Prelims
a) R1C34 = {89}
b) R5C23 = {18/27/36/45}, no 9
c) R5C78 = {16/25/34}, no 7,8,9
d) R9C67 = {29/38/47/56}, no 1
e) 9(3) cage at R1C1 = {126/135/234}, no 7,8,9
f) 10(3) cage at R8C1 = {127/136/145/235}, no 8,9
g) 28(4) cage at R2C8 = {4789/5689}, no 1,2,3
h) 16(5) cage at R1C6 = {12346}
i) 28(7) cage at R1C5 = {1234567}, no 8,9
1. Naked pair {89} in R1C34, locked for R1
1a. 8,9 in N3 only in R2C89 + R3C9, locked for 28(4) cage at R2C8, no 8,9 in R4C9
1b. 8,9 in N2 only in R123C4, locked for C4
2. 45 rule on N3 1 outie R4C9 = 3 innies R2C7 + R3C78 + 1, min R2C7 + R3C78 = 6, max R4C9 = 7 -> R2C7 + R3C78 = 6 = {123}, locked for N3 and 16(5) cage at R1C6, R4C9 = 7
2a. R4C9 = 7 -> 28(4) cage at R2C8 = {4789}, 4 locked for N3
2b. Naked triple {567} in 18(3) cage at R1C7, locked for R1 -> R12C6 = [46], clean-up: no 5,7 in R9C7
3. 28(7) cage at R1C5 = {1234567}, 7 locked for N2, R4C78 = {46}, locked for R4 and N6, clean-up: no 1,3 in R5C78
3a. Naked pair {25} in R5C78, locked for R5 and N6, clean-up: no 4,7 in R5C23
4. 9(3) cage at R1C1 = {135/234}
4a. 4,5 only in R2C1 -> R2C1 = {45}
4b. 3 only in R1C12, locked for R1 and N1
5. 16(3) cage at R5C9 = {169/358} (cannot be {259/268} because 2,5,6 only in R7C9, cannot be {349} which clashes with 28(4) cage at R2C8, ALS block)
5a. 5,6 only in R7C9 -> R7C9 = {56}
5b. Naked pair {56} in R17C9, locked for C9
6. 2 in C9 only in R89C9, locked for N9, clean-up: no 9 in R9C6
6a. 10(3) cage at R8C9 contains 2 = {127/235}, no 4,6
6b. 5,7 in R9C8 only in R9C8 -> R9C8 = {57}
6c. 4 in C9 only in R23C9, locked for N3
7. 45 rule on N5 2 innies R4C6 + R6C4 = 5 = [14]/{23}
7a. 28(7) cage at R1C5 = {1234567}, 5 locked for N2
8. 45 rule on N69 (using R4C78 = {46} = 10) 3 outies R789C6 = 12 = {129/138/237}, no 5, clean-up: no 6 in R9C7
8a. Killer triple 1,2,3 in R4C6 and R789C6, locked for C6
9. 28(7) cage at R1C5 = {1234567}, CPE no 1,2,3 in R456C5
10. 45 rule on R1234 2 innies R4C45 = 1 outie R5C1 + 7
10a. Max R4C45 = 14 -> max R5C1 = 7
11. 45 rule on R6789 2 innies R6C56 = 1 outie R5C9 + 4
11a. Min R6C56 = 9 -> no 1,3 in R5C9
11b. 16(3) cage at R5C9 (step 5) = {169/358}
11c. 1,3 only in R6C9 -> R6C9 = {13}
11d. 1,3 in N6 only in R6C789, locked for R6, clean-up: no 2 in R4C6 (step 7)
11e. 28(7) cage at R1C5 = {1234567}, 2 locked for C5 and N2
12. 2 in C6 only in R789C6, locked for N8
12a. R789C6 (step 8) = {129/237}, no 8, clean-up: no 3 in R9C7
12b. 8 in N8 only in R789C5, locked for C5 and 38(7) cage at R6C2, no 8 in R6C23
12c. 38(7) cage = {1256789/1346789/2345789}, CPE no 9 in R6C5
13. Hidden killer pair 1,3 in R123C5 + R4C6 for 28(7) cage at R1C5, R4C6 = {13} -> R123C5 must contain one of 1,3
13a. Hidden killer pair 1,3 in R123C5 and R789C5 for C5, R123C5 contains one of 1,3 -> R789C5 must contain one of 1,3
13b. Killer pair 1,3 in R789C5 and R789C6, locked for N8
13c. 38(7) cage at R6C2 = {1256789/2345789} (cannot be {1346789} because R789C5 only contains one of 1,3), 2 locked for R6
14. 45 rule on N7 3(1+2) outies R6C1 + R89C4 = 15
14a. Min R89C4 = 9 -> max R6C1 = 6
14b. R6C1 + R89C4 = 4{47}/4{56}/5{46}/6{45}, CPE no 4 in R6C4
14c. R6C4 = 2 -> R4C6 = 3 (step 7)
15. R789C6 (step 12a) = {129} (only remaining combination) -> R9C6 = 2, R78C6 = {19}, locked for C6 and N8, R9C7 = 9
16. R8C9 = 2 (hidden single in N9)
16a. 45 rule on R9 2 remaining innies R9C45 = 12 = [48] (cannot be {57} which clashes with R9C8)
17. 38(7) cage at R6C2 (step 13c) = {2345789} (only remaining combination) -> R6C23 = {49}, locked for R6 and N4
18. R5C59 = [49] (hidden pair in R5)
18a. R5C9 = 9 -> R67C9 = 7 = [16], R9C9 = 3, R9C8 = 5 (cage sum)
19. R6C1 + R89C4 = 15 (step 14)
19a. R8C4 = 6 (hidden single in N8), R9C4 = 4 -> R6C1 = 5, R2C1 = 4 -> R1C12 = 5 = {23}, locked for R1 and N1, R1C5 = 1
20. R5C1 = 7 (hidden single in N4) -> R34C1 = 9 = {18} (only possible combination), locked for C1, R9C1 = 6
21. Naked pair {17} in R9C23, locked for N7
21a. R6C1 = 5 -> 21(4) cage at R6C1 = {3459} (only possible combination), R8C2 = 4, R78C1 = {39}, locked for C1 and N7, R1C12 = [23], R5C23 = [63] (hidden pair in N4), R6C23 = [94]
22. R3C34 = [69] (hidden pair in R3), R4C3 = 1 (cage sum)
and the rest is naked singles.