Prelims
a) R12C1 = {18/27/36/45}, no 9
b) R12C4 = {49/58/67}, no 1,2,3
c) R12C9 = {19/28/37/46}, no 5
d) R3C34 = {14/23}
e) R4C67 = {89}
f) R6C34 = {15/24}
g) R7C67 = {12}
h) R89C1 = {19/28/37/46}, no 5
i) R89C6 = {16/25/34}, no 7,8,9
j) R89C9 = {19/28/37/46}, no 5
Steps resulting from Prelims
1a. Naked pair {89} in R4C67, locked for R4
1b. Naked pair {12} in R7C67, locked for R7
2. 45 rule on C1 2 outies R23C2 = 10 = {19/28/37/46}, no 5
2a. 45 rule on N1 2 remaining innies (using R23C2) R3C13 = 9 = [54/63/72/81]
3. 45 rule on C9 2outies R78C8 = 10 = {37/46}/[82/91], no 5, no 8,9 in R8C8
3a. 45 rule on N9 2 remaining innies (using R78C8) R7C79 = 7 = [16/25]
4. 45 rule on C1234 2 outies R89C5 = 10 = {19/28/37/46}, no 5
4a. 45 rule on C1234 3 innies R7C34 + R8C4 = 20 = {389/479/569/578}, no 1,2
5. 45 rule on C6789 2 outies R12C5 = 7 = {16/25/34}, no 7,8,9
6. 45 rule on N78 3 innies R7C156 = 12 = {138/147/237/246} (cannot be {129} because 1,2 only in R7C6, cannot be {156} which clashes with R7C9, cannot be {345} because R7C6 only contains 1,2), no 5,9
6a. 45 rule on N9 1 remaining innie R7C9 (using R78C8 = 10, step 3) = 1 outie R7C6 + 4 -> R7C69 = [15/26]
6b. R7C156 = 12 = {138/147/237} (cannot be {246} which clashes with R7C69, CCC), no 6
7. 45 rule on N7 2 innies R7C13 = 1 outie R9C4 + 4
7a. Min R7C13 = 7 -> min R9C4 = 3
8. 36(7) cage at R2C2 contains 9 in R23C2 + R56C1, CPE no 9 in R56C2
9. 18(3) cage at R8C7 = {189/279/369/378/459/468} (cannot be {567} which clashes with R7C9)
9a. 5 in N9 only in R7C79 (step 3a) = [25] or 18(3) cage = {459} -> 18(3) cage = {189/369/378/459/468} (cannot be {279}, locking-out cages), no 2
9b. 1 of {189} must be in R89C7 (R89C7 cannot be {89} which clashes with R4C7), no 1 in R9C8
10. Hidden killer pair 3,7 in R78C8, 18(3) cage at R8C7 and R89C9 for N9, R78C8 (step 3) contains both or neither of 3,7, R89C9 contains both or neither of 3,7 -> 18(3) cage (step 9a) must contain both or neither of 3,7 = {189/378/459/468} (cannot be {369} which contains 3 but not 7)
[No candidate eliminations from this step]
11. 45 rule on N23 3 innies R3C459 = 12 = {129/138/156/246/345} (cannot be {147/237} which clash with R3C34, CCC), no 7
11a. 45 rule on N1 1 remaining innie R3C1 (using R23C2 = 10, step 2) = 1 outie R3C4 + 4 -> R3C14 = [51/62/73/84]
11b. R3C459 = 12 = {129/138/246/345} (cannot be {156} which clashes with R3C14, CCC)
[Note that {246} can only be 4{26} but this doesn’t lead to any candidate eliminations at this stage.]
12. 45 rule on N14 5(4+1) outies R3456C4 + R7C1 = 16
12a. Min R7C1 = 3 -> max R3456C4 = 13, no 8,9 in R5C4
12b. Min R3456C4 = 10 -> no 7,8 in R7C1
12c. R7C156 (step 6b) = {138/147/237}
12d. 7,8 only in R7C5 -> R7C5 = {78}
13. 30(5) cage at R7C3 = {25689/34689/35679} (cannot be {15789/24789/45678} which clash with R7C5, no 1, clean-up: no 9 in R89C5 (step 4)
13a. 3,7 of {35679} must be in R89C5 (step 4) -> no 7 in R7C34 + R8C4
13b. 9 in N8 only in R789C4, locked for C4, clean-up: no 4 in R12C4
13c. 1 in N8 only in R789C6, locked for C6
14. 1,2 in C4 only in R3456C4, R12C4 = {58/67}
14a. R3456C4 + R7C1 = 16 (step 12)
14b. R7C1 = {34} -> R3456C4 = 12,13 = {1236/1245/1237/1246}
14c. Combined cage R3456C4 + R12C4 = {1236}{58}/{1245}{67}/{1237}{58}/{1246}{58}, 5 locked for C4
[Cracked. The rest is fairly straightforward.]
