Prelims
a) R12C6 = {79}
b) R67C9 = {79}
c) 15(2) cage at R5C5 = {69/78}
d) 23(3) cage at R7C4 = {689}
e) 18(5) cage at R1C1 = {12348/12357/12456}, no 9
f) 18(5) cage at R1C8 = {12348/12357/12456}, no 9
g) 18(5) cage at R7C3 = {12348/12357/12456}, no 9
h) 18(5) cage at R7C7 = {12348/12357/12456}, no 9
1. 45 rule on R5/C5 1 innie R5C5 = 9 -> R6C6 = 6, placed for D\
1a. 45 rule on N7 1 innies R9C3 = 9
1b. 9 in N1 only in R3C12, locked for R3
1c. 9 in N3 only in R12C7, locked for C7
Steps resulting from Prelims
2a. Naked pair {79} in R12C6, locked for C6 and N2
2b. Naked pair {79} in R67C9, locked for C9
2c. R8C4 = 9 (hidden single in R8)
2d. Naked pair {68} in R79C4, locked for C4 and N8
2e. 18(5) cage at R1C1 = {12348/12357/12456}, 1,2 locked for N1
2f. 18(5) cage at R1C8 = {12348/12357/12456}, 1,2 locked for N3
2g. 18(5) cage at R7C3 = {12348/12357/12456}, 1,2 locked for N7
2h. 18(5) cage at R7C7 = {12348/12357/12456}, 1,2 locked for N9
2i. 7 in N8 only in R789C5, locked for C5
3. 17(3) cage at R3C6 = {278/368/458} (cannot be {467} because no 6,7 in R4C7), no 1
3a. 6,7 of {278/368} must be in R4C7 -> no 2,3 in R4C7
4. 18(3) cage at R7C1 = {378/468/567}
4a. 4 of {468} must be in R7C12 (R7C12 cannot be {68} which clashes with R7C4) -> no 4 in R8C3
5. 6 in N2 only in 18(4) cage at R1C5 = {1368/3456}, no 2, 3 locked for C5
5a. 18(4) cage at R6C5 = {1278/2457}
5b. 8 of {1278} must be in R6C5 -> no 1 in R6C5
5c. 3 in N8 only in R789C6, locked for C6
5d. 17(3) cage at R3C6 (step 3) = {278/458}, no 6
6. 45 rule on C89 6(2+4) outies R57C6 + R3567C7 = 16
6a. Min R3567C7 = 10 -> max R57C6 = 6, no 8 in R5C6
6b. Min R57C6 = 3 -> max R3567C7 = 13, no 8
6c. 8 in C6 only in R34C6, locked for 17(3) cage at R3C6 -> no 8 in R4C7
7. 45 rule on R1234 5(2+1+2) innies R12C7 + R3C1 + R4C12 = 39
7a. Max R12C7 + R3C1 = 17 + 9 -> min R4C12 = 13, no 1,2,3
7b. Max R3C1 + R4C12 = 9 + 17 -> min R12C7 = 13, no 3
7c. Max R12C7 + R4C12 = 17 + 17 -> min R3C1 = 5
8. 45 rule on N3 2 innies R12C7 = 2 outies R4C89 + 9, max R12C7 = 17 -> max R4C89 = 8, no 8,9
8a. 9 in R4 only in R4C12, locked for N4
9. 9 in C8 only in R67C8 -> 18(4) cage at R6C7 = {1269/1359/2349}, no 7,8
9a. 8 in N6 only in R5C89, locked for R5
10. 18(4) cage at R6C5 (step 5a) = {1278/2457}, 18(4) cage at R6C7 (step 9) = {1269/1359/2349}
10a. 9 in R6 only in R6C89
10b. 45 rule on R6 4 innies R6C5789 = 21 contains 9 = {1389/1479/2379/3459}
10c. 2 of {2379} must be in R6C5 -> no 2 in R6C78
10d. Consider combinations for R6C5789
R6C5789 = {1389/2379/3459} => 3 in R6C78 => 18(4) cage at R6C7 = {1359/2349}
or R6C5789 = {1479} = [4197] => 18(4) cage at R6C5 = 4{257}, 2 locked for N8 => 18(4) cage at R6C7 = {1359}
-> 18(4) cage at R6C7 = {1359/2349}, no 6
10e. 2 of {2349} must be in R7C6 -> no 4 in R7C6
10f. 2 of {2349} in R7C6 => R6C5 = 2 (hidden single in C5) => R6C5789 = [2397] -> no 4 in R6C78
10g. 4 of R6C5789 = {3459} must be in R6C5 -> no 5 in R6C5
11. 18(4) cage at R6C5 (step 5a) = {1278/2457}, R6C5789 (step 10b) = {1389/1479/2379/3459}
11a. Max R4C89 = 8 (step 8) -> R4C89 must contain at least one of 1,2,3
11b. Consider combinations for 17(3) cage at R3C6 (step 5d) = {278/458}
17(3) cage = {278} = [287], 8 placed for N5
or 17(3) cage = {278} = [827] => R4C89 must contain at least one of 1,3 => R6C5789 cannot be {1389) = 8{13}9
or 17(3) cage = {458} => 1,2 in C6 only in R5789C6 => R789C6 must contain at least one of 1,2 => 18(4) cage at R6C5 cannot be {1278} = 8{127}
-> no 8 in R6C5
11c. 18(4) cage at R6C5 = {2457} (only remaining combination), locked for C5, 5 also locked for N8
