Prelims
a) R1C89 = {59/68}
b) R2C89 = {49/58/67}, no 1,2,3
c) R4C23 = {16/25/34}, no 7,8,9
d) R6C78 = {15/24}
e) R8C12 = {39/48/57}, no 1,2,6
f) R9C12 = {49/58/67}, no 1,2,3
g) 9(3) cage at R1C3 = {126/135/234}, no 7,8,9
h) 20(3) cage at R3C3 = {389/479/569/578}, no 1,2
h) 20(3) cage at R8C6 = {389/479/569/578}, no 1,2
i) 14(4) cage at R4C6 = {1238/1247/1256/1346/2345}, no 9
1. 45 rule on N3 2 outies R1C6 + R4C7 = 17 = {89}, locked for 35(7) cage at R1C6, CPE no 8 in R4C6
1a. 35(7) cage must contain 5, locked for N3, clean-up: no 9 in R1C89, no 8 in R2C89
1b. Naked pair {68} in R1C89, locked for R1 and N3 -> R1C6 = 9, R4C7 = 8, clean-up: no 7 in R2C89
1c. Naked pair {49} in R2C89, locked for R2 and N3
1d. 9 in C7 only in R789C7, locked for N9
2. 1,2 in N7 only in R7C123 + R8C23, locked for 31(7) cage at R6C3, no 1,2 in R6C3 + R9C4
2a. 45 rule on N7 2 outies R6C3 + R9C4 = 11 = {38/47/56}, no 9
3. 45 rule on C1234 2 outies R89C5 = 12 = {39/48/57}, no 1,2,6
3a. R89C5 = 12 -> R78C4 = 11 = {29/38/47/56}, no 1
3b. 1 in N8 only in R7C56, locked for R7
3c. 1 in N7 only in R89C3, locked for C3, clean-up: no 6 in R4C2
4. 45 rule on C6789 2 outies R12C5 = 6 = [15/42/51]
4a. R12C5 = 6 -> R23C6 = 13 = {58/67}
4b. 20(3) cage at R8C6 = {389/479/578} (cannot be {56}9 which clashes with R23C6), no 6
4c. 9 of {389/479} must be in R9C7 -> no 3,4 in R9C7
4d. 7 of {578} must be in R9C7 (cannot be {78}5 which clashes with R23C6) -> no 5 in R9C7
4e. So 20(3) cage = {38}9/{47}9/{58}7
4f. Killer pair 7,8 in R23C6 and R89C6, locked for C6
4g. R89C5 (step 3) = {39/57} (cannot be {48} which clashes with R89C6), no 4,8
5. 45 rule on N6 2 outies R45C6 = 1 innie R6C9
5a. Min R45C6 = 3 -> min R6C9 = 3
5b. Hidden killer pair 1,2 in R45C6 and R67C6 for C6, min R67C6 = 4 cannot contain both of 1,2 -> R45C6 must contain one or both of 1,2
5c. Max R45C6 = 8 -> no 9 in R6C9
5d. 9 in N6 only in 17(3) cage at R4C8 = {179/269/359}, no 4
5e. 45 rule on N9 2 innies R79C7 = 1 outie R6C9 + 10
5f. Max R79C7 = 16 -> max R6C9 = 6
5g. Min R6C9 = 3 -> min R79C7 = 13, no 2,3 in R7C7
6. 45 rule on N2 2 innies R3C45 = 1 outie R1C3 + 8
6a. Min R1C3 = 2 -> min R3C45 = 10, no 9 in R3C4 -> no 1 in R3C5
7. 45 rule on N1 2 innies R13C3 = 1 outie R4C1 + 9
7a. Max R13C3 = 14 -> max R4C1 = 5
7b. Min R13C3 = 10, max R1C3 = 5 -> min R3C3 = 6 (since cannot be [55])
8. 45 rule on N8 3 innies R7C56 + R9C4 = 1 outie R9C7 + 2 -> max R7C56 + R9C4 = 11, no 9 in R7C5
8a. 9 in N8 only in 23(4) cage at R7C4 = {2579/3479/3569} (cannot be {2489} because 2,4,8 only in R78C4), no 8, clean-up: no 3 in R78C4 (step 3a)
8b. 20(3) cage in R8C6 (step 4e) = {38}9/{47}9/{58}7
