Prelims
a) R23C6 = {59/68}
b) R78C4 = {29/38/47/56}, no 1
c) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
d) 8(3) cage at R3C3 = {125/134}
e) 21(3) cage at R4C5 = {489/579/678}, no 1,2,3
f) 10(3) cage at R4C6 = {127/136/145/235}, no 8,9
g) 7(3) cage at R7C8 = {124}
h) 10(3) cage at R8C5 = {127/136/145/235}, no 8,9
1a. 45 rule on NR1C1 2 innies R13C3 = 12 = [75/84/93]
1b. 8(3) cage at R3C3 = {125/134}, 1 locked for R3 and NR3C4
1c. Law of Leftovers (LoL) for R123 10(3) cage at R4C6 must contain the same digits as R3C456 -> R3C6 = {56}, 10(3) cage at R4C6 must contain 1 and one of 5,6 = {136/145}, no 2,7, 1 locked for R4 and NR1C9
1d. No 2 in 10(3) cage -> no 2 in R3C45 -> 8(3) cage at R3C3 = {134}, locked for R3
1e. R3C3 = {34} -> R1C3 = {89}
1f. R3C6 = {56} -> R2C6 = {89}
2a. 2 in NR3C4 only in R7C456, locked for R7
2b. Naked pair {14} in R7C89, locked for R7 and NR7C7 -> R8C9 = 2
2c. 45 rule on NR7C7 2 innies R79C7 = 13 = {58/67}, no 3,9
2d. Min R9C7 = 5 -> max R89C6 = 9, no 9 in R89C6
2e. LoL for R789, 14(3) cage at R6C2 must contain the same digits as R7C456 -> R7C456 = 14(3)
2f. R7C456 contains 2 = {239/257}, no 6,8
2g. R7C456 = {239/257} -> 14(3) cage at R6C2 = {239/257}, no 1,4,6,8, 2 locked for R6 and NR6C2
2h. 2 in R4 only in R4C1234, locked for NR4C1
2i. R7C456 = 14(3), 18(3) cage at R7C5 -> R7C7 4 more than R7C4 -> R7C4 = {23}, R7C7 = {67} -> R8C4 = {89}, R9C7 = {67}
2j. Naked pair {67} in R79C7, locked for C7 and NR7C7
2k. Min R9C7 = 6 -> max R89C6 = 8, no 8 in R89C6
2l. 8 in NR3C4 only in 21(3) cage at R4C5, locked for C5
2m. 21(3) cage = {489/678}, no 5
3a. 45 rule on NR1C9 2 innies R3C78 = 15 = [87/96]
3b. R3C78 = 15 -> R1C78 + R2C7 = 12
3c. R2C8 = 2 (hidden single in NR1C9)
3d. 2 in R3 only in 16(3) cage at R2C1 = {259/268}, no 1,3,4,7
3e. 7 in R3 only in R3C89, locked for NR1C9
4a. 45 rule on NR6C2 2 innies R7C23 = 12 = {39/57}, no 6,8
4b. R7C23 = 12 -> R8C3 + R9C23 = 19 = {289/469/478/568} (cannot be {379} which clashes with R7C23), no 1,3
4c. LoL for C123 3 outies R456C4 must contain the same digits as 3 innies R8C3 + R9C23 -> no 1,3 in R456C4
4d. R7C1 = 8 (hidden single in R7)
4e. R8C12 + R9C1 = {146} (hidden triple in NR6C2)
4f. R7C7 = 6 (hidden single in R7) -> R7C56 = 12 = {39/57}, no 2
4g. R7C4 = 2 (hidden single in R7) -> R8C4 = 9
4h. R6C4 = {57} -> 14(3) cage at R6C2 (step 2g) = {257}, 5,7 locked for R6 and NR6C2
4i. Naked pair {39} in R7C23, locked for R7
4j. Naked pair {57} in R6C56, locked for NR3C4 -> R3C6 = 6, R2C6 = 8, R3C8 = 7 -> R3C7 = 8 (step 3a)
4k. 21(3) cage at R4C5 = {489}, 4,9 locked for C5 and NR3C3
4l. Naked pair {13} in R3C45, locked for R3 -> R3C3 = 4, R1C3 = 8 (step 1a)
4m. LoL for R123 (step 1c) R3C456 = {13}6 -> 10(3) cage at R4C6 = {136} -> R4C8 = 6, R4C67 = {13}, locked for R4 and NR1C9
4n. Naked triple {459} in R123C9, locked for C9
5a. 16(3) cage at R2C1 (step 3d) = {259} (only remaining combination), locked for NR1C1
5b. R1C3 = 8 -> R12C4 = 11 = {47/56}, no 3
5c. Killer pair 5,7 in R12C4 and R6C4, locked for C4
5d. 8 in C4 only in R45C4, locked for NR4C1
5e. R9C2 = 8 (hidden single in C2), R8C3 + R9C23 = 19 (step 4b) -> R89C3 = 11 = {56}, locked for C3 and NR8C3
5f. LoL for C123 (step 4c) R8C3 + R9C23 exactly equals R456C4 -> R456C4 = [865]
5g. R45C4 = [86] = 14 -> R4C3 + R5C23 = 6 = {123} -> R4C3 = 2, R5C23 = {13}, locked for R5 and NR4C1
5h. R6C23 = [27]
5i. R7C3 = 9 (hidden single in C3) -> R7C2 = 3, R5C23 = [13], R2C3 = 1
5j. Naked pair {47} in R12C4, locked for C4 and NR1C4
5k. R9C7 = 7 -> R89C6 = 7 = {34}, locked for C6 and NR8C3
and the rest is naked singles.