Prelims
a) R12C5 = {13}
b) R56C5 = {15/24}
c) 11(3) cage at R5C3 = {128/137/146/236/245}, no 9
d) 26(4) cage at R2C9 = {2789/3689/4589/4679/5678}, no 1
1a. Naked pair {13} in R12C5, locked for C5 and N2
1b. R56C5 = {24}, locked for C5 and N5
2a. 45 rule on R89 2 innies R8C37 = 12 = {39/48/57}, no 1,2,6
2b. R8C37 ‘see’ all of N8 except for R9C456 -> 17(3) cage at R9C4 = 12+5 = {359/458}, no 1,2,6,7, 5 locked for R9 and N8
2c. Since 5 is the other number in 17(3) cage, R8C37 = {39/48}, no 5,7
2d. 15(3) cage at R8C4 = {168/267} (cannot be {249/348} which clash with R8C37), no 3,4,9, 6 locked for R8 and N8
2e. 45 rule on N8 3 innies R7C456 = 13 = {139/148/247} (cannot be {238} which clashes with 15(3) cage)
2f. R7C5 = {789} -> no 7,8,9 in R7C46
2g. Killer pair 3,4 in R7C456 and R8C37, locked for 34(7) cage at R7C3
2h. R7C456 = 13, R8C37 = 12 -> R7C37 = 9 = {18/27}, no 5,6,9
2i. 34(7) cage at R7C3 = {1234789}, 1,2,7 locked for R7
3a. 45 rule on R1234 2 outies R5C46 = 14 = {59/68}
3b. 45 rule on R789 2 outies R6C19 = 8 = {17/26/35}, no 4,8,9
3c. 45 rule on C12 2 outies R19C3 = 10 = {19/28/37/46}, no 5 in R1C3
3d. 45 rule on C89 2 outies R19C7 = 11 = {29/38/47}/[56], no 1, no 6 in R1C7
4a. R6C19 (step 3b) = {17/26/35}
4b. 45 rule on N7 2 innies R78C3 = 1 outie R6C1 + 5
4c. R6C1 = {156} (cannot be 2,3 because R78C3 cannot total 7,8, cannot be 7 because R78C3 = 12 clashes with R8C37, combo crossover clash CCC) -> R6C19 = [17/53/62]
4d. Consider permutations for R6C17
R6C19 = [17] => R78C3 = 6 = [24] => R7C37 = [27], R8C37 = [48]
or R6C19 = [53] => R78C3 = 10 = [28/73] => R7C37 = [27/72], R8C37 = [39/84] (R78C3 = 10 cannot be [19] because R7C37 = [18] clashes with 16(3) cage at R6C9 = 3{58}, only place for 5 in R7 when R6C1 = 5)
or R6C19 = [62] => R56C5 = [24], 2 placed for both diagonals, no 2 in R7C37, R78C3 = 11 = [83] => R7C37 = [81], R8C37 = [39]
-> R7C37 = [27/72/81], R8C37 = [39/48/84]
[Taking one of these a bit further]
4e. R6C19 = [17] => R78C3 = 6 = [24] => R7C37 = [27], R8C37 = [48] => R7C5 = 9 (hidden single in 34(7) cage at R7C3, step 2i) => 15(3) cage at R6C1 = 1{68} for 1 in R6C1
4f. 15(3) cage at R6C1 = {168/456} (cannot be {348} because R6C1 only contains 1,5,6), no 3,9
4g. Consider combinations for 15(3) cage
15(3) cage = {168}, R6C19 = [17] => R7C37 = [27], R8C37 = [48} (step 4d)
or 15(3) cage = {456}, 4 locked for R7 => 4 in 34(7) cage only in R8C37 = {48} => R6C19 = [53] (step 4d), R78C3 = 10 = [28] => R7C37 = [27], R8C37 = [84]
-> R6C19 = [17/53], R7C37 = [27], 2 placed for D/, 7 placed for D\, R8C37 = {48}, locked for R8, clean-up: no 8 in R19C3 (step 3c), no 4 in R19C7 (step 3d)
4h. 15(3) cage = {168/456}, 6 locked for R7 and N7, clean-up: no 4 in R1C3 (step 3c)
