Prelims
a) R23C5 = {19/28/37/46}, no 5
b) R5C34 = {15/24}
c) R5C67 = {14/23}
d) R78C5 = {29/38/47/56}, no 1
e) 21(3) cage at R2C3 = {489/579/678}, no 1,2,3
f) 11(3) cage at R3C4 = {128/137/146/236/245}, no 9
g) 9(3) cage at R3C6 = {126/135/234}, no 7,8,9
h) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2
i) 19(3) cage at R6C6 = {289/379/469/478/568}, no 1
j) 19(3) cage at R7C7 = {289/379/469/478/568}, no 1
1. R5C34 = {15} (cannot be {24} which clashes with R5C67), locked for R5, clean-up: no 4 in R5C67
1a. Naked pair {23} in R5C67, locked for R5
2. 45 rule on R1 2 outies R2C19 = 7 = {16/25/34}, no 7,8,9
3. 45 rule on R9 2 outies R8C19 = 9 = {18/27/36/45}, no 9
4. 45 rule on C5 2 innies R19C5 = 4 = {13}, locked for C5, clean-up: no 7,9 in R23C5, no 8 in R78C5
4a. 18(3) cage at R9C7 = {189/369/378} (only combinations containing 1 or 3), R9C5 = {13} -> R9C46 = {69/78/89}
5. 45 rule on N1 2(1+1) outies R2C4 + R4C1 = 12, no 1,2,9 in R4C1
6. 45 rule on N3 2(1+1) outies R2C6 + R4C9 = 13 = {49/58/67}, no 1,2,3
7. 45 rule on N7 2(1+1) outies R6C1 + R8C4 = 7 = {16/25/34}
8. 45 rule on N9 2(1+1) outies R6C9 + R8C6 = 10, no 9 in R6C9
9. 45 rule on C1234 2 innies R19C4 = 17 = {89}, locked for C4, clean-up: no 3,4 in R4C1 (step 5)
9a. 21(3) cage at R2C3 = {489/579/678}
9b. 4 of {489} must be in R2C4 -> no 4 in R23C3
10. 45 rule on C6789 2 innies R19C6 = 11 = [29/38/47/56]
11. 14(3) cage at R1C4 = {149/158/239} (cannot be {248} because R1C5 only contains 1,3)
11a. R1C5 = {13} -> no 3 in R1C6, clean-up: no 8 in R9C6 (step 10)
12. 45 rule on C12 2 outies R19C3 = 10 = {19/28/37/45}, no 5
13. 45 rule on C89 2 outies R19C7 = 12 = {39/48/57}, no 1,2,6
14. 45 rule on R1234 3 innies R4C258 = 21 = {489/579/678}, no 1,2,3
15. 1 in C6 only in R34C6, locked for 9(3) cage at R3C6, no 1 in R4C7
15a. 9(3) cage = {126/135}, no 4
16. 1 in N6 only in R6C89, locked for R6, clean-up: no 6 in R8C4 (step 7)
16a. 1 in N4 only in R45C3, locked for C3, clean-up: no 9 in R19C3 (step 12)
16b. 1 in N6 only in R6C89, CPE no 1 in R78C8
17. 1 in C7 only in R23C7, locked for N3, clean-up: no 6 in R2C1 (step 2)
17a. 1 in C7 only in 15(3) cage at R2C6 = {159/168}, no 2,3,4,7, clean-up: no 6,9 in R4C9 (step 6)
17b. 7 in N2 only in R23C4, locked for C4
17c. 7 in N2 only in R23C4, CPE no 7 in R3C3
18. 9 in R4 only in R4C258 (step 14) = {489/579}, no 6
19. 45 rule on N2 R23C46 = 21 contains 7 = {1578/2379/3567} (cannot be {1479/2478} which clash with 14(3) cage at R1C4), no 4, clean-up: no 8 in R4C1 (step 5)
[Can make a further elimination, using interactions with R2C4 + R4C1 and R2C6 + R4C9, but that’s beyond the SS score so I’ll leave it for now.]
