Prelims
a) R12C9 = {16/25/34}, no 7,8,9
b) R78C5 = {79}
c) R78C8 = {18/27/36/45}, no 9
d) Disjoint cage R9C47 = {39/48/57}, no 1,2,6
e) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
f) 7(3) cage at R2C6 = {124}
g) 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9
h) 30(4) cage at R1C7 = {6789}
Steps resulting from Prelims
1a. Naked pair {79} in R78C5, locked for C5 and N8, clean-up: no 3,5 in R9C7
1b. Naked quad {6789} in 30(4) cage at R1C7, locked for N3, clean-up: no 1 in R12C9
1c. Naked triple {124} in 7(3) cage at R2C6, CPE no 1,2,4 in R2C9 + R3C456, clean-up: no 3,5 in R1C9
1d. R23C9 = {35} (hidden pair in N3), locked for C9
1e. 1 in N3 only in R3C78, locked for R3 and 7(3) cage
2a. 45 rule on N36 R26C6 = 10 = [28/46]
2b. 45 rule on N14789 1 outie R1C4 = 8, clean-up: no 4 in R9C7
[Or, of course, 45 rule on N2356]
2c. 8 in N3 only in R2C78, locked for R2
2d. 19(3) cage at R1C1 = {379/469}, no 2,5, 9 locked for N1
2e. R1C4 = 8 -> R123C3 = 11 = {137/146/245} (cannot be {236} which clashes with 19(3) cage)
2f. 45 rule on N1 3 remaining outies R45C1 + R6C2 = 9 = {126/135/234}, no 7,8,9
2g. 45 rule on N89 2 innies R78C4 = 8 = {26/35}
2h. 8 in N1 only in R3C12
2i. 45 rule on N1 3 remaining innies R2C1 + R3C12 = 15 = {168/348} (cannot be {258} which clashes with R45C1 + R6C2), no 2,5,7
2j. R123C3 = {245} (cannot be {137/146} which clash with R2C1 + R3C12), locked for C3, 4 locked for N1
2k. R2C1 + R3C12 = {168} -> R2C1 = 1, R3C12 = {68}, 6 locked for R3 and N1
2l. R45C1 + R6C2 = {234} (only remaining combination), locked for N4
2m. 3 in C3 only in R789C3, locked for N7
2n. R3C46 = {79} (hidden pair in R3), 7 locked for N2
2o. Naked pair {79} in R3C46, CPE no 7,9 in R6C4
2p. Naked pair {35} in R3C59, 5 locked for R3
3a. 45 rule on N14 3 innies R5C3 + R6C13 = 18 = {189/567}
3b. 5 of {567} must be in R6C1 -> no 6,7 in R6C1
3c. R56C3 = {18/19/67} = 9,10,13 -> R7C34 = 12,11,8 = [75/93/65/83/35] (cannot be 21(4) cage at R5C3 cannot be {19}[92] or {67}[62]), no 1 in R7C3, no 2,6 in R7C4
3d. R78C4 (step 2g) = {35} (only remaining combination), locked for C4 and N8, R9C4 = 4 -> R9C7 = 8, clean-up: no 1 in R78C8
3e. R2C8 = 8 (hidden single in N3)
3f. 8 in N8 only in R78C6, locked for C6, R6C6 = 6 -> R2C6 = 4 (step 2a)
3g. R9C5 = 6 (hidden single in N8)
3h. Naked triple {128} in R789C6, 1,2 locked for C6 and 26(6) cage at R7C6
3i. R2C4 = 6 (hidden single in N2) -> 14(4) cage at R1C5 = {1256} (only remaining combination) -> R1C6 = 5, R12C5 = [12], R3C59 = [35], R2C9 = 3 -> R1C9 = 4
3j. R345C6 = {379} = 19 -> R5C5 + R6C45 = 13 = {148} -> R6C4 = 1, R56C5 = {48} locked for N5 -> R4C5 = 5
3k. 18(3) cage at R4C2 = {189/567}
3l. 5 of {567} must be in R5C2 -> no 6,7 in R5C2