4i. 34(7) cage at R7C3 = {1234789} -> R7C5 = 9, R7C46 = {13}, locked for N8, 3 locked for R7
4j. R56C5 = [42], 4 placed for both diagonals
4k. Naked triple {458} in 17(3) cage at R9C4, 4,8 locked for R9, 8 locked for N8, clean-up: no 6 in R1C3 (step 3c), no 3 in R1C7 (step 3d)
4l. Naked triple {267} in 15(3) cage at R8C4, 2,7 locked for R8
4m. Naked triple {458} in R7C89 + R8C7, 5 locked for R7 and N9
5a. 11(3) cage at R5C3 = {137/146}, no 5,8
5b. 11(3) cage at R5C3 = {137/146}, CPE no 1 in R6C12
[I originally saw a clash with R6C19 + R8C3 but the CPE is much simpler]
5c. R6C1 = 5 -> R6C9 = 3 (step 4g), R78C3 = 10 (step 4b) -> R8C3 = 8, R8C7 = 4
5d. 3 of 11(3) cage only in R5C3, no 7 in R5C3
5e. 4 of 11(3) cage only in R6C3, no 6 in R6C3
5f. 3 in N5 only in R4C46, locked for R4
5g. R8C2 = 5 (hidden single in N7), placed for D/
6a. 18(3) cage at R5C7 = {189} (only possible combination), CPE no 1,8,9 in R6C8
6b. Double hidden killer pair 8,9 in 18(3) cage at R5C1, R5C46 and 18(3) cage at R5C7 for R56, 18(3) cage at R5C7 contains both of 8,9, R5C46 contains one of 8,9, 18(3) cage at R5C1 must contain at least one of 8,9 -> 18(3) cage at R5C1 must only contain one of 8,9, no 8,9 in 15(3) cage at R6C8
6c. 15(3) cage at R5C8 = {267} (cannot be {456} which clashes with R5C46), locked for N6, 2 locked for R5
6d. 4 in N6 only in R4C89, locked for R4 and 26(4) cage at R2C9
6e. 26(4) cage = {4589/4679}, no 2
6f. 2 in R4 only in R4C12, locked for 16(4) cage at R2C1
6g. 18(3) cage at R5C1 = {369/378/468} (cannot be {189} because this 18(3) cage only contains one of 8,9, step 6b), no 1
6h. 5 in R6 only in R5C46 (step 3a) = {59}, locked for N5
6i. R3C3 = 5 (hidden single on D\) -> R5C46 = [95]
[Cracked. Fairly straightforward from here.]
7a. 18(3) cage at R5C7 = {189} -> R6C7 = 9, clean-up: no 2 in R19C7 (step 3d)
7b. Naked pair {18} in R45C7, locked for C7, 8 locked for N6
7c. R1C7 = 5 -> R9C7 = 6 (step 3d), R3C7 = 3, placed for D/
7d. R2C7 = 2 -> R12C6 = 16 = {79}, locked for N2, 7 locked for C6
7e. R4C89 = {45} = 9 -> R23C9 = 17 = {89}, locked for C9 and N3 -> R89C9 = [12], 2 placed for D\, R7C89 = [85], R4C89 = [54]
7f. Naked pair {39} in R8C18, CPE no 3,9 in R1C1 using D\
7g. 23(4) cage at R3C4 = {2678} (only remaining combination) -> R4C5 = 7, R38C5 = [86], R3C46 = {26}, locked for R3 and N2
7h. R4C12 = {29} (hidden pair in R4) = 11 -> R23C1 = 5 = {14}, locked for N1, 4 locked for C1 -> R7C12 = [64], R1C1 = 8, placed for D\
7i. R12C4 = [45] -> R2C3 = 9 (cage sum), R3C2 = 7, R1C3 = 3 -> R9C3 = 7 (step 3c), R12C2 = [26], 6 placed for D\
7j. R6C6 = 1 -> R4C4 = 3, placed for D\
and the rest is naked singles, without using the diagonals