Prelims
a) R1C78 = {49/58/67}, no 1,2,3
b) R12C9 = {19/28/37/46}, no 5
c) R4C67 = {15/24}
d) R67C4 = {29/38/47/56}, no 1
e) R78C1 = {18/27/36/45}, no 9
f) R9C12 = {89}
g) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3
h) 19(3) cage at R7C5 = {289/379/469/478/568}, no 1
i) 14(4) cage at R8C4 = {1238/1247/1256/1346/2345}, no 9
1. Naked pair {89} in R9C12, locked for R9 and N7, clean-up: no 1 in R78C1
2. 45 rule on N6 2 innies R4C79 = 4 = [13] -> R4C6 = 5, clean-up: no 7 in R12C9, no 6 in R7C4
2a. 45 rule on N3 1 remaining outie R3C6 = 8
2b. 3 in N3 only in R23C7 -> 15(3) cage at R2C7 = {348}, 3,4 locked for C7 and N3, clean-up: no 9 in R1C78, no 6 in R12C9
2c. 2 in C7 only in R789C7, locked for N9
2d. 19(3) cage at R7C5 = {289/379/469/478} (cannot be {568} because 5,8 only in R7C5)
2e. 8 of {289} must be in R7C5 -> no 2 in R7C5
3. 45 rule on N12 2 remaining innies R3C15 = 11 = {29/47/56}, no 1,3
3a. 45 rule on N1 2 innies R1C3 + R3C1 = 9 = {27/45}/[36], no 1,8,9, no 6 in R1C3, clean-up: no 2 in R3C5
4. 45 rule on N8 2 innies R79C4 = 12 = {57}/[84/93], no 1,2,6, no 3,4 in R7C4, clean-up: no 7,8,9 in R6C4
4a. 45 rule on N78 2 outies R6C34 = 10 = {46}/[73/82], R6C3 = {4678}
5. 45 rule on N14 3 innies R156C3 = 15 = {249/258/267/348/357/456} (cannot be {159} because 1,9 only in R5C3, cannot be {168} because no 1,6,8 in R1C3), no 1
6. 21(5) cage at R3C1 = {12459/12468/12567/23457} (cannot be {12369/12378/13458/13467} because 1,3 only in R5C1), CPE no 2 in R6C1
6a. 1,3 only in R5C1 -> R5C1 = {13}
6b. 5 of {12567/23457} must be in R3C1 -> no 7 in R3C1, clean-up: no 2 in R1C3 (step 3a), no 4 in R3C5 (step 3)
6c. R156C3 (step 5) = {258/267/348/357/456} (cannot be {249} because 2,9 only in R5C3), no 9
6d. 2 of {267} must be in R5C3, 7 of {357} must be in R6C3 -> no 7 in R5C3
7. R1C3 + R3C1 (step 3a) = [36/45/54/72], 21(5) cage at R3C1 (step 6) = {12459/12468/12567/23457}
7a. 45 rule on N4 2 innies R56C3 = 1 outie R3C1 + 6
7b. R3C1 = {2456} -> R56C3 = 8,10,11,12 = [37/38/56/57] (cannot be [26/28/46/48/64/84] which clash with 21(5) cage = {12468}, cannot be [47] which clashes with R1C3 + R3C1 = [45]) -> R3C1 = {456}, R5C3 = {35}, R6C3 = {678}, clean-up: no 7 in R1C3 (step 3a), no 9 in R3C5 (step 3), no 6 in R6C4 (step 4a) -> no 5 in R7C4, no 7 in R9C4 (step 4)
7c. 21(5) cage = {12459/12468/12567/23457}, 2 locked for R4 and N4
8. 45 rule on R789 3 innies R7C234 = 15 = {159/168/249/258/348/357} (cannot be {26}7/{46}5 because 14(3) cage at R6C3 cannot be 6{26}/4{46})
8a. 7 of {357} must be in R7C4 -> no 7 in R7C23
9. 45 rule on N5 4 remaining innies R4C45 + R56C4 = 23 = {2489/2678/3479} (cannot be {1679} because R6C4 only contains 2,3,4), no 1
9a. R4C45 + R56C4 = {2489/3479} (cannot be {2678} because R3C5 + R4C45 + R5C34 = 5{678}3 only totals 29), no 6, 4,9 locked for N5
9b. 3 of {3479} must be in R5C4 (30(5) cage at R3C5 cannot be 5{479}5/7{479}3) -> no 3 in R6C4, clean-up: no 7 in R6C3 (step 4a), no 8 in R7C4, no 4 in R9C4 (step 4)
[Cracked. The rest is fairly straightforward.]
10. R156C3 (step 6c) = {348/456} -> R1C3 = 4 -> R3C1 = 5 (step 3a) -> R3C5 = 6 (step 3), clean-up: no 4 in R78C1
10a. 4 in N2 only in 15(3) cage at R1C6 = {249} (only possible combination), locked for N2, 4 also locked for R2 -> R23C7 = [34]
10b. Naked quad {1357} in R1239C4, locked for C4 -> R7C4 = 9, R6C4 = 2, R9C4 = 3 (step 4), R6C3 = 8 (step 4a) -> R5C3 = 3 (hidden 15(3) cage sum), R5C1 = 1
10c. R1C5 = 3 (hidden single in N2)
10d. Naked pair {48} in R45C4, locked for C4 and N4 -> R8C4 = 6, R456C5 = [971], R56C6 = [63], clean-up: no 3 in R7C1
10e. 19(3) cage at R7C5 = {478} (only remaining combination) -> R7C5 = 8, R78C6 = {47}, locked for C6 and N8
10f. Naked pair {29} in R12C6, locked for C6 and N2 -> R2C5 = 4, R9C6 = 1
10g. R35C1 = [51] = 6 -> R4C123 = 15 = {267}, locked for R4 and N4
11. 21(3) cage at R5C7 = {579/678} (cannot be {489} which clashes with R4C8), no 4, 7 locked for N6
12. R6C1 = 4 (hidden single in C1) -> naked pair {59} in R56C2, locked for C2 -> R9C12 = [98]
13. R8C1 = 3 (hidden single in C1) -> R7C1 = 6
13a. R7C8 = 3 (hidden single in N9)
13b. 27(5) cage at R7C7 contains 2,3 = {23589/23679}, no 1,4, 9 locked for N9
13c. 1 in R7 only in R7C23 -> 14(3) cage at R6C3 = [815], R7C79 = [27], R78C6 = [47] -> R89C7 = [96], R8C23 = [42], R9C3 = 7, R4C3 = 6, R89C5 = [52], clean-up: no 7 in R1C8
14. R3C2 = 3 (hidden single in N1)
14a. 2 in R3 only in R3C89, locked for N3, clean-up: no 8 in R12C9
14b. Naked pair {19} in R12C9, locked for C9 and N3 -> R3C89 = [72], R2C8 = 6 (cage sum)
14c. Naked pair {19} in R2C39, locked for R2
14d. 21(3) cage at R5C7 = {579} (only remaining combination) = [579]
and the rest is naked singles.