Prelims
a) 7(2) cage at R1C1 = {16/25/34}, no 7,8,9
b) R1C23 = {16/25/34}, no 7,8,9
c) 14(2) cage at R1C9 = {59/68}
d) 13(2) cage at R2C1 = {49/58/67}, no 1,2,3
e) R23C9 = {19/28/37/46}, no 5
f) R34C1 = {49/58/67}, no 1,2,3
g) 6(2) cage at R4C4 = {15/24}
h) 14(2) cage at R4C5 = {59/68}
i) R4C89 = {14/23}
j) R5C89 = {29/38/47/56}, no 1
k) R78C5 = {49/58/67}, no 1,2,3
l) R9C45 = {29/38/47/56}, no 1
m) 21(3) cage at R7C7 = {489/579/678}, no 1,2,3
n) 9(3) cage at R7C8 = {126/135/234}, no 7,8,9
1a. Killer triple 4,5,6 in 7(2) cage at R1C1, R1C23 and 13(2) cage at R2C1, locked for N1, clean-up: no 7,8,9 in R4C1
1b. 7(2) cage at R1C1 = {16/34} (cannot be {25} which clashes with 6(2) cage at R4C4), no 2,5
1c. Killer pair 1,4 in 7(2) cage and 6(2) cage, locked for D\
1d. 45 rule on D\ 2 innies R3C3 + R6C6 = 11 = {29/38} (cannot be {56} which are only in R6C6)
1e. 21(3) cage at R7C7 = {579/678}, 7 locked for N9
1f. 45 rule on R12 2 outies R3C29 = 6 = [42/51] -> R2C19 = {89}, locked for R2, clean-up: no 5,6 in R1C9
1g. Naked pair {89} in R12C9, locked for C9 and N3, clean-up: no 2,3 in R5C8
1h. 6 in N1 only in 7(2) cage and R1C23 = {16}{25}/{16}{34}, 1 locked for N1
[Alternatively 45 rule on N1 3 innies R2C3 + R3C13 = 18 = {279/378} (cannot be {189} which clashes with R2C1), no 1]
1i. 45 rule on R789 2 innies R78C4 = 8 = {17/26/35}, no 4,8,9
1j. 45 rule on R789 3 outies R6C234 = 20 = {389/479/569/578}, no 1,2
1k. 45 rule on R6789 1 outie R5C7 = 1 innie R6C1 + 4, no 1,2,3,4 in R5C7, no 6,7,8,9 in R6C1
1l. 15(3) cage at R5C1 = {168/249/258/348/357} (cannot be {456} which clashes with R4C1, cannot be {159/267} which clash with R5C7 + R6C1)
1m. 1 of {168} must be in R6C1 -> no 1 in R5C12
1n. 45 rule on C1234 3 outies R259C5 = 9 = {126/135/234}, no 7,8,9, clean-up: no 2,3,4 in R9C4
1o. 45 rule on R1234 4 outies R5C3456 = 15 must contain 1 for R5 = {1239/1248/1257/1356} (cannot be {1347} because R5C6 only contains 5,6,8,9)
1p. 8,9 of {1239/1248} must be in R5C6 -> no 8,9 in R5C34
1q. 45 rule on N6 2 outies R6C56 = 1 innie R4C7
1r. Min R6C56 = 4 (cannot be [12] which clashes with 6(2) cage at R4C4) -> min R4C7 = 4
1s. Max R4C7 = 9 -> max R6C56 = 9, no 8,9 in R6C5, no 9 in R6C6, clean-up: no 2 in R3C3
1t. R2C3 + R3C13 = {279/378}
1u. 7 of {279} must be in R3C1 -> no 9 in R3C1, clean-up: no 4 in R4C1
1v. 2 on D\ only in R4C4 + R5C5 + R6C6, locked for N5
2a. 7 in R12 only in 15(4) cage at R1C4 and 30(6) cage at R1C5 -> each must contain 7
2b. 15(4) cage must contain 7 = {1257/1347}, no 6,8,9, 1 locked for N2
2c. 1 in R3 only in R3C789, locked for N3
3a. 45 rule on N9 3 innies R8C7 + R9C78 = 15 = {159/168/249/348} (cannot be {258/456} which clash with 9(3) cage at R7C8)
3b. 45 rule on N9 3 outies R789C6 = 13 = {157/247/256/346} (cannot be 139/148} which clash with R8C7 + R9C78, cannot be {238} which clashes with R6C6), no 8,9
3c. 1 in N8 only in R78C4 = {17} or in R789C6 -> R789C6 = {157/256/346} (cannot be {247} (locking out cages)
3d. R8C7 + R9C78 = {159/249/348} (cannot be {168} which clashes with R789C6), no 6