8c. Combined 23(4) cage + R89C6 = {2579}{38}/{3479}{58}/{3569}{47}, 3,5,7 locked for N8, clean-up: no 4,6,8 in R6C3 (step 2a)
8d. R9C7 = 7,9 -> R7C56 + R9C4 = 9,11 and must contain 1 in R7C56 = {126/128/146}
8e. 8 of {128} must be in R9C4 -> no 8 in R7C5
9. 14(4) cage at R4C6 = {1247/1256/1346/2345}
9a. 45 rule on N6 3 innies R5C78 + R6C9 = 14 = {167/347/356} (cannot be {257} which clashes with R6C78), no 2
9b. 3 of {347} must be in R6C9 (cannot be {37}4 because 14(4) cage cannot contain both of 3,7), no 4 in R6C9
9c. R79C7 = R6C9 + 10 (step 5e)
9d. R6C9 = {356} -> R79C7 = 13,15,16 = [49/67/69/79], no 5 in R7C7
[I ought to have seen the first part of this step sooner. Step 10 has been available immediately after doing Prelims, but the key step 10a depended on R9C4 being reduced to 4,8 in steps 8c and 10]
10. 6 in N7 only in R7C123 + R8C3 + R9C123, CPE no 6 in R9C4, clean-up: no 5 in R6C3 (step 2a)
10a. R9C4 ‘sees’ all cells in N7 except for R8C12, R9C4 = {48} -> R8C12 must contain at least one of 4,8 = {48}, locked for R8 and N7, clean-up: no 5,9 in R9C12
10b. Naked pair {67} in R9C12, locked for R9 and N7 -> R9C7 = 9, R89C6 = 11 = [38/74]
10c. Naked pair {48} in R9C46, locked for R9 and N8
10d. 45 rule on N9 1 remaining innie R7C7 = 1 outie R6C9 + 1 -> R6C9 + R7C7 = [34/56/67]
10f. 13(3) cage at R6C6 = {157/247/256} (cannot be {346} = [364] which clashes with R6C9 + R7C7 = [34], IOD clash), no 3
10g. 7 of {247} must be in R7C7 -> no 4 in R7C7, clean-up: no 3 in R6C9
10h. R7C7 = {67} -> no 6 in R67C6
10i. 4,5 of {157/247/256} only in R6C6 -> R6C6 = {45}
10j. Killer pair 4,5 in R6C6 and R6C78, locked for R6 -> R6C9 = 6, R1C89 = [68]
10k. R6C9 = 6 -˃ R79C7 = 16 (step 5e) = [79]
10l. R7C8 + R8C7 = [86] (hidden pair in N9) = 14 -˃ R89C8 = 4 = {13}, locked for C8 and N9, clean-up: no 5 in R6C7
10m. Naked pair {25} in R89C9, locked for C9 -> R7C9 = 4, R2C89 = [49], clean-up: no 2 in R6C7
10n. R4C8 = 9 (hidden single in N6) -> R45C9 = 8 = {17}, locked for C9 and N6
10o. R5C8 = 5, R6C78 = [42], R5C7 = [35] = 8 -> R45C6 = 6 = {24}, locked for C6 and N6, R67C6 = [51], R9C46 = [48], R8C6 = 3 (hidden single in C6), R89C8 = [13], R9C359 = [152], R8C9 = 5, R3C89 = [73], R23C6 = [76], R6C3 = 7 (step 2a), clean-up: no 1 in R12C5 (step 4)
10p. R12C5 = [42], R37C5 = [86]
10q. R3C34 = [95] -> R4C4 = 6 (cage sum), clean-up: no 1 in R4C2
10r. Naked pair {13} in R12C4, locked for C4, R1C3 = 5 (cage sum), R78C3 = [32], R4C3 = 4 -> R4C2 = 3
10s. R37C5 = [86] = 14 -> R456C5 = 13 = [193] (only remaining permutation)
10t. R5C34 + R6C4 = [678] = 21 -> R5C2 = 2
10u. R2C3 = 8 -> R123C2 = 11 = [164] (only remaining permutation)
and the rest is naked singles.