Prelims
a) R1C34 = {29/38/47/56}, no 1
b) R1C89 = {49/58/67}, no 1,2,3
c) R2C45 = {17/26/35}, no 4,8,9
d) R23C6 = {39/48/57}, no 1,2,6
e) R23C9 = {16/25/34}, no 7,8,9
f) R34C1 = {16/25/34}, no 7,8,9
g) R3C78 = {16/25/34}, no 7,8,9
h) R4C23 = {39/48/57}, no 1,2,6
i) R56C1 = {39/48/57}, no 1,2,6
j) R56C2 = {19/28/37/46}, no 5
k) R89C1 = {19/28/37/46}, no 5
l) 19(3) cage at R8C2 = {289/379/469/478/568}, no 1
m) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9
1a. 45 rule on N1 2 innies R1C3 + R3C1 = 12 = [75/84/93] -> R1C4 = {234}, R4C1 = {234}
1b. Hidden killer quad 6,7,8,9 in R4C23, R56C1, R56C2 and R56C3 for N4, R4C23, R56C1 and R56C2 must each contain one of 6,7,8,9 -> R56C3 must contain at least one of 6,7,8,9
1c. 45 rule on N14 3 innies R1C3 + R56C3 = 16 = {169/178/268/367} (cannot be {259/349/358/347} because R1C3 = {789} and R56C3 must contain one of 6,7,8,9), no 4,5 in R56C3
1d. 5 in N4 only in R4C23 = {57} or R56C1 = {57} (locking cages), 7 locked for N4, clean-up: no 3 in R56C2
2a. 45 rule on N3 2 outies R1C56 = 6 = {15/24}
2b. Killer triple 4,5,6 in R1C89, R23C9 and R3C78, locked for N3
2c. R2C45 = {17/26} (cannot be {35} which clashes with R1C56 + R23C6), no 3,5
2d. Killer pair 1,2 in R1C56 and R2C45, locked for N2, clean-up: no 9 in R1C3, no 3 in R3C1 (step 1a), no 4 in R4C1
2e. R1C3 + R56C3 (step 1c) = {178/268/367} (cannot be {169} because R1C3 only contains 7,8), no 9
2f. Killer triple 3,4,5 in R1C4, R1C56 and R23C6, locked for N2
3a. R1C34 = [74/83], R1C89 = {49/58/67} -> combined cage R1C34 + R1C89 = [83]{49}/[83]{67} (cannot be [74]{58} which clashes with R1C56) -> R1C34 = [83], R3C1 = 4 (step 1a), R4C1 = 3, clean-up: no 5 in R1C89, no 8,9 in R2C6, no 3 in R2C9, no 9 in R3C6, no 3 in R3C78, no 4,9 in R4C2, no 9 in R4C3, no 8,9 in R56C1, no 6,7 in R89C1
3b. Naked pair {57} in R56C1, locked for C1 and N4 -> R4C23 = [84], clean-up: no 2,6 in R56C2
3c. Naked pair {19} in R56C2, locked for C2, 1 locked for N4
3d. Naked pair {26} in R56C3, locked for C3 and 21(5) cage at R5C3
3e. 6 in N7 only in 19(3) cage at R8C2 = {469} -> R9C3 = 9, R89C2 = {46}, locked for C2, clean-up: no 1 in R89C1
3f. Naked pair {28} in R89C1, locked for C1 -> R7C1 = 1
3g. R56C3 = {26}, R7C1 = 1 -> R7C24 = 12 = [39/57/75], no 4,8
3h. Combined half cage R7C234 = [359/379/537/735], 3 locked for R7 and N7
3i. 29(5) cage at R7C3 = {23789/25679/34589/34679/35678} (cannot be {14789/15689/24689} because R78C3 must contain two of 3,5,7), no 1
3j. 29(5) cage = {23789/34589/35678} (cannot be {25679} because R78C3 = {57} so R8C5 + R9C45 = {269} clashes with R7C234 = [359/379], cannot be {34679} which clashes with R9C2), 8 locked for N8
3k. 9 of {23789/34589} must be in R8C5 -> no 2,4 in R8C5
4a. 9 in N2 only in R3C45, min R3C45 = {69} = 15 -> max R45C4 = 7, no 7,8,9 in R45C4
4b. Killer pair 6,9 in R1C1 and R1C89, locked for R1
4c. 45 rule on N3 3 innies R1C7 + R7C78 = 18 = {189/378} (cannot be {279} which clashes with R1C89), no 2
4d. R1C7 = {17} -> no 1,7 in R2C78
5a. 45 rule on N9 4(2+2) outies R56C8 + R79C6 = 11
5b. Min R56C8 = 3 -> max R79C6 = 8, no 9 in R7C6, no 7 in R9C6
5c. Min R79C6 = 3 -> max R56C8 = 8, no 8,9 in R56C8
5d. 45 rule on N9 2 innies R7C79 = 1 outie R9C6 + 11
5e. R7C234 (step 3h) = [359/379/537/735]