3m. R5C3 + R6C13 = {189/567}
3n. 1,6 only in R5C3 -> R5C3 = {16}
4a. 45 rule on N9 2 remaining innies R78C7 = 9 = {45} (locked for C7 and N9)
4b. 3 in C7 only in R456C7, locked for N6
4c. 5 in R9 only in R9C12, locked for N7
5a. Variable hidden killer pair 3,7 in R9C123 and R9C89 for R9, R9C89 cannot be [37] which clashes with R78C8 -> R9C123 must have at least one of 3,7
5b. 5 in R9 only in R9C12 -> 19(4) cage at R8C1 = {1567/2359/3457} (cannot be {1459/2458} which don’t contain 3 or 7), no 8
5c. 4,6 of {1567/3457} must be in R8C1 -> no 7 in R8C1
5d. 3 of {2359} must be in R9C3 -> no 9 in R9C3
6a. R5C3 + R6C13 (step 3a) = {189/567} = 1{89}/[657], R78C8 = {27/36}
6b. R3C9 = 5, 6 in N6 only in 23(5) cage at R3C9 = {12569/13568/14567/23567}
6c. Consider placement for 8 in C9
8 in R45C9 -> 23(5) cage = {13568}
or R6C9 = 8 => R5C3 + R6C13 = [657] => R7C34 = [35] => R9C8 = 3 (hidden single in R9) => R78C8 = {27} => 2 in C9 only in R45C9 => 23(5) cage = {12569/23567}
[Ed pointed out that after R78C8 = {27} I’d missed => R45C9 = {27} which would have then reduced the 23(5) cage to {13568/23567} and simplified the rest on my walkthrough by omitting the need for steps 7c and 7d.]
-> 23(5) cage = {12569/13568/23567}, no 4
6d. R4C1 = 4 (hidden single in R4)
6e. R56C8 = {45} (hidden pair in N6)
6f. Hidden killer pair 2,3 in R6C2 and R6C79 for R6, R6C2 = {23} -> R6C79 must contain one of 2,3
6g. 33(6) cage at R5C7 contains 4,5,6 = {245679/345678} (cannot be {145689} which doesn’t contain 2 or 3), no 1, 7 locked for N6
6h. 2,3 of {245679/345678} must be in R6C79 (cannot be 2{79}/[378] because R6C79 must contain one of 2,3), no 2,3 in R5C7
6i. Naked pair {79} in R25C7, locked for C7 -> R1C7 = 6
6j. Naked pair {23} in R6C27, 2 locked for R6
6k. Naked quad {2379} in R5C1467, 2,9 locked for R5
7a. 18(3) cage at R4C2 (step 3k) = {189/567} must have 6 or 9 in R4
7b. 23(5) cage at R3C9 (step 6c) = {12569/13568}
7c. {12569} cannot be 5{269}1 which clashes with 18(3) cage
7d. 23(5) cage = {13568} (cannot be 5{129}6 which clashes with R4C234 = {67}{29}) -> R4C7 3, R4C89 + R5C9 = {168}, 8 locked for N6
7e. R6C7 = 2, R5C1 + R6C2 = [23]
7f. Naked pair {79} in R12C2, locked for C2 and N1
7g. R3C78 = [12], clean-up: no 7 in R78C8
7h. Naked pair {36} in R78C8, locked for N9, 6 locked for C8 -> R4C8 = 1
7i. Naked pair {68} in R34C2, locked for C2
8a. 19(4) cage at R8C1 (step 5b) = {1567/2359}
8b. Killer pair 1,2 in R9C23 and R9C6, locked for R9
8c. Naked pair {79} in R9C89, locked for R9 and N9
8d. R9C1 = 5, R9C3 = 3 (hidden single in R9) -> R8C1 + R9C2 = 11 = [92]
8e. R6C1 = 8, R4C2 = 6, R5C23 = [51], R4C3 = 7 (cage sum)
and the rest is naked singles.