20. 21(3) cage at R2C3 = {579/678}, 7 locked for R2
21. Hidden killer pair 8,9 in 20(3) cage at R4C5 and R6C6 for N5, 20(3) cage contains one of 8,9 -> R6C6 = {89}
21a. 7 in N5 only in 20(3) cage, locked for C5, clean-up: no 4 in R78C5
21b. 20(3) cage = {479/578}, no 6
22. 18(3) cage at R9C7 (step 4a) = {189/378} (cannot be {369} which clashes with R78C5), no 6 -> R9C4 = 8, R1C4 = 9, clean-up: no 2 in R1C3 (step 12), no 5 in R1C6 (step 10), no 4 in R4C9 (step 6), no 2 in R6C9 (step 8)
22a. Killer pair 2,4 in R1C6 and R23C5, locked for N2
23. 15(3) cage at R2C6 (step 17a) = {159/168}
23a. 5 of {159} must be in R2C6 -> no 5 in R23C7
24. Hidden killer pair 4,7 in R19C6 and R78C6 for C6, R19C6 contains both or neither of 4,7 -> R78C6 must contain both or neither of 4,7
24a. 45 rule on N8 4 innies R78C46 = 16 = {1249/1456/2347} (cannot be {1267/2356} which clash with R78C5, cannot be {1357} which clashes with R9C5)
24b. 4,7 of {2347} must be in R78C6 -> no 3 in R78C6, clean-up: no 7 in R6C9 (step 8)
24c. 5,6 of {1456} must be in R78C6 -> no 5,6 in R78C4, clean-up: no 2 in R6C1 (step 7)
24d. 1,4 of {1249} must be in R78C4
24e. R78C4 = {14/23}
25. 11(3) cage at R3C4 = {137/146/236/245} (cannot be {128} because R34C4 = [12] clashes with R78C4), no 8
25a. 5 of {245} must be in R34C4 -> no 5 in R4C34
25b. 7 of {137} must be in R3C4 (R34C4 cannot be {13} which clashes with R78C4), no 7 in R4C3
26. 1,2,3 in R4 only in R4C3467, R3C46 must contain one of 1,3
26a. Combined cage 11(3) cage at R3C4 and 9(3) cage at R3C6 = 20 must contain 1,2,3 and another of 1,3 = {123167/123356} (cannot be {123347} because 11(3) cage cannot contain both of 4,7), no 4
26b. 11(3) cage at R3C4 (step 25) = {137/236}, no 5
26c. 7 of {137} must be in R3C4 -> no 1 in R3C4
27. 4 in R4 only in R4C258 (step 18) = {489} (only remaining combination), locked for R4, clean-up: no 5 in R2C6 (step 6)
27a. Killer pair 6,8 in R23C5 and R2C6, locked for N2, clean-up: no 6 in R4C1 (step 5)
27b. Naked pair {57} in R4C19, locked for R4
28. 15(3) cage at R2C6 (step 17a) = {168} (only remaining combination), CPE no 6,8 in R2C89, clean-up: no 1 in R2C1 (step 2)
29. 9(3) cage at R3C6 (step 15a) = {126/135}
29a. 3 of {135} must be in R4C7 -> no 3 in R34C6
29b. R5C6 = 3 (hidden single in C6), R5C7 = 2
29c. R4C7 = {36} -> no 6 in R4C6
30. 11(3) cage at R3C4 (step 26b) = {137/236}
30a. 1 of {137} must be in R4C4 -> no 1 in R4C3
30b. 1 in R4 only in R4C46, locked for R4 -> R5C4 = 5, R5C3 = 1, R2C4 = 7, R3C4 = 3, R1C5 = 1, R1C6 = 4 (cage sum), R9C5 = 3, R9C6 = 7 (cage sum), clean-up: no 3,7 in R1C3 (step 12), no 5 in R1C7 (step 13), no 6 in R23C5, no 2 in R78C4 (step 24e), no 6 in R9C3 (step 12), no 4,5 in R6C1 (step 7), no 3,6 in R6C9 (step 8)
31. R3C6 = 5 -> R4C67 = 4 = [13], clean-up: no 5 in R6C9 (step 8), no 9 in R9C7 (step 13)
32. Naked pair {28} in R23C5, locked for C5 and N2 -> R2C6 = 6, R4C9 = 7 (step 6), R4C1 = 5, clean-up: no 2 in R2C9 (step 2), no 4 in R6C9 (step 8), no 9 in R78C5
33. Naked pair {18} in R23C7, locked for C7 and N3 -> R1C7 = 7, R9C7 = 5 (step 13)
34. 45 rule on N6 2 remaining innies R6C79 = 10 = [91], R67C6 = [82], R8C6 = 9
34a. Naked pair {46} in R78C7, locked for N9
35. R9C8 = 1 (hidden single in N9)
35a. R9C78 = [51] = 6 -> R89C9 = 11 = [29] (cannot be {38} because 3,8 only in R8C9), R8C1 = 7 (step 3)
35b. Naked triple {246} in R9C123, locked for N7
36. R6C3 = 7 (hidden single in C3), R67C4 = 6 = [24], R4C34 = [26], R8C4 = 1, R6C1 = 6 (step 7), R78C7 = [64], R78C5 = [56], 20(3) cage at R4C5 = [974], R6C28 = [35], R9C13 = [24], R9C2 = 6, R1C3 = 6 (step 12)
37. R8C4 = 1 -> R78C3 = 11 = {38} (only remaining combination), locked for C3 and N7 -> R23C3 = [59], R8C2 = 5
38. 8 in R1 only in R1C12, locked for N1
38a. 19(4) cage at R1C1 contains 6,8 = {2368} (only remaining combination) -> R1C2 = 2, R12C1 = [83]
and the rest is naked singles.