Prelims
a) R12C1 = {14/23}
b) R12C6 = {19/28/37/46}, no 5
c) R34C1 = {39/48/57}, no 1,2,6
d) R3C45 = {18/27/36/45}, no 9
e) R45C3 = {39/48/57}, no 1,2,6
f) R4C78 = {18/27/36/45}, no 9
g) R56C7 = {59/68}
h) R6C23 = {18/27/36/45}, no 9
i) R67C9 = {16/25/34}, no 7,8,9
j) R7C56 = {19/28/37/46}, no 5
k) R89C4 = {19/28/37/46}, no 5
l) R89C5 = {16/25/34}, no 7,8,9
m) R89C9 = {29/38/47/56}, no 1
n) 24(3) cage at R1C2 = {789}
o) 9(3) cage at R2C2 = {126/135/234}, no 7,8,9
p) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
q) 8(3) cage at R8C3 = {125/134}
r) 13(4) cage at R5C4 = {1237/1246/1345}, no 8,9
s) 27(4) cage at R7C2 = {3789/4689/5679}, no 1,2
Steps resulting from Prelims
1a. Naked triple {789} in 24(3) cage at R1C2, locked for R1, clean-up: no 1,2,3 in R2C6
1b. 8(3) cage at R8C3 = {125/134}, 1 locked for N7
1c. 27(4) cage at R7C2 = {3789/4689/5679}, 9 locked for N7
1d. 13(4) cage at R5C4 = {1237/1246/1345}, 1 locked for C4, clean-up: no 8 in R3C5, no 9 in R89C4
1e. 16(3) cage at R1C7 must contain one of 7,8,9 -> R2C7 = {789}
2. 5(2) cage at R1C1 + 9(3) cage at R2C2 = 14
2a. Min 5(2) cage + R23C2 = 10 -> max R4C2 = 4
[Alternatively 9(3) cage cannot be {12}6/{13}5 which clash with 5(2) cage, no 5,6 in R4C2]
2b. Max 5(2) cage + R23C2 = 13(4) must contain 1, locked for N1
2c. 9(3) cage at R2C2 = {126/135/234} -> R23C2 = {16/26/15/35/23} (cannot be {24/34} which clash with 5(2) cage), no 4 in R23C2
3. 45 rule on N3 2 innies R3C79 = 13 = {49/58/67}, no 1,2,3
4. 45 rule on N7 2 innies R7C13 = 10 = {37/46}/[82]
5. 45 rule on C1 3 outies R578C2 = 21 = {489/579/678}
5a. Killer triple 7,8,9 in R1C2 and R578C2, locked for C2, clean-up: no 1,2 in R6C3
5b. 1 in C3 only in R89C3, locked for N7
6. 45 rule on C9 3 outies R235C8 = 9 = {126/135/234}, no 7,8,9
6a. Hidden killer triple 7,8,9 in R2C7, R2C9 and R3C79 for N3, R2C7 = {789}, R3C789 contains one of 7,8,9 -> R2C9 = {789}
7. 45 rule on C1234 2 innies R34C4 = 12 = [39]/{48/57}, clean-up: no 3,7 in R3C5
8. 45 rule on C6789 2 innies R67C6 = 10 = {19/28/37/46}, no 5
9. 45 rule on R89 2 outies R7C27 = 1 innie R8C8 + 4, IOU no 4 in R7C2
10. 45 rule on C123 2 outies R12C4 = 1 innie R7C3 + 10
10a. Min R7C3 = 2 -> min R12C4 = 12, no 2 in R2C4
11. 45 rule on C789 2 outies R89C6 = 1 innie R3C7 + 8
11a. Min R3C7 = 4 -> min R89C6 = 12, no 1,2 in R89C6
12. 45 rule on N4 2 innies R4C12 = 1 outie R7C1 + 2, IOU no 2 in R4C2
13. 45 rule on N6 2 innies R6C89 = 1 outie R3C9 + 2, IOU no 2 in R6C8
14. 45 rule on C6789 1 outie R7C5 = 1 innie R6C6
14a. Whichever value is in R6C6 and R7C5 must be in R123C4, no 1,2 in R123C4 -> no 1,2 in R6C6 + R7C5, clean-up: no 8,9 in R7C6
14b. 9 in N8 only in R7C5 + R89C6 -> 9 in R689C6, locked for C6, clean-up: no 1 in R1C6
15. 45 rule on N8 3 innies R7C4 + R89C6 = 18
15a. 5 in N8 only in R7C4 + R89C6 = {459/567} or in R89C5 = {25} -> R7C4 + R89C6 cannot be {279} (locking-out cages) -> no 2 in R7C4
15b. 1 in N8 only in R7C4 + R89C6 = {189} or R7C56 = [91] or R89C5 = {16} -> R7C4 + R89C6 cannot be {369} (locking-out cages)
15c. R7C4 + R89C6 = 18 = {189/378/459/468/567}
16. 45 rule on N3689 2(1+1) innies R3C7 + R7C4 = 10 = [46/55/64/73/91], clean-up: no 5 in R3C9 (step 3)
16a. R7C4 + R89C6 (step 15c) = {189/378/459/468/567}
16b. 3 of {378} must be in R7C4 -> no 3 in R89C6
16c. Min R8C6 = 4 -> max R78C7 = 9, no 9 in R78C7
17. 45 rule on C89 3 innies R149C8 = 17 = {179/269/278/359/458/467} (cannot be {368} which clashes with R235C8)
17a. 1 of {179} must be in R1C8 -> no 1 in R49C8, clean-up: no 8 in R4C7
17b. 9 of {269/359} must be in R9C8, 2 of {278} must be in R1C8 -> no 2,3 in R9C8
18. 45 rule on N47 3(2+1) innies R4C12 + R7C3 = 12 = 5+7/6+6/8+4/9+3/10+2 -> R4C12 = [41/51/53/71/54/81/73/91] -> no 3 in R4C1, clean-up: no 9 in R3C1
18a. R7C13 (step 4) = {37/46}/[82]
18b. R4C12 + R7C13 = [5146/7164/8173/7382/9182] (cannot be [4137] which clashes with R12C1, cannot be [5364] which clashes with R45C3, cannot be [5473] which clashes with R34C1 = [57]) -> no 4 in R4C12, no 3 in R7C1, no 7 in R7C3, clean-up: no 8 in R3C1
18c. 9(3) cage at R2C2 = {126/135}
18d. R4C12 + R7C13 = [5146/7164/8173/9182] (cannot be [7382] because R34C1 = [75] clashes with 9(3) cage = {15}3) -> R4C2 = 1, clean-up: no 8 in R4C8, no 8 in R6C3
18e. 1 in N1 only in R12C1 = {14}, locked for C1 and N1, clean-up: no 8 in R4C1, no 6 in R7C3
18f. R4C12 + R7C13 = [7164/9182], clean-up: no 7 in R3C1
18g. 9(3) cage at R2C2 = {126} (only remaining combination, cannot be {35}1 which clashes with R3C1), 2,6 locked for C2 and N1, clean-up: no 3,7 in R6C3
[Now things get a lot easier.]