15. 5 in N8 only in R89C6 = {25}, locked for C6 and N8 -> R7C6 = 1, R7C7 = 2, placed for D\, R7C9 = 5 (step 3a), clean-up: no 7 in R2C1, no 7 in R3C1 (step 2a), no 3 in R3C4, no 8 in R7C8 (step 3), no 8 in R89C5 (step 4), no 8 in R89C9
16. R12C5 (step 5) = {16/25} (cannot be {34} which clashes with R89C5), no 3,4
17. 30(5) cage at R7C3 (step 13) = {34689/35679}
17a. 4,6 of {34689} must be in R89C5 (step 4) -> no 4 in R7C34 + R8C4
18. R7C13 = R9C4 + 4 (step 7)
18a. R7C13 cannot total 8 -> no 4 in R9C4
19. 4 in N8 only in R89C5 (step 4) = {46}, locked for C5, N8 and 30(5) cage at R7C3 (no 6 in R7C3), clean-up: no 1 in R12C5 (step 5)
19a. Naked pair {25} in R12C5, locked for C5 and N2, clean-up: no 8 in R12C4, no 3 in R3C3, no 6 in R3C1 (step 2a)
19b. Naked pair {67} in R12C4, locked for C4 and N2
19c. Naked triple {389} in R789C4, locked for C4
20. Naked pair {14} in R3C34, locked for R3
20a. R3C4 = 1 (hidden single in N2), R3C3 = 4, placed for D\, R3C1 = 5 (step 2a), R4C4 = 5, clean-up: no 1,5 in R6C3, no 2 in R6C4, no 6 in R7C8 (step 3), no 6 in R8C9
20b. R6C3 = 2, R6C4 = 4, placed for D/, R5C4 = 2, clean-up: no 6 in R2C9, no 6 in R8C1
21. R3456C4 + R7C1 = 16 (step 12)
21a. R3456C4 = [1524] = 12 -> R7C1 = 4, clean-up: no 6 in R9C1, no 6 in R8C8 (step 3)
22. R4C4 = 5 -> R4C23 = 9 = {36}, locked for R4 and N4
22a. R4C89 = {24} (hidden pair in R4), locked for N6
23. R5C2 = 4 (hidden single in N4), placed for centre dot group -> R8C5 = 6, placed for centre dot group, R9C5 = 4
23a. R5C24 = [42] = 6 -> R5C3 + R6C2 = 13 = {58}, locked for N4
24. Naked triple {179} in R456C1, locked for C1 and 36(7) cage at R2C2, clean-up: no 2,8 in R12C1, no 3 in R89C1
24a. Naked pair {36} in R12C1, locked for N1 -> R2C2 = 8, placed for centre dot group, R3C2 = 2, R6C2 = 5, R5C3 = 8, clean-up: no 2 in R1C9
24b. Naked triple {389} in R7C34 + R8C4, 8 locked for C4
25. 14(3) cage at R6C6 = {167} (only remaining combination), locked for R6, 1 also locked for N6 -> R6C1 = 9
26. 1 in C9 only in R12C9 = {19} or R89C9 = {19}, locking cages, no other 9 in C9
27. 13(3) cage at R9C2 = {139} (only remaining combination, cannot be {157} because R9C4 only contains 3,9), locked for R9, 1 also locked for N7, clean-up: R8C9 = {34}
27a. Naked triple {678} in R9C789, locked for R9 and N9 -> R9C1 = 2, placed for D/, R8C1 = 8, R89C6 = [25], clean-up: no 3 in R78C8 (step 3)
28. R7C8 = 9, R8C8 = 1, placed for D\
28a. R12C9 = {19} (hidden pair in C9), locked for N3
[I’d realised for some time that R23C2/R89C1 and R12C9/R78C8 were “clone pairs” but I’ve allowed them to come out with simpler steps.]
29. R7C34 = [38], R8C4 = 9, R9C4 = 3, R7C5 = 7, R7C2 = 6, R8C2 = 7, placed for D/ and centre dot group, R8C3 = 5, clean-up: no 3 in R2C9
30. R12C5 = {25} = 7 -> R23C6 + R3C7 = 18 = {369/468} -> R3C7 = 6
31. Naked pair {67} in R6C6 + R9C9, locked for D\ -> R1C1 = 3, placed for D\, R2C1 = 6, R5C5 = 9, R4C67 = [89]
32. R1C9 = 1 (hidden single on D/), R2C9 = 9
33. R23C6 + R3C7 (step 30) = {369} (only remaining combination) -> R2C6 = 3, R3C6 = 9, R3C5 = 8, R6C5 = 3, R3C9 = 3, R8C9 = 4, R9C9 = 6, placed for D\
34. R1C6 = 4 -> R1C78 = 10 = [82]
and the rest is naked singles, without using the diagonals or the centre dot group.