11d. 8 in N5 only in R4C56, locked for R4
11e. 1 in N8 only in R789C6, locked for C6
12. R12C7 + R3C1 + R4C12 (step 7) = 39
12a. Max R3C1 + R4C12 = 9 + 16 -> min R12C7 = 14, no 4 in R12C7
12b. Max R12C7 + R4C12 = 17 + 16 -> min R3C1 = 6
13. 17(3) cage at R3C6 (step 5d) = {278/458}
13a. R57C6 + R3567C7 = 16 (step 6)
13b. Consider combinations for R3567C7
R3567C7 = 10 = {1234}, locked for R7 => R34C6 = {28/48} => R57C6 cannot be [42]
or R3567C7 = 11,12,13 => R57C6 = 5,4,3 => no 2 in R7C6
-> no 2 in R7C6
13c. 18(4) cage at R6C7 (step 10d) = {1359} (only remaining combination), no 4 in R7C8
13d. 18(4) cage at R6C7 = {1359}, CPE no 5 in R45C8
14. R6C5789 (step 10b) = {1479/2379/3459}, 18(4) cage at R6C7 = {1359} -> R6C5789 + R7C68 = [4197][35]/[2397][15]/[4{35}9][19] -> no 3 in R7C8
15. 45 rule on N9 4 innies R7C89 + R89C7 = 27 = {5679} (only possible combination, cannot be {3789} because 18(4) cage at R8C6 cannot be {34}{38}, cannot be {4689} because 4,6,8 only in R89C7), locked for N9, 6 also locked for C7
16. 8 in R5 only in 18(4) cage at R5C6 = {1278/1458/2358} (cannot be {1368} because R5C6 only contains 2,4,5), no 6
16a. 6 in N6 only in R4C89, locked for R4 and 18(4) cage at R3C8, no 6 in R3C89
17. R12C7 = {89} (hidden pair in C7), locked for N3
17a. 45 rule on N3 4 innies R12C7 + R3C89 = 27, R12C7 = 17 -> R3C89 = 10 = [73]
17b. R3C89 = 10 -> R4C89 = 8 = {26}, locked for R4 and N6
18. 3,7 on D/ only in R6C4 and 18(5) cage at R7C3 -> 18(5) cage must contain at least one of 3,7 = {12348/12357}, no 6, 3 locked for N7
18a. 6 on D/ only in R1C9 + R2C8, locked for N3
19. 5,7 on D\ only in 18(5) cage at R1C1 and R4C4 -> 18(5) cage must contain at least one of 5,7 = {12357/12456}, no 8, 5 locked for N1
19a. 8 on D\ only in R8C8 + R9C9, locked for N9
20. 45 rule on N1 4 innies R12C3 + R3C12 = 27 = {4689} (only possible combination, cannot be {3789} because 18(4) cage at R1C3 cannot be {37}{35}), locked for N1
20a. 18(4) cage at R1C3 = {1368/1458/3456} (cannot be {2358} because R12C3 only contain 4,6,8) -> R12C4 = {13/15/35}, no 2,4
20b. R3C46 = {24} (hidden pair in N3), locked for R3
20c. 4 in N1 only in R12C3, locked for C3
20d. 5 in N2 only in R12C4, locked for C4
21. 17(3) cage at R3C6 (step 5d) = {278/458} -> R4C6 = 8, placed for D/, R4C7 = {57}
21a. Naked triple {567} in R489C7, locked for C7 -> R3C7 = 1, placed for D/, R3C3 = 5, R56C7 = [43], R7C7 = 2, placed for D\, R7C6 = 1
21b. Naked pair {59} in R67C8, locked for C8
21c. 1,2 in C3 only in R456C3, locked for N4
22. R5C6 = 5 (hidden single in C6)
22a. Naked pair {18} in R5C89, locked for R5
22b. Naked triple {246} in R124C8, locked for C8, 4 also locked for N3
23. 18(4) cage at R3C2 = {1278/1467/2349/2367} (cannot be {1269/1368} because 6,8,9 only in R3C2)
23a. 17(3) cage at R3C6 (step 5d) = {278/458} = [287/485]
23b. 18(4) cage = {1278/2349/2367} (cannot be {1467} = [64]{17} which clashes with 17(3) cage) -> R3C4 = 2, R3C6 = 4, R4C7 = 5 (cage sum)
23c. R5C3 = 2 (hidden single in R5)
24. R6C5 = 2 (hidden single in R6), R7C8 = 5 (hidden single in N9)
24a. 18(3) cage at R7C1 (step 4) = {468}, locked for N7, 4 also locked for R7
24b. 18(4) cage at R6C1 = {1458} (only possible combination) -> R6C3 = 1, R6C4 = 4, placed for D/
25. R12C7 + R3C1 + R4C12 = 39 (step 7)
25a. R12C7 = {89} = 17, R4C12 = {49} (hidden pair in R4) = 13 -> R3C1 = 9
26. R9C9 = 4 (hidden single on D\), R8C9 = 1, R9C8 = 3, R8C8 = 8, R8C3 = 6
26a. R7C35 = [37], R3C3 = 7, R3C2 = 6 (hidden single in N1) -> R4C4 = 3 (cage sum), placed for D\
and the rest is naked singles, without using the diagonals.