Prelims
a) R1C12 = {69/78}
b) R1C89 = {16/25/34}, no 7,8,9
c) R23C9 = {39/48/57}, no 1,2,6
d) R78C1 = {16/25/34}, no 7,8,9
e) R9C12 = {29/38/47/56}, no 1
f) R9C89 = {69/78}
g) 22(3) cage at R3C4 = {589/679}
h) 21(3) cage at R6C5 = {489/579/678}, no 1,2,3
i) 14(4) cage at R8C7 = {1238/1247/1256/1346/2345}, no 9
j) 16(5) cage at R3C8 = {12346}
k) 17(5) cage at R5C3 = {12347/12356}
Steps resulting from Prelims
1a. 22(3) cage at R3C4 = {589/679}, CPE no 9 in R12C5
1b. 16(5) cage at R3C8 = {12346}, CPE no 1,2,3,4,6 in R6C8
1c. 17(5) cage at R5C3 = {12347/12356}, 1,2,3 locked for R5
1d. Killer pair 4,6 in 17(5) cage and R5C8, locked for R5
2. 45 rule on N1 3 innies R123C3 = 8 = {125/134}, 1 locked for C3 and N1
3. 45 rule on R6789 2 outies R5C29 = 15 = {78} (only possible combination), locked for R5
3a. 17(5) cage at R5C3 = {12356} (only remaining combination), locked for R5 -> R5C1 = 9, R5C8 = 4, clean-up: no 6 in R1C2, no 3 in R1C9, no 2 in R9C2
4. 9 in C3 only in R789C3, locked for N7 and 36(7) cage at R6C4, no 9 in R679C4, clean-up: no 2 in R9C1
5. 45 rule on R123 2 outies R4C56 = 2 innies R3C38 + 13
5a. Max R4C56 = 17 -> max R3C38 = 4 -> R3C38 = {12/13}, 1 locked for R3
5b. Min R3C38 = 3 -> min R4C56 = 16 -> R4C45 = {79/89}, 9 locked for N5
5c. 16(5) cage at R3C8 = {12346}, 6 locked for R4 and N6
5d. 7,8,9 in N6 only in R6C789, locked for 35(6) cage at R5C9, no 7,8 in R6C6, no 7,8,9 in R7C7
5e. 5 in N6 only in R5C7 + R6C789, CPE no 5 in R7C7
6. Hidden killer triple 7,8,9 in 36(7) cage at R1C6 and R23C9 for N3, R23C9 contains one of 7,8,9 -> 36(7) cage must contain two of 7,8,9 in N3
6a. 36(7) cage also contains one of 7,8,9 in R4C6 -> contains all three of 7,8,9 in N3 + R4C6, no 7,8,9 in R13C6
6b. 36(7) cage = {1236789/1245789}, CPE no 1 in R1C89, clean-up: no 6 in R1C89
6c. 6 in N3 only in R123C7 + R2C8, locked for 36(7) cage, no 6 in R13C6
6d. 36(7) cage contains 6 = {1236789} (only remaining combination), no 4,5
6e. Naked triple {123} in R3C368, locked for R3, clean-up: no 9 in R2C9
6f. 4 in N3 only in R123C9, locked for C9
7. Killer triple 1,2,3 in 36(7) cage at R1C6 (must contain one of 1,2,3 in N3), R1C89 and R3C8, locked for N3, clean-up: no 9 in R3C9
7a. 9 in N3 only in R123C7 + R2C8, locked for 36(7) cage, no 9 in R4C6
7b. R4C5 = 9 (hidden single in R4), R3C45 = {58/67}
8. Killer pair 7,8 in R23C9 and R5C9, locked for C9, clean-up: no 7,8 in R9C8
8a. Naked pair {69} in R9C89, locked for R9 and N9, clean-up: no 5 in R9C12
8b. R78C1 = {16/25} (cannot be {34} which clashes with R9C12), no 3,4 in R78C1
9. R6C9 = 9 (hidden single in C9), R9C89 = [96]
10. 17(4) cage at R7C8 = {1358/2357}, 3,5 locked for N9
10a. 5 in C7 only in R56C7, locked for N6
10b. Naked pair {78} in R5C9 + R6C8, locked for N6
11. 7,8,9 in N6 only in 35(6) cage at R5C9 = {146789/236789/245789}
11a. 6 of {146789/236789} must be in R6C6 -> no 1,3 in R6C6
11b. 4,6 of {146789} must be in R6C6 + R7C7 -> no 1 in R7C7
12. 45 rule on N9 2 outies R9C56 = 1 innie R7C7 + 1
12a. R7C7 = {24} -> R9C56 = 3,5 = {12/14/23}, no 5,7,8 in R9C56
13. 5 in R9 only in R9C34, locked for 36(7) cage at R6C4, no 5 in R6C4 + R7C34 + R8C23
