Prelims
a) R1C34 = {49/58/67}, no 1,2,3
b) R1C67 = {17/26/35}, no 4,8,9
c) R34C1 = {13}
d) R34C9 = {39/48/57}, no 1,2,6
e) R67C1 = {49/58/67}, no 1,2,3
f) R67C9 = {59/68}
g) R9C34 = {19/28/37/46}, no 5
h) R9C67 = {49/58/67}, no 1,2,3
i) 11(3) cage at R6C3 = {128/137/146/236/245}, no 9
j) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
k) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9
l) 45 cage at R3C5 = {123456789}
1a. Naked pair {13} in R34C1, locked for C1
1b. Min R12C1 = 6 -> max R1C2 = 7
2a. 45 rule on N1 2 innies R1C3 + R3C1 = 7 = [43/61] -> R1C4 = {79}
2b. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = [39/57/75] -> R1C6 = {135}, R4C9 = {357}
2c. R67C9 = {68} (cannot be {59} which clashes with R34C9)
2d. 45 rule on N9 2 innies R7C9 + R9C7 = 17 = [89] -> R6C9 = 6, R9C6 = 4
2e. 45 rule on N7 2 outies R6C1 + R9C4 = 17 = [98] -> R7C1 = 4, R9C3 = 2
2f. 19(3) cage at R8C1 = {568} (only remaining combination) -> R8C1 = 8, R9C12 = {56}, locked for R9 and N7
2g. 11(3) cage at R8C9 = {137} (only remaining combination, cannot be {245} because 2,4,5 only in R8C9), locked for N9
2h. Killer triple 1,3,7 in R34C9 and R89C9, locked for C9, 1 locked for N9
2i. 14(3) cage at R1C8 = {149/239/248/257} (cannot be {158/167/347/356} because 1,3,6,7,8 only in R1C8), no 6
2j. 1,3,7,8 only in R1C8 -> R1C8 = {1378}
2k. Combined half-cage R1C67 + R3C9 = [175/357/539] -> no 5 in R1C9
2l. 13(3) cage at R1C1 = {157/247/256} (cannot be {346} which clashes with R1C3), no 3
2m. 1,4 of {157/247} must be in R1C2 -> no 7 in R1C2
3a. 45 rule on R89 4 outies R7C2378 = 15 = {1257/1356} (cannot be {1239} because 1,3,9 only in R7C23) -> R7C23 = {13/17}, 1 locked for R7 and N7, R7C78 = {25/56}, 5 locked for R7 and N9
3b. 45 rule on N8 3 remaining innies R7C456 = 18 = {279/369}, 9 locked for N8
3c. 9 in R7 only in R7C56, CPE no 9 in R5C6
3d. 45 rule on R12 4 outies R3C2378 = 26 = {2789/3689/4589/4679/5678}, no 1
3e. 9 in C3 only in R238C3
3f. 45 rule on C12 4 outies R2378C3 = 20 contains 9 = {1379} (cannot be {1469} which clashes with R1C3), 1,3,7 locked for C3
3g. 5,8 in C3 only in R456C3, locked for N4
3h. 8 in N1 only in 25(4) cage at R2C2, R23C3 both odd -> one of R23C2 must be odd -> no 2,4,6 in R23C2
3i. 25(4) cage = {1789/3589}
3j. Killer pair 1,3 in 25(4) cage and R3C1, locked for N1
3k. 4 in N1 only in R1C23, locked for R1
3l. 13(3) cage at R1C1 (step 2l) = {247/256}
3m. 7 of {247} must be in R2C1 (R1C12 cannot be [74] which clashes with R1C34) -> no 7 in R1C1
3n. 7 in C1 only in 13(3) cage = [247] or in R5C1 -> no 2 in R5C1 (blocking cage)
3o. 2 in C1 only in R12C1, locked for N1
3p. 45 rule on C1 2 outies R19C2 = 1 innie R5C1 + 4
3q. R5C1 = {67} -> R19C2 = 10,11 = [46]/{56}, 6 locked for C2
4a. 11(3) cage at R6C3 = {128/146/245} (cannot be {137/236} because R6C3 only contains 4,5,8), no 3,7
4b. R7C4 = {26} -> no 2 in R6C4
4c. Naked triple {256} in R7C467, locked for R7
4d. 18(3) cage at R6C6 = {189/279/378/459}
4e. 4 of {459} must be in R6C7 -> no 5 in R6C7
4f. 13(3) cage at R3C4 = {148/157/238/247/256/346} (cannot be {139} because no 1,3,9 in R4C3), no 9
4g. 13(3) cage = {148/157/238/256/346} (cannot be {247} which clashes with R1C34)
4h. 13(3) cage = {148/238/256/346} (cannot be {157} which combined with 11(3) cage = [452] clashes with R1C34), no 7
4i. 5 of {256} must be in R34C4 (R34C4 cannot be {26} which clashes with R7C4) -> no 5 in R4C3
4j. 13(3) cage = {148/238/346} (cannot be {256} which combined with 11(3) cage = [416] clashes with R1C34), no 5
4k. 5 in C3 only in R56C3, CPE no 5 in R6C5
[Just spotted, but with hindsight step 5b could have been used after step 3k, which may have simplified my solving path but I'm happy to leave step 4 unchanged.]
5a. R1C3 + R3C1 (step 2a) = [43/61], R1C34 = [49/67], R1C67 = [17]/{35}, R1C7 + R3C9 (step 2b) = [39/57/75]
5b. Consider placement for 1 in N3
R1C8 = 1 => R1C67 = {35}
or 1 in R2C78 => R3C1 = 1 (hidden single in N1) => R1C3 = 6, R1C4 = 7 => R1C67 = {35}
-> R1C67 = {35}, locked for R1, clean-up: no 5 in R3C9, no 7 in R4C9
5c. Naked triple {246} in R1C123, 2,6 locked for R1 and N1
5d. R1C9 = 9 -> R3C9 = 7, R4C9 = 5, R1C7 = 5, R1C6 = 3, R1C4 = 7 -> R1C3 = 6, R3C1 = 1, R4C1 = 3, R1C12 = [24] -> R2C1 = 7 (cage sum), R5C1 = 6
5e. Naked pair {39} in R23C3, locked for C3 and N1 -> R78C3 = [17], R78C2 = [39]
5f. R7C456 (step 3b) = 18, R7C56 = {79} = 16 -> R7C4 = 2 (cage sum), R7C78 = [65]
5g. R1C9 = 9 -> R1C8 + R2C9 = 5 = [14]
5h. R9C8 = 7 (hidden single in N9)
5i. R5C9 = 2 -> R456C8 = 20 = {389} (only remaining combination), 3,8 locked for C8 and N6
5j. R1C5 = 8, 1 in N2 only in R2C456 -> 24(4) cage at R1C5 = {1689} (only possible combination), 6,9 locked for R2 and N2
5k. R3C4 = 4, R4C3 = 8 -> R4C4 = 1 (cage sum), R6C34 = [45], R5C3 = 5 -> R3C5 = 2
5l. Naked quad {3479} in R5C4 + R567C5, locked for 45(9) cage at R3C5
and the rest is naked singles.
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