Prelims
a) R23C4 = {39/48/57}, no 1,2,6
b) R34C1 = {19/28/37/46}, no 5
c) R34C2 = {16/25/34}, no 7,8,9
d) R89C9 = {19/28/37/46}, no 5
e) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
f) 10(3) cage at R1C4 = {127/136/145/235}, no 8,9
g) 21(3) cage at R5C9 = {489/579/678}, no 1,2,3
h) 11(3) cage at R7C8 = {128/137/146/236/245}, no 9
i) 18(5) cage at R1C8 = {12348/12357/12456}, no 9
1a. 18(5) cage at R1C8 = {12348/12357/12456}, 1,2 locked for N3
1b. 45 rule on N1 2 innies R3C12 = 8 = [26/35/62/71] -> R4C1 = {3478}, R4C2 = {1256}
1c. 45 rule on R789 3 innies R7C359 = 22 = {589/679}, 9 locked for R7
1d. 45 rule on N14 2 outies R5C4 + R7C3 = 12 = [39/48/57/75]
1e. 45 rule on C9 4 innies R1234C9 = 14 = {1238/1256/1346/2345} (cannot be {1247} which clashes with R89C9), no 7,9
1f. 45 rule on C9 1 outie R4C8 = 1 innie R1C9 + 6 -> R1C9 = {123}, R4C8 = {789}
1g. 45 rule on R1 3 innies R1C789 = 16 = {169/178/259/268/349/358/367} (cannot be {457} because R1C9 only contains 1,2,3)
1h. R1C9 = {123} -> no 1,2,3 in R1C78
1i. 9 of {349} must be in R1C7 -> no 4 in R1C7
1j. Min R23C9 + R4C8 = 14 -> max R4C9 = 6
1k. 45 rule on C89 2 outies R35C7 = 3 = {12}, locked for C7
1l. 13(3) cage at R5C7 = {139/148/157/238/247/256} (cannot be {346} because R5C7 only contains 1,2)
1m. R5C7 = {12} -> no 1,2 in R56C8
1n. R4C9 + R5C7 = {12} (hidden pair in N6)
1o. 45 rule on N9 1 innie R7C9 = 1 outie R7C6 + 7 -> R7C6 = {12}, R7C9 = {89}
2a. 9 in N3 only in R12C7, locked for C7 and 31(5) cage at R1C7
2b. 9 in N9 only in R789C9, locked for C9
2c. 45 rule on N23 2 outies R4C89 = 1 innie R3C6 + 1
2d. Min R4C89 = 8 -> min R3C6 = 7
2e. 20(4) cage at R2C9 = {1469/1568/2378/2459/2567} (cannot be {1289} because 1,2 only in R4C9, cannot be {1379} because 7,9 only in R4C8, cannot be {1478} which clashes with R1C9 + R4C8 = [17] , cannot be {2369} which clashes with R1C9 + R4C8 = [39], cannot be {2468} which clashes with R1C9 + R4C8 = [28], cannot be {3458/3467} because R4C9 only contains 1,2)
2f. 20(4) cage = {1469/2459/2567} (cannot be {1568/2378} which clash with 21(3) cage at R5C9), no 3,8, clean-up: no 2 in R1C9
2g. Killer triple 4,5,6 in 20(4) cage and 21(3) cage, locked for C9
2h. 18(5) cage at R1C8 = {12348/12357} (cannot be {12456} which clashes with 20(4) cage), no 6, 3 locked for N3
2i. 20(4) cage = {1469/2567} (cannot be {2459} which clashes with 18(5) cage), 6 locked for C9 and N3
2j. Killer pair 4,5 in 18(5) cage and 20(4) cage, locked for N3
2k. 21(3) cage at R5C9 = {489/579} -> R7C9 = 9, R7C6 = 2, clean-up: no 3 in R5C4, no 1 in R89C9
2l. 10(3) cage at R1C4 = {127/145/235} (cannot be {136} which clashes with R1C9), no 6
2m. 6 in R1 only in R1C123, locked for N1, clean-up: no 2 in R3C12 (step 1b), no 4,8 in R4C1, no 1,5 in R4C2
2n. 19(3) cage at R1C1 contains 6 = {469/568}, no 2,3,7
2o. Naked pair {37} in R34C1, locked for C1
2p. 2 in R1 only in R1C456, locked for N2
