Thanks Afmob for a couple of corrections
Prelims
a) R1C34 = {39/48/57}, no 1,2,6
b) R1C78 = {79}
c) R23C4 = {29/38/47/56}, no 1
d) R23C9 = {18/27/36/45}, no 9
e) R45C2 = {49/58/67}, no 1,2,3
f) R67C2 = {39/48/57}, no 1,2,6
g) 9(2) cage at R7C7 = {18/27/36/45}, no 9
h) R8C23 = {69/78}
i) 10(3) cage at R1C9 = {127/136/145/235}, no 8,9
j) 27(4) cage at R4C9 = {3789/4689/5679}, no 1,2
k) 13(4) cage at R5C1 = {1237/1246/1345}, no 8,9
l) 38(8) cage at R7C5 = {12345689}, no 7
Steps resulting from Prelims
1a. Naked pair {79} in R1C78, locked for R1 and N3, clean-up: no 3,5 in R1C34, no 2 in R23C9
1b. Naked pair {48} in R1C34, locked for R1
1c. 13(4) cage at R5C1 = {1237/1246/1345}, 1 locked for C1
1d. 27(4) cage at R4C9 = {3789/4689/5679}, 9 locked for N6
2. 45 rule on N2 1 innie R1C4 = 1 outie R2C7 -> R2C7 = {48}
2a. 45 rule on N3 2 innies R2C7 + R3C8 = 10 = [46/82]
[I originally limited 17(3) cage at R2C6 and 12(3) cage at R3C8; these steps have been deleted because step 4a places R2C7 and R3C8. Step 3 could also have been omitted, but I’ll keep it in.]
3. 45 rule on N2 2 outies R1C3 + R2C7 = 12 = {48}, CPE no 4,8 in R2C123
4. 45 rule on N6 2 outies R37C8 = 1 innie R6C9 + 11
4a. Min R37C8 = 12 -> R3C8 = 6, R2C7 = 4 (step 2a), R1C4 = 4 (step 2), R1C3 = 8; clean-up: no 5,7 in R2C4, no 3,5 in R23C9, no 7 in R3C4, no 3 in R7C7, no 7 in R8C2, no 5 in R8C8
4b. R2C7 = 4 -> R23C6 = 13 = [58/67/85]
4c. R3C8 = 6 -> R4C78 = 6 = [15/24/51]
4d. R23C4 = {29/38} (cannot be [65] which clashes with R23C6)
5. Naked pair {18} in R23C9, locked for C9 and N3
5a. Naked triple {235} in 10(3) cage at R1C9, locked for D/
5b. 12(3) cage at R6C9 = {237/246/345}, no 9
5c. Min R6C4 + R7C3 = 5 -> max R7C4 = 7
6. 45 rule on N6 1 remaining outie R7C8 = 1 innie R6C9 + 5 -> R7C8 = {789}, R6C9 = {234}
7. 45 rule on N1 1 outie R4C1 = 1 remaining innie R3C3 + 4 -> R4C1 = {56789}, R3C3 = {12345}
8. 45 rule on R1234 3 innies R4C269 = 20 = {389/479/569/578}, no 1 in R4C6
9. 45 rule on N36 3 remaining innies R6C789 = 12 = {138/237/246} (cannot be {147/345} which clash with R4C78, cannot be {156} because R6C9 only contains 2,3,4), no 5
9a. R6C789 = {237/246} (cannot be {138} because 17(3) cage at R6C7 cannot be {18}8), no 1,8, 2 locked for R6 and N6, clean-up: no 4 in R4C8 (step 4c)
9b. Naked pair {15} at R4C78, locked for R4 and N6, clean-up: no 1 in R3C3 (step 7), no 8 in R5C2
10. 15(4) cage at R3C3 = {2346} (only remaining combination), 6 locked for R4, clean-up: no 2 in R3C3, no 9 in R4C1 (both step 7), no 7 in R5C2
11. R6C789 (step 9a) = {237/246}
11a. 17(3) cage at R6C7 = {269/278/467} (cannot be {368} because R6C789 only contains one of 3,6), no 3 in R6C78
12. 15(3) cage at R1C1 = {159/267/357}
12a. 7,9 only in R2C1 -> R2C1 = {79}