5e. Min R56C8 + R7C6 = 6 -> max R7C79 = 15 (cannot be {79} which clashes with R7C234) -> max R9C6 = 4
5f. Min R7C79 = 12, no 2 in R7C79
5g. 2 in R7 only in R7C568, CPE no 2 in R9C6
6a. R1C56 (step 2a) = {15/24}, R23C6 = [48/57/75]
6b. R2C45 = {26} (cannot be {17} which clashes with R1C56 + R23C6), locked for R2 and N2 -> R12C1 = [69], clean-up: no 4 in R1C56, no 7 in R1C89, no 1,5 in R3C9
6c. R2C6 = 4 (hidden single in N2) -> R3C6 = 8, clean-up: no 3 in R3C9
6d. Naked pair {15} in R1C56, locked for R1 -> R1C27 = [27]
6e. Naked pair {38} in R2C78, 3 locked for R2
6f. Naked pair {79} in R3C45, 7 locked for R3
6g. R3C45 = {79} = 16 -> R45C4 = 6 = [15/24/51]
7a. R7C234 (step 3h) = [359/379/537/735]
7b. R9C6 = {13} -> R7C79 (step 5d) = 12,14 = {48/68} (cannot by {57/59} which clash with R7C234), no 5,7,9, 8 locked for N9
7c. 9 in N9 only in 23(5) cage at R7C8 = {12569/23459} (cannot be {12479} which clashes with R7C79 + R9C6 = {48}1, cannot be {13469} which clashes with R7C79), no 7
7d. 7 in N9 only in 11(3) cage at R8C9 = {137}, 1,3 locked for N9
7e. Naked pair {137} in R9C689, 3,7 locked for R9, 7 locked for N9
7f. 22(5) cage at R5C8 = {12478/12568/13468/23458}
7g. 4 of {12478/23458} must be in R7C79, 1,3 of {13468} must be in R56C8 -> no 4,6 in R56C8
8a. 8 in N8 only in R8C5 + R9C45
8b. 45 rule on N5689, R45C4 = 6 (step 6g) -> 4 remaining innies R7C4 + R8C5 + R9C45 = 26 = {3689/4589/5678} (cannot be {2789} because R9C45 = {28} clashes with R9C1), no 2
9a. R7C79 = R9C6 + 11 (step 5d)
9b. Consider combinations for 22(5) cage at R5C8 (step 7f) = {12478/12568/13468/23458}
22(5) cage = {12478/12568/13468}, 1 locked for C8 => 1 in N9 only in R89C9
or 22(5) cage = {23458} => R7C79 = {48} => R9C6 = 1 => R8C9 = 1 (hidden single in N9)
-> 1 in R89C9, locked for C9 and N9 -> R2C9 = 5, R3C9 = 2, R2C23 = [71], clean-up: no 5 in R7C4 (step 3g)
9c. Naked pair {79} in R37C4, locked for C4
9d. 7 in C3 only in R78C3, locked for 29(5) cage at R7C3
9e. 29(5) cage at R7C3 (step 3j) = {35678}, no 4,9, 6 locked for N8
9f. 6 in R7 only in R7C789, locked for N9
10a. 19(4) cage at R4C8 = {1369/2368/2467} (cannot be {1279/1459/1567/2359/2458} because 1,2,5 only in R4C8, cannot be {1378/3457} which clashes with R89C9, ALS block, cannot be {1468} which clashes with R7C9)
10b. 1,2 only in R4C8 -> R4C8 = {12}
10c. 19(4) cage = {1369/2368/2467}, 6 locked for C9 and N6
11a. 45 rule on N78 using R7C124 = 13 (step 3g), 2 remaining innies R79C6 = 1 outie R6C5 + 1
11b. R79C6 cannot total 2,4,7,9 -> no 1,3,6,8 in R6C5
11c. 18(4) cage at R6C5 = {2349/2457} (cannot be {1359} which clashes with R9C6), no 1
11d. R9C6 = 1 (hidden single in N8) -> R1C56 = [15], R7C79 (step 5d) = 12 = {48}, 4 locked for R7 and N9
11e. R9C6 = 1 -> R6C5 = R7C9 = {27}
11f. R9C2 = 4 (hidden single in R9) -> R8C2 = 6
11g. R8C4 = 4 (hidden single in R8) -> R45C4 (step 6g) = {15}, locked for N5
11h. R8C4 = 4 -> 18(4) cage = {2457} -> R7C5 = 5, R8C6 = {27}
11i. Naked pair {27} in R78C6, locked for C6, 7 locked for N8 -> R7C4 = 9, R7C2 = 3, R78C3 = [75], R7C6 = 2, R8C6 = 7 -> R6C5 = 2, R2C45 = [26], R9C45 = [68], R8C5 = 3, R3C45 = [79]
11j. R45C5 = [74], R6C4 = 8 -> R6C67 = 12 = {39}, locked for R6
11k. R6C9 = 4 (hidden single in R6), R17C9 = [98], R4C9 = 6 -> R4C8 + R5C9 = 9 = [27]
11l. R7C679 = [248] -> R56C8 = 8 = [35]
and the rest is naked singles.