14. 17(4) cage at R1C3 = {1259/1349/1358/1457/2348/2357/2456} (cannot be {1268/1367} which clash with R1C12)
14a. Hidden killer quad 6,7,8,9 in R1C12, 17(4) cage and R1C7 for R1, R1C12 = {6789}, 17(4) cage contains one of 8,9 -> R1C7 = {6789}
14b. 36(7) cage at R1C6 (step 6d) = {1236789}, CPE no 1,2,3 in 17(3) cage at R2C4
14c. 1 in N2 only in R1C456, locked for R1
15. 17(3) cage at R2C4 = {458/467}, no 9, 4 locked for R2 and N2, clean-up: no 8 in R3C9
16. R1C4 = 9 (hidden single in N2), clean-up: no 6 in R1C1
16a. Naked pair {78} in R1C12, locked for R1 and N1 -> R1C7 = 6
16b. R1C56 + R3C6 = {123} (hidden triple in N2)
16c. Killer triple 1,2,3 in R1C56 and R1C89, locked for R1
16d. R123C3 = 8 = {125/134}
16e. R1C3 = {45} -> no 5 in R2C3
16f. R4C8 = 6 (hidden single in N6)
17. Naked pair {78} in R15C2, locked for C2, clean-up: no 3,4 in R9C1
17a. Naked pair {78} in R19C1, locked for C1
18. 6,9 in N1 only in 22(4) cage at R2C1 = {2569/3469}
18a. [25] of {2569} must be in R23C1 (cannot be [26] which clashes with R78C1), no 5 in R2C1, no 2,5 in R2C2, no 5 in R3C2
19. 45 rule on R9 2 innies R9C34 = 1 outie R8C7 + 5
19a. 5 in R9 only in R9C34 -> R8C7 must be the same as the other number in R9C34, no 3 in R9C34
20. 22(4) cage at R2C1 (step 18) = {2569/3469}
20a. Consider combinations for R3C45 (step 7b) = {58/67}
R3C45 = {58}, locked for R3, no 5 in R3C1
or R3C45 = {67}, locked for R3 and N2 => 17(3) cage at R2C4 = {458}, locked for R2 => R2C9 = 7, R3C9 = 5, no 5 in R3C1
-> 22(4) cage = {3469}, locked for N1
21. R1C3 = 5, clean-up: no 2 in R1C89
21a. R1C89 = [34], clean-up: no 8 in R2C9
21b. Naked pair {57} in R23C9, locked for C9 and N3 -> R5C9 = 8, R6C8 = 7, R5C2 = 7, R1C12 = [78], R9C1 = 8, R9C2 = 3
21c. R2C1 = 3 (hidden single in R2)
21d. R3C6 = 3 (hidden single in R3)
21e. R9C4 = 5 (hidden single in R9), clean-up: no 8 in R3C5 (step 7b)
22. 17(4) cage at R7C8 (step 10) = {1358} (only remaining combination), locked for N9
22a. Naked pair {13} in R78C9, locked for C9 and 17(4) cage
22b. Naked triple {247} in R789C7, locked for C7
22c. R4C9 = 2, R3C8 = 1, R4C7 = 3, R23C3 = [12], R1C56 = [21]
22d. Naked pair {89} in R23C7, locked for 36(7) cage at R1C6 -> R2C8 = 2, R4C6 = 7
23. R4C1234 = {1458}, 5 locked for N4
23a. R9C5 = 1 (hidden single in R9)
23b. 2 in R9 only in R9C67, locked for 14(4) cage at R8C7, no 2 in R8C7
24. R5C2 = 7, 2 in N4 only in R6C12 -> 21(5) cage at R5C2 = {12567/23457} (cannot be {12378} because 3,8 only in R6C3), no 8 -> R7C2 = 5, R78C8 = [85], clean-up: no 2 in R78C1
24a. Naked pair {16} in R78C1, locked for C1 and N7 -> R3C1 = 4, R4C1 = 5, R8C2 = 2
24b. Naked triple {479} in R789C3, locked for C3, N7 and 36(7) cage at R6C6, no 4,7 in R67C4 -> R4C3 = 8, R6C1 = 2
24c. Naked pair {36} in R56C3, locked for N4
25. R7C7 = 2 (hidden single in R7)
25a. R9C6 = 2 (hidden single in R9)
26. R5C9 + R6C89 + R7C7 = [8792] = 26 -> R6C67 = 9 = [45], R6C2 = 1, R6C3 = 6 (cage sum)
27. R6C56 = [38], R7C4 = 6, R7C6 = 9, R7C5 = 4 (cage sum), 18(3) cage at R8C4 = [738], R3C4 = 8, R3C5 = 5 (cage sum)
and the rest is naked singles.