no 1, 2 locked for R4

23. 1 in R4 only in R4C59
23a. R5C23 = R4C59 + 1 (step 10)
23b. R5C23 = [32/62] = 5,8 -> R4C59 = 4,7 = {13/16}, no 4
23c. Naked triple {136} in R4C259, locked for R4 -> R4C4 = 4, R3C3 = 6 (cage sum)

24. 20(3) cage at R1C1 = {479/578}, 7 locked for R1 and N1

25. 19(3) cage at R6C9 = {469/478} (cannot be {568} which clashes with R1C9), no 5, 4 locked for C9

26. R6C2 = 7 -> R7C12 = 10 = [64]

[Just spotted, it’s been available since step 21a]
27. R7C7 = 1 (hidden single in R7), R6C67 = 12 = [39] (cannot be [84] which clashes with R6C1) -> R6C6 = 3, R6C7 = 9

28. 10(3) cage at R9C7 (step 4a) = {235} (only remaining combination) -> R9C9 = 5, R9C78 = {23}, locked for R9 and N9
28a. Naked triple {789} in R9C123, locked for R9 and N7
28b. Naked pair {35} in R78C3, locked for C3
28c. Naked pair {35} in R78C3, CPE no 5 in R8C4
28d. Naked triple {146} in R9C456, locked for N8

29. 39(7) cage at R8C3 = {1356789} (only remaining combination), 5 locked for R8

30. R9C6 = 4 (hidden single in R9), R8C678 = 21 = {678} (only remaining combination), locked for R8 -> R8C4 = 9, R8C9 = 4

31. Naked triple {789} in R347C8, locked for C8 -> R8C8 = 6

32. 34(7) cage at R6C3 = {1235689} (only remaining combination) -> R6C4 = 6, R7C3456 = {2358}, locked for R7, 8 also locked for N8 -> R8C67 = [78]
32a. R4C5 = 1, R45C9 = [31], R45C2 = [63], R9C45 = [16]

33. 45 rule on N5 1 remaining innie R4C6 = 8, R4C78 = [27], R7C89 = [97], R3C89 = [89], R1C9 = 6, R6C9 = 8, R56C1 = [84], R6C8 = 5, R6C5 = 2

34. R1C6 = 1 (hidden single in R1) -> 35(7) cage at R1C5 = {1345679} (only remaining combination), no 8, 9 locked for N2

35. 8 in R1 only in 20(3) cage at R1C1 (step 24) = {578} (only remaining combination) -> R1C1 = 7, R1C2 = 5, R1C3 = 8

and the rest is naked singles.

I'll rate my walkthrough for Pinata #38 at Hard 1.5. I used a double hidden killer triple and a short forcing chain.