Prelims
a) R1C12 = {59/68}
b) R56C1 = {29/38/47/56}, no 1
c) R56C2 = {39/48/57}, no 1,2,6
d) R7C12 = {39/48/57}, no 1,2,6
e) R89C3 = {69/78}
f) R8C45 = {29/38/47/56}, no 1
g) R89C9 = {59/68}
h) R9C45 = {29/38/47/56}, no 1
i) 20(3) cage at R2C6 = {389/479/569/578}, no 1,2
j) 22(3) cage at R4C7 = {589/679}
k) 10(3) cage at R5C8 = {127/136/145/235}, no 8,9
l) 14(4) cage at R3C2 = {1238/1247/1256/1346/2345}, no 9
m) 14(4) cage at R6C7 = {1238/1247/1256/1346/2345}, no 9
n) 26(4) cage at R2C7 = {2789/3689/4589/4679/5678}, no 1
1a. 45 rule on N7 1 innie R7C3 = 2
1b. 45 rule on C12 1 innie R3C2 = 2
1c. 45 rule on R89 1 innie R8C7 = 3, clean-up: no 8 in R8C45
1d. 14(4) cage at R6C7 = {1238/1346/2345}, no 7
1e. 2 of {1238/2345} only in R6C7 -> no 5,8 in R6C7
1f. 22(3) cage at R4C7 = {589/679}, 9 locked for N6
1g. 2 in N9 only in R8C8 + R9C78, locked for 20(5) cage at R8C6
1h. 2 in N8 only in R8C45 = {29} or R9C45 = {29}, 9 locked for N8 (locking cages)
2a. 45 rule on N2 3 innies R1C6 + R23C4 = 11 = {128/137/146/236/245}, no 9
2b. 45 rule on N3 2 outies R1C6 + R4C9 = 11 = {38/47/56}, no 1,2
2c. 30(7) cage at R1C6 = {1234569/1234578}, 2 locked for N3
2d. 5,6 of {1234569} must be in R1C6 + R4C9, otherwise clash with 26(4) at R2C7 = {5678}, no 6 in {1234578} -> no 6 in R1C789 + R23C9
2e. 6 in N3 only in 26(4) cage = {3689/4679/5678}
[Alternatively whatever pair are in R1C6 + R4C9 must be in 26(4) cage with the remaining two numbers in that cage totalling 15 -> 26(4) cage cannot be {4589}.]
3a. 45 rule on N6789 2 outies R56C3 = 1 innie R4C9
3b. Min R56C3 = 4 -> min R4C9 = 4, clean-up: no 8 in R1C6 (step 2b)
3c. Max R56C3 = 8, no 8,9 in R56C3
3d. Max R56C3 = 8, R7C3 = 2 -> min R7C45 = 12, no 1,3 in R7C45
3e. 3 in R7 only in R7C12 = {39}, locked for N7, 9 locked for R7, clean-up: no 6 in R89C3
3f. Naked pair {78} in R89C3, locked for C3 and N7
3g. R56C2 = {48/57} (cannot be {39} which clashes with R7C2), no 3,9
3h. R56C1 = {29/38/56} (cannot be {47} which clashes with R56C2), no 4,7
3i. 1 in N8 only in R789C6, locked for C6
3j. 45 rule on N6 3 innies R4C9 + R6C78 = 13 = {148/238/247/346} (cannot be {157/256} which clash with 22(3) cage at R4C7), no 5, clean-up: no 6 in R1C6 (step 2b)
3k. 3 of {346} must be in R6C8 -> no 6 in R6C8
3l. R1C6 + R23C4 (step 2a) = {137/146/236/245} (cannot be {128} because R1C6 only contains 3,4,5,7), no 8
3m. 45 rule on N6 5 outies R7C6789 + R8C7 = 1 innie R4C9 + 14
3n. Min R7C6789 = {1456} = 16, R8C7 = 3 -> no 4 in R4C9, clean-up: no 7 in R1C6 (step 2b)
3o. R4C9 + R6C78 = {148/238/247/346}
3p. R4C9 = {678} -> no 6,7,8 in R6C78
3q. R1C6 + R23C4 = {137/146/236/245}
3r. 3 of {137/236} must be in R1C6 -> no 3 in R23C4
3s. Consider permutations for R1C6 + R4C9 (step 2b) = [38/47/56]
R1C6 + R4C9 = [38] => 3 in N3 only in R23C8 => R4C9 + R6C78 = {148}
or R1C6 + R4C9 = [47] => R4C9 + R6C78 = {247}
or R1C6 + R4C9 = [56] => R4C9 + R6C78 = {346}
