Thanks Afmob for your comments and corrections.
Prelims
a) R34C4 = {49/58/67}, no 1,2,3
b) R34C6 = {18/27/36/45}, no 9
c) R45C1 = {13}
d) R45C5 = {69/78}
e) R45C9 = {19/28/37/46}, no 5
f) R67C1 = {17/26/35}, no 4,8,9
g) R67C5 = {17/26/35}, no 4,8,9
h) R67C9 = {69/78}
i) R78C2 = {15/24}
j) R78C8 = {15/24}
k) R89C5 = {16/25/34}, no 7,8,9
l) R9C45 = {29/38/47/56}, no 1
m) R9C67 = {18/27/36/45}, no 9
n) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
o) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
1. Naked pair {13} in R45C1, locked for C1 and N4, clean-up: no 5,7 in R67C1
1a. Naked pair {26} in R67C1, locked for C1
2. 45 rule on C1234 1 innie R2C4 = 1, clean-up: no 8 in R4C6
3. 45 rule on C6789 1 innie R2C6 = 5, clean-up: no 4 in R34C6, no 8 in R4C4, no 4 in R9C7
4. 45 rule on C5 3 innies R123C5 = 15 = {249/348} (cannot be {267} which clashes with R45C5), no 6,7, 4 locked for C5 and N2, clean-up: no 9 in R4C4, no 3 in R89C5
5. R67C5 = {17/35} (cannot be {26} which clashes with R89C5), no 2,6
6. 45 rule on C12 2 outies R67C3 = 10 = {28/46}/[73/91], no 5, no 7,9 in R7C3
6a. 45 rule on C12 2 innies R56C2 = 13 = {49/58/67}, no 2
7. 45 rule on C89 2 outies R67C7 = 16 = {79}, locked for C7 and 24(4) cage at R5C8, no 7,9 in R56C8, clean-up: no 2 in R9C6
7a. 45 rule on C89 2 innies R56C8 = 8 = {26/35}
7b. Killer pair 2,5 in R56C8 and R78C8, locked for C8
7c. 1 in R6 only in R6C56, locked for N5, clean-up: no 8 in R3C6
8. 45 rule on R1234 3 innies R4C159 = 16 = {169/178/349/367} (cannot be {268} because R4C1 only contains 1,3), no 2, clean-up: no 8 in R5C9
8a. R4C1 = {13} -> no 1,3 in R4C9, clean-up: no 7,9 in R5C9
9. 45 rule on R1234 3 outies R5C159 = 13 = {139/148/238/346} (cannot be {247} because R5C1 only contains 1,3), no 7, clean-up: no 8 in R4C5
9a. 4 of {346} must be in R5C9 -> no 6 in R5C9, clean-up: no 4 in R4C9
10. 45 rule on N9 4 innies R789C7 + R7C9 = 26 = {2789/3689/4679/5678}, no 1, clean-up: no 8 in R9C6
11. 17(3) cage at R7C6 = {269/278/359/368/458/467} (cannot be {179} because no 1,7,9 in R8C7), no 1
11a. 5 of {458} must be in R8C7, 4 of {467} must be in R78C6 (R78C6 cannot be {67} which clashes with R34C6) -> no 4 in R8C7
11b. R789C7 + R7C9 (step 10) = {2789/3689/5678}, 8 locked for N9
12. 45 rule on R89 4 outies R7C2468 = 17 = {1259/1349/1358/1457/2348/2357} (cannot be {1268/2456} which clash with R7C1, cannot be {1367} because two of 1,2,4,5 are required in R7C28), no 6 in R7C46
13. R56C2 (step 6a) = {49/58/67}, R67C3 (step 6) = {28/46}/[73/91],
13a. 23(4) cage at R5C2 cannot be {58}{46} which clashes with R7C1 + R78C2, no 4,6 in R67C3
14. 4 in R7 only in R7C2468 (step 12) = {1349/1457/2348}
14a. 3,8 of {2348} must be in R7C46 -> no 2 in R7C46
14b. 3 must be in R7C46 + R7C5, locked for R7 and N8, clean-up: no 7 in R6C3 (step 6), no 8 in R9C3, no 6 in R9C7
14c. 1 must be in R7C28 + R7C3, locked for R7, clean-up: no 7 in R6C5
15. R789C7 + R7C9 (step 11) = {2789/3689/5678}
15a. 6 of {5678} must be in R8C7 (R7C79 cannot be [76] which would put two 9s in R6C79), no 5 in R8C7
15b. 6 of {3689} must be in R7C9 (R7C79 cannot be [98] which would put two 7s in R6C79)
15c. 17(3) cage at R7C6 (step 11) = {269/278/368} (cannot be {467} = {47}6 which clashes with R9C67 = [45] because 6 in R8C7 must be part of R789C7 + R7C9 = {5678}, steps 15a and 15b), no 4 in R78C6
15d. 9 of {269} must be in R7C6 -> no 9 in R8C6
[I ought to have spotted this after step 14.]
16. R7C2468 (step 14) = {1349/1457/2348}
16a. Hidden killer pair 3,5 in R7C2468 and R7C5 for R7, R7C2468 contains one of 3,5 -> R7C5 = {35}, clean-up: no 1 in R6C5
16b. Naked pair {35} in R67C5, locked for C5, clean-up: no 2 in R89C5
16c. Naked pair {16} in R89C5, locked for C5 and N8, clean-up: no 9 in R45C5, no 5 in R9C3, no 3,8 in R9C7
17. R45C8 = [78], clean-up: no 6 in R3C4, no 2 in R3C6, no 3 in R5C9, no 5 in R6C2 (step 6a)
17a. Naked triple {249} in R123C5, locked for N2, clean-up: no 4 in R4C4
17b. R4C159 (step 8) contains 7 = {178/367} -> R4C9 = {68}, clean-up: no 1 in R5C9
17c. Killer pair 6,8 in R4C9 and R67C9, locked for C9
17d. R56C8 (step 7a) = {35} (cannot be {26} which clashes with R45C9), locked for C8 and N6, clean-up: no 1 in R78C8
17e. Naked pair {24} in R78C8, locked for C8 and N9 -> R9C7 = 5, R9C6 = 4, clean-up: no 6,7 in R9C3, no 7 in R9C4
18. R6C6 = 1 (hidden single in R6) -> R5C67 = 11 = [92], R5C9 = 4 -> R4C9 = 6, R4C4 = 5 -> R3C4 = 8, R67C5 = [35], R4C6 = 2 -> R3C6 = 7, R56C4 = [64], R5C3 = 5 (cage sum), R5C2 = 7, R6C2 = 6 (step 6a), R67C1 = [26], R1C46 = [36], R78C6 = [38], R8C7 = 6
[Routine clean-ups omitted.]
19. R7C2468 (step 14) = {1349} (only remaining combination) -> R7C4 = 9, R7C2 = 1 -> R8C2 = 5, R78C8 = [42], R9C4 = 2, R8C4 = 7, R8C3 = 3 (cage sum)
20. R7C79 = [78] -> R6C79 = [97], R67C3 = [82], R9C3 = 9, R8C1 = 4, R4C3 = 4, R4C2 = 9, R3C1 = 5, R3C2 = 2 (cage sum)
[Steps 20 and 21 simplified and combined; step 22 deleted, Afmob pointed out that it’s naked singles after my original step 21.]
and the rest is naked singles.
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