2q. 10(3) cage contains 2 = {127/235}, no 4
2r. R23C4 = {39/48} (cannot be {57} which clashes with 10(3) cage
2s. Combined cage 20(4) at R1C9 + 21(3) at R5C9 = {1469}{57}9/{2357}{48}9, 7 locked for N6
2t. 17(4) cage at R7C6 = {2357/2456} (cannot be {2348} which clashes with R89C9), no 8, 5 locked for C7 and N9
2u. 1 in N9 only in R789C8, locked for C8
3a. 45 rule on N6 3 outies R237C9 = 2 innies R46C7 + 9, R7C9 = 9 -> R23C9 = R46C7
3b. R23C9 contains 6 for N3 = {46/56} = 10,11 -> R46C7 = 10,11 = {46/38}
3c. R56C9 = {57} (cannot be {48} which clashes with R46C7), locked for C9 and N6 -> R4C8 = 9, R4C9 = 1 (cage sum), R1C9 = 3, R35C7 = [12], R3C2 = 5 -> R4C2 = 2, R3C1 = 3 (step 1b) -> R4C1 = 7, clean-up: no 9 in R2C4
3d. Naked pair {28} in R89C9, locked for N9
3e. Naked pair {46} in R23C9, 4 locked for N3
3f. R23C9 = {46} = 10 -> R46C7 = 10 = {46}, locked for C7 and N6
3g. Naked pair {38} in R56C8, locked for C8
3h. R4C89 = [91] = 10 -> R3C6 = 9 (step 2c), clean-up: no 3 in R2C4
3i. Naked pair {48} in R23C4, locked for C4 and N2, clean-up: no 8 in R7C3 (step 1d)
3j. 19(3) cage at R1C1 = {469} (only remaining combination), 4,9 locked for N1, 9 locked for R1
3k. 10(3) cage at R1C4 = {127} (only remaining combination), 1,7 locked for N2, 7 locked for R1 -> R1C78 = [85], R3C5 = 6, R23C9 = [64], R23C4 = [48]
3l. Naked pair {27} in R23C8, 7 locked for C8 and N3
3m. R7C359 (step 1c) = 22 = [589], R5C4 = 7, R56C9 = [57]
3n. R6C1 = 5 (hidden single in C1) -> R5C1 + R6C2 = 12 = [48/84/93]
3o. 45 rule on N8 3 remaining innies R789C4 = 18 = {369} (only remaining combination), locked for C4 and N8 -> R4C4 = 5
3p. 35(6) cage at R3C6 = {345689} (only remaining combination), no 1, 3 locked for N5
4a. 45 rule on N7 1 outie R9C4 = 1 remaining innie R8C3 + 2, R9C4 = {369} -> R8C3 = {147}
4b. 21(4) cage at R7C1 = {1389/2469/2478} (cannot be {1479} which clashes with R8C3, cannot be {2379} because 3,7 only in R7C2, cannot be {3468} which clashes with R15C1, ALS block)
4c. 1 of {1389} must be in R7C1 -> no 1 in R7C2 + R89C1
4d. 4,6,7 of {2469/2478} must be in R7C12 -> no 4,6 in R89C1
4e. 16(3) cage at R7C4 = {169/367} (cannot be [349] which clashes with 21(4) cage at R7C1), no 4, 6 locked for C4
4f. Consider placement for 3 in N7
R7C2 = 3 -> 21(4) cage at R7C1 = {1389}
or 3 in R8C2 + R9C23, locked for 21(4) cage at R8C2 => R9C4 = 9 => R8C3 = 7 => 21(4) cage at R7C1 = {2469}
-> 21(4) cage at R7C1 = {1389/2469}, no 7, 9 locked for C1 and N7, clean-up: no 3 in R6C2 (step 3n)
4g. Naked pair {48} in R5C1 + R6C2, locked for N4
4h. 45 rule on R1234 1 outie R5C6 = 1 innie R4C3 = {36}
4i. 16(3) cage at R7C4 = {367} (cannot be [619] which clashes with 21(4) cage at R7C1) -> R8C3 = 7, R9C4 = 9, R2C3 = 2
4j. R89C1 = [92] (hidden pair in C1) -> R7C12 = {46}, locked for R7 and N7
4k. Naked pair {46} in R17C1, 4 locked for C1
and the rest is naked singles.