13. 26(5) cage at R2C2 = {12689/13589/14678/23678} (cannot be {13679/14579/23579} which clash with R2C1, cannot be {23489/34568} which clash with R3C3, cannot be {24569/24578} which clash with 15(3) cage at R1C1) -> R4C1 = 8, R3C3 = 4 (step 7), placed for D\, clean-up: no 5 in R5C2, no 4 in R7C2, no 5 in R7C7
13a. Naked triple {236} in R4C345, locked for R4
14. 12(3) cage at R6C4 = {129/138/156} (cannot be {237} because 2,3 only in R7C4), no 7
14a. 2,3,5 only in R7C4 -> R7C4 = {235}
14b. 1 in R6C4 + R7C3, locked for D/
15. 8 in R6 only in R6C456, locked for N5
15a. 27(6) cage at R4C6 = {123579/124569/234567}, 2 locked for R5
15b. 2 in N4 only in R45C3, locked for C3
16. 45 rule on R6789 1 innie R6C3 = 1 outie R5C1 + 2, no 6 in R5C1, no 1 in R6C3
17. 45 rule on C1234 4 outies R45C56 = 16 = {1249/1267/2347} (cannot be {1357/1456} because 1,5 only in R5C6, cannot be {2356} because R4C6 only contains 4,7,9), no 5, 2 locked for N5
17a. 1,2,3 only in R4C5 + R5C6 -> R4C5 = {23}, R5C6 = {123}
17b. 4 of {1249} must be in R4C6 -> no 9 in R4C6
17c. 9(2) cage at R7C7 = {18/27} (cannot be [63] which clashes with R4C4), no 3,6
18. R45C56 (step 17) = {1249/1267/2347}
18a. 27(6) cage at R4C6 (step 15a) = {124569/234567} (cannot be {123579} because 7,9 must be in R4C6 + R5C5 and R45C56 only contains one of 7,9) -> R4C6 = 4, placed for D/, clean-up: no 9 in R5C2
18b. R45C56 = {1249/2347} -> R5C5 = {79}
18c. 27(6) cage only contains one of 7,9 -> no 7,9 in R5C34 + R6C3, clean-up: no 5,7 in R5C1 (step 16)
[Cracked, the rest is fairly straightforward.]
19. 27(4) cage at R4C9 = {3789} (only remaining combination, cannot be {4689} which clashes with R5C2), locked for N6
19a. Naked quad {3789} in R5C5789, locked for R5
20. Naked pair {24} in R6C89, locked for R6 -> R6C7 = 6 -> R67C8 = 11 = [29/47]
20a. Naked pair {79} in R17C8, locked for C8, clean-up: no 2 in R7C7
21. 27(6) cage at R4C6 (step 18a) = {234567} (only remaining combination, cannot be {124569} which clashes with R5C12, ALS block) -> R5C5 = 7, placed for both diagonals, R5C6 = 2, R6C3 = 3, R4C5 = 3, R4C4 = 6, placed for D\, R4C3 = 2, R5C34 = [65], R5C2 = 4 -> R4C2 = 9, R4C9 = 7, R5C1 = 1, clean-up: no 3,8 in R7C2, no 2 in R8C8
21a. Killer pair 2,3 in R23C4 and R7C4, locked for C4
22. R8C23 = {78} (cannot be [69] which clashes with R9C1) -> R8C2 = 8, placed for D/, R8C3 = 7, R67C2 = [75], R8C8 = 1, R7C7 = 8, both placed for D\ -> R6C6 = 9, placed for D\, R6C4 = 1, R7C3 = 9, R7C4 = 2 (cage sum), R8C4 = 9, R7C8 = 7, R6C8 = 4 (cage sum)
23. Naked pair {38} in R23C4, locked for C4 and N2, clean-up: no 5 in R23C6 (step 4b)
24. R89C4 = [97], R9C13 = [61] -> R9C2 = 2 (cage sum), R2C2 = 3, placed for D\
and the rest is naked singles, without using the diagonals.
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