19. R578C2 (step 5) = {489/579}, 9 locked for C2
19a. 9 in N1 only in R123C3, locked for C3, clean-up: no 3 in R45C3
19b. R6C23 = [36] (cannot be {45} which clashes with R45C3), clean-up: no 8 in R5C7, no 4,7 in R7C6 (step 8) -> no 3,6 in R7C5, no 1,4 in R7C9
20. 17(3) cage at R2C3 = {359/368} (cannot be {458} which clashes with R45C3, cannot be {467} because 4,6 only in R2C4), no 4,7
20a. 7 in N1 only in R1C23, locked for R1
20b. R12C4 = R7C3 + 10 (step 10), R7C3 = {24} -> R12C4 = 12,14 = [93/95] (cannot be [86] which clashes with R34C4 + R89C4, killer ALS block) -> R1C4 = 9, clean-up: no 3 in R3C4 (step 7), no 6 in R3C5
20c. Naked pair {78} in R1C23, locked for N1
21. 13(4) cage at R5C4 = {1237/1246/1345}
21a. Variable hidden killer pair 2,6 in 13(4) cage and R89C4 for C4, R89C4 can only contain one of 2,6 -> 13(4) cage must contain at least one of 2,6 in C6 -> 13(4) cage = {1246} (only possible combination, cannot be {1237} which must have 2 in R7C3, cannot be {1345} which doesn’t contain 2 or 6), 6 locked for C4, clean-up: no 5,7 in R3C7 (step 16), no 6,8 in R3C9 (step 3), no 4 in R89C5
22. 2 in C1 only in 22(4) cage at R5C1 = {2569/2578} (cannot be {2479} because R7C1 only contains 6,8), no 4
22a. R7C1 = {68} -> no 8 in R5C12 + R6C1
22b. 8(3) cage at R8C3 = {125/134}
22c. R9C2 = {45} -> no 4,5 in R89C3
22d. R45C3 = {48} (hidden pair in N4), locked for C3 -> R1C23 = [87], R7C3 = 2, R7C1 = 8 (step 4), clean-up: no 8 in R6C6 (step 8), no 5 in R6C9
22e. Naked pair {13} in R89C3, locked for C3 and N7, R9C2 = 4 (cage sum), clean-up: no 3 in R8C5, no 7 in R8C9
22f. Naked pair {59} in R23C3, locked for N1 and 17(3) cage at R2C3 -> R2C4 = 3, R3C1 = 3 -> R4C1 = 9, clean-up: no 7 in R2C6, no 7 in R89C4
22g. R34C4 = {57} (hidden pair in C4), clean-up: no 1,5 in R3C5
23. R3C6 = 8 (hidden single in R3), clean-up: no 2 in R1C6
23a. Naked pair {46} in R12C6, locked for C6 and N2, R3C5 = 2 -> R3C4 = 7, R4C4 = 5, clean-up: no 6 in R3C7 (step 3), no 4 in R4C78
23b. Naked pair {15} in R12C5, locked for C5, clean-up: no 6 in R89C5
23c. R89C5 = [43], R7C6 = 1 -> R7C5 = 9, R6C5 = 9 (step 8), R7C4 = 6, clean-up: no 5 in R5C7, no 1 in R6C9
23d. R45C6 = {23} (hidden pair in C6), R3C6 = 8 -> R3C7 = 4 (cage sum), R3C9 = 9, clean-up: no 2,8 in R8C9, no 2,7 in R9C9
24. R7C8 = 4 (hidden single in R7) -> R68C8 = 15 = {78} (cannot be {69} because 6,9 only in R8C8), locked for C8, clean-up: no 2 in R4C7
24a. Naked pair {78} in R6C58, locked for R6, R6C7 = 5 -> R5C7 = 9, R6C1 = 2, R6C9 = 4 -> R7C9 = 3, clean-up: no 8 in R9C9
24b. Naked pair {56} in R89C9, locked for C9 and N9, R7C7 = 7, R8C6 = 5 -> R8C7 = 1 (cage sum), clean-up: no 2 in R4C8
24c. R2C7 = 8
24d. R3C8 = 1 (hidden single in R3), R1C9 = 2, R2C9 = 7 -> R2C8 = 6 (cage sum)
and the rest is naked singles.