-> R4C9 + R6C78 = {148/247/346}, 4 locked for R6 and N6, clean-up: no 8 in R5C2
4a. 45 rule on C789 4 outies R1789C6 = 14 = {1346}, 3,4,6 locked for C6, 6 locked for N8, clean-up: no 6 in R4C9 (step 2b), no 5 in R8C45, no 5 in R9C45
4b. 5 in N8 only in R7C45, locked for R7 and 22(5) cage at R5C3
4c. 22(5) cage at R5C3 = {12568/23458}, 8 locked for R7 and N8, clean-up: no 3 in R9C45
4d. Naked quad {2479} in R89C45, 4,7 locked for N8
4e. R19C6 = [43] (hidden pair in C6) -> R4C9 = 7 (step 2b), clean-up: no 6 in 22(3) cage at R4C7
4f. Naked triple {589} in 22(3) cage, 5 locked for N6
4g. 10(3) cage at R5C8 = {136} (only remaining cage), 1,3 locked for N6
4h. R7C9 = 4 (hidden single in C9) -> R6C78 = [42], R7C8 = 7 (cage total/hidden single in R7), clean-up: no 9 in R5C1
4i. 4,6,7 in N3 only in 26(4) cage at R2C7 = {4679}, 9 locked for N3
4j. R9C7 = 2 (hidden single in N9), clean-up: no 9 in R9C45
4k. Naked pair {47} in R9C45, locked for R9 and N8 -> R89C3 = [78]
4l. Naked pair {29} in R8C45, 9 locked for R8
4m. R9C9 = 9 (hidden single in C9), R8C9 = 5
4n. R8C8 = 8 (hidden single in N9)
4o. 5 in N3 only in R1C78, locked for R1, clean-up: no 9 in R1C12
4p. Naked pair {68} in R1C12, locked for R1 and N1
4q. 9 in C3 only in R12C3, locked for N1
4r. 16(3) cage at R1C3 = {169/259} (cannot be {349} because no 3,4,9 in R2C4), no 3,4,7
4s. 2,6 only in R2C4 -> R2C4 = {26}
4t. R1C6 + R23C4 = 11 (step 2a), R1C6 = 4 => R23C4 = 7 = [25/61]
4u. 7 in R1 only in R1C45, locked for N2
4v. 14(3) cage at R1C4 = {167/257}, no 3,8,9
4w. 5,6 only in R2C5 -> R2C5 = {56}
4x. R3C5 = 3 (hidden single in N2), R23C6 = {89} (hidden pair in N2), locked for C6
4y. Naked triple {257} in R456C6, locked for N5
4z. R1C3 = 9 (hidden single in R1)
5a. 22(4) cage at R4C5 contains 2 and one of 2,5,7 in R45C6 = {2479/2569} (cannot be {2578} because 2,5,7 only in R45C6) -> R45C5 = {49/69}, 9 locked for C5 and N5
5b. R8C45 = [92]
6a. R7C3 = 2, R7C45 = {58} = 13 -> R56C3 = 7 = [16/43/61], no 3 in R5C3
6b. 45 rule on N4 3 remaining innies R4C123 = 15 = {168/348} (cannot be {159} which clashes with R4C8, cannot be {258} which clashes with R4C6, cannot be {456} which clashes with R56C2, cannot be {249} which clashes with R4C68, ALS block), 8 locked for R4 and N4, clean-up: no 3 in R56C1, no 4 in R5C2
6c. Naked pair {57} in R56C2, locked for C2, 5 locked for N4, clean-up: no 6 in R56C1
6d. R56C1 = [29] -> R7C12 = [39]
6e. Naked pair {59} in R4C78, locked for R4 and N6 -> R4C6 = 2, R5C7 = 8
6f. R9C1 = 5 (hidden single in N7)
6f. 6 in C3 only in R456C3, locked for N4
7a. Consider placements for R2C5 = {56}
R2C5 = 5 => R3C24 = [21] = 3 => R34C3 = 11 = [56]
or R2C5 = 6, R4C5 = 4 => R5C3 = 4 (hidden single in R5)
-> no 4 in R3C3
7b. R3C2 = 2, R3C34 = {15} -> R4C3 = 6 (cage sum)
7c. Naked pair {15} in R23C3, 1 locked for C3 and N1
7d. R4C5 = 4, R9C45 = [47], R1C5 = 1, R3C45 = [15], R2C345 = [526]
7e. R4C56 = [42] = 6, R5C5 = 9 -> R5C6 = 7 (cage sum)
and the rest is naked singles.