3e. R78C5 = {49/58} (cannot be {67} which clashes with R789C6), no 6,7
3f. Hidden killer pair 8,9 in R78C5 and R9C4 for N8, R78C5 contains one of 8,9 -> R9C4 = {89}, R9C5 = {23}
3g. Killer pair 4,5 in R78C5 and R789C6, locked for N8, clean-up: no 3 in R78C4
3h. R259C5 (step 1n) = {135/234}, 3 locked for C5
3i. Killer pair 4,5 in R259C5 and R78C5, locked for C5, clean-up: no 9 in R5C6
3j. Combined cage R78C5 + R9C45 = {49}[83]/{58}[92]
3k. R259C5 = {15}3/[342] (cannot be {24}3 which clashes with combined cage) -> R2C5 = {135}, R5C5 = {145}, clean-up: no 4 in R4C4
4a. R5C3456 (step 1o) = {1248/1356} (cannot be {1257} = [2715] which clashes with 6(2) cage at R4C4 = {15}, CCC), no 7
4b. 2 of {1248} must be in R5C3 -> no 4 in R5C3
4c. R5C89 = {47/56}/[92] (cannot be [83] which clashes with R5C3456), no 3,8
4d. 45 rule on R6789 3 outies R5C127 = 19 = {289/379/478} (cannot be {469/568} which clash with R5C3456), no 5,6, clean-up: no 1,2 in R6C1 (step 1k)
4e. Hidden killer pair 1,2 in R6C56 and R6C789 for R6, R6C45 cannot contain both of 1,2 which clashes with 6(2) cage at R4C4, CCC, R6C789 cannot contain both of 1,2 which clashes with R4C89 -> R6C56 and R6C789 each contain one of 1,2
4f. Killer pair 1,2 in 6(2) cage at R4C4 and R6C56, locked for N5
4g. Killer pair 1,2 in R4C89 and R6C789, locked for N6, clean-up: no 9 in R5C8
4h. 2 in R5 only in R5C123, locked for N4
4i. 3 in R5 only in R5C1234, CPE no 3 in R4C23
4j. 9 in R5 only in R5C127 = {289/279}, no 4
5a. Consider combinations for R5C3456 (step 4a) = {1248/1356}
R5C3456 = {1248} = [2418]
or R5C3456 = {1356}, 3 in R5C34 locked for 29(6) cage at R3C3, no 3 in R3C3 => no 8 in R6C6 (step 1d)
-> no 8 in R6C6, clean-up: no 3 in R3C3
[Cracked at last, first placement follows.]
5b. Naked pair {89} in R2C1 + R3C3, locked for N1 -> R3C1 = 7, R4C1 = 6, clean-up: no 1 in R2C2, no 8 in R5C6
5c. R5C3456 = {1356} (only remaining combination), locked for R5, 6 locked for N5, clean-up: no 2 in R4C4
5d. Naked pair {15} in 6(2) cage at R4C4, locked for N5 and D\
[Routine clean-ups omitted from here]
5e. R5C6 = 6 -> R4C5 = 8, R5C4 = 3, R6C5 = 7, R6C6 = 2 -> R3C3 = 9 (step 1d), placed for D\, R2C1 = 8 -> R3C2 = 5, R2C9 = 9 -> R3C9 = 1, R1C9 = 8 -> R2C8 = 6, both placed for D/
5f. Naked pair {34} in 7(2) cage at R1C1, locked for N1 -> R2C3 = 2
5g. Naked pair {16} in R1C23, locked for R1
5h. Naked pair {47} in R5C89, locked for N6, 7 locked for R5, clean-up: no 1 in R4C8
5i. R2C3 = 2 -> 15(4) cage at R1C4 = {1257} (only remaining combination), 5,7 locked for N2
5j. Naked triple {157} in R124C4, 1,7 locked for C4
5k. Naked pair {26} in R78C4, locked for C4, 2 locked for N8
5l. R9C5 = 3 -> R9C4 = 8, R3C4 = 4, R6C4 = 9, R4C6 = 4, both placed for D/
5m. R6C4 = 9, R78C4 = {26} -> R6C23 = 11 = {38}, locked for R6 and N4
5n. Naked pair {29} in R5C12, 9 locked for R5, R6C1 = 4 (cage sum), R1C1 = 3
5o. 14(3) cage at R7C3 = {257} (only remaining combination), locked for N7, 2,5 locked for D/
5p. Naked pair {19} in R78C1, locked for N7, 9 locked for C1, R7C2 = 8 (cage sum)
and the rest is naked singles, not using the diagonals.