Prelims
a) R12C4 = {69/78}
b) R23C1 = {17/26/35}, no 4,8,9
c) R2C23 = {18/27/36/45}, no 9
d) R23C7 = {18/27/36/45}, no 9
e) R45C4 = {16/25/34}, no 7,8,9
f) R56C6 = {49/58/67}, no 1,2,3
g) R78C3 = {12}
h) R78C9 = {19/28/37/46}, no 5
i) R89C6 = {49/58/67}, no 1,2,3
j) R8C78 = {39/48/57}, no 1,2,6
k) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
l) 9(3) cage at R1C5 = {126/135/234}, no 7,8,9
m) 24(3) cage at R2C9 = {789}
n) 11(3) cage at R3C4 = {128/137/146/236/245}, no 9
1a. Naked pair {12} in R78C3, locked for C3 and N7, clean-up: no 7,8 in R2C2
1b. Naked triple {789} in 24(3) cage at R2C9, locked for N3, clean-up: no 1,2 in R23C7
1c. 45 rule on N1 2 outies R45C3 = 13 = {49/58/67}, no 3
1d. 45 rule on N1 2 innies R3C23 = 9 = [18/27]/{36/45}, no 9, no 7,8 in R3C2
1e. 9 in N1 only in 19(3) cage at R1C1 = {289/379/469}, no 5, 9 locked for R1, clean-up: no 6 in R2C4
1f. 9(3) cage at R1C5 = {126/135} (cannot be {234} which clashes with 19(3) cage), no 4, 1 locked for R1
1g. 9 in R3 only in R3C89, locked for N3
1h. 45 rule on N6 2 innies R56C7 = 10 = {19/28/37/46}, no 5
1i. 45 rule on N6 2 outies R7C78 = 10 = {19/28/37/46}, no 5
1j. 45 rule on N3 2 outies R2C56 = 1 innie R1C7 + 10, min R2C56 = 11, no 1 in R2C56
1k. 45 rule on R89 3 innies R8C139 = 10 = {127/136/145/235}, no 8,9, clean-up: no 1,2 in R7C9
1l. 5 of {145} must be in R8C1 -> no 4 in R8C1
2a. 19(3) cage at R1C1 (step 1e) = {289/379/469}
2b. Consider combinations for R12C4 = [69]/{78}
R12C4 = [69]
or R12C4 = {78}, naked pair {78} in R2C49, locked for R2 => R2C23 = {36/45} => 19(3) cage = {289/379} (cannot be {469} which clashes with R2C23)
-> 19(3) cage = {289/379}, no 4,6
2c. 4 in R1 only in R1C89, locked for N3 and 29(5) disjoint cage at R1C8, clean-up: no 5 in R23C7 (step 1d)
2d. Naked pair {36} in R23C7, locked for C7 and N3, clean-up: no 4,7 in R56C7 (step 1h), no 4,7 in R7C8 (step 1i), no 9 in R8C8
2e. 4 in N2 only in 11(3) cage at R3C4 = {146/245}, 4 locked for R3, no 3,7,8
2f. 4 in N1 only in R2C23 = {45}, 5 locked for R2 and N1, clean-up: no 3 in R23C1
2g. R3C23 = 9 (step 1d) = [18] (cannot be [27] which clashes with R23C1, cannot be {36} which clashes with R3C7), clean-up: no 7 in R23C1, no 6 in 11(3) cage, no 5 in R45C3 (step 1c)
2h. Naked triple {245} in 11(3) cage, 2,5 locked for N2, 2 locked for R3 -> R23C1 = [26], R23C7 = [63], R2C8 = 1, clean-up: no 9 in R7C7 (step 1i)
2i. Naked triple {379} in 19(3) cage, 3,7 locked for R1, clean-up: no 8 in R2C4
2j. Naked pair {16} in R1C56 -> R1C7 = 2 (cage sum), clean-up: no 8 in R56C7 (step 1h), no 8 in R7C8 (step 1i)
2k. R1C4 = 8 (hidden single in R1) -> R2C49 = [78], clean-up: no 2 in R8C9
2l. Naked pair {19} in R56C7, locked for C7, N6 and 20(4) cage at R5C7, clean-up: no 3 in R8C8
2m. Naked quad (4578) in R7C7 + R8C78 + R9C7, locked for N9, clean-up: no 3,6 in R78C9
2n. R78C9 = [91] -> R3C89 = [97], R78C3 = [12]
2o. R8C39 = [21] -> R8C1 = 7 (step 1k), clean-up: no 5 in R8C78, no 6 in R9C6
2p. Naked pair {48} in R8C78, locked for R8 and N9 -> R79C7 = [75], R7C8 = 3 (step 1i), clean-up: no 9 in R9C6
2q. Naked pair {26} in R9C89, locked for R9
2r. R8C1 = 7 -> R7C12 = 11 = [56]
2s. Naked triple {248} in 14(3) cage at R7C4, 4,8 locked for N8, R9C6 = 7 -> R8C6 = 6, R1C56 = [61]
2t. Naked triple {359} in R8C245, 3,9 locked for 22(5) disjoint cage at R8C2 -> R9C12 = {48}, 4 locked for N7
2u. Killer triple 3,7,9 in R1C3, R45C3 and R9C3, locked for C3
[It’s flowed up to here; now it’s time so start nibbling at the combinations in the middle three rows.]
3a. 12(3) cage at R4C1 = {129/138} (cannot be {147} which clashes with R45C3, cannot be {237} because 2,7 only in R4C2, cannot be {345} which clashes with R45C3 + R6C3, killer ALS block), no 4,5,7, 1 locked for N4
3b. 2 of {129} must be in R4C2 -> no 9 in R4C2
3c. R45C4 = {16/34} (cannot be {25} which clashes with R37C4 (ALS block), no 2,5
3d. 14(3) cage at R5C9 = {248/257/347/356}
3e. 7,8 of {248/257/347} must be in R6C8 -> no 2,4 in R6C8
3f. Consider permutations for R8C78 = {48}
R8C78 = [48] => 14(3) cage = {257/347/356}
or R8C78 = [84] => R1C89 = [54] => 14(3) cage = {257/356}
-> 14(3) cage = {257/347/356}, no 8
4a. 2,7 in N5 only in 25(5) cage at R4C5 = {12679/23479/23578}
4b. 6 of {12679} only in R6C4 -> no 1 in R6C4
4c. 20(4) cage at R5C2 = {2459/3458} (cannot be {2369/2468/3467} which clash with R45C3, cannot be {2378} which clashes with 12(3) cage at R4C1 (step 3a), cannot be {2567} because no 2,5,6,7 in R6C1), 4 locked for N4, clean-up: no 9 in R45C3 (step 1c)
4d. 3 of {3458} must be in R56C2 (R6C1 cannot be 3 which clashes with R1C1 = {39} + R45C1 {19}), no 3 in R6C1
4e. Naked pair {67} in R45C3, locked for C3, 7 locked for N4
4f. 8 in N6 only in 21(4) cage at R4C7 = {2478/2568/3468}
4g. 5 of {2568} must be in R45C8 (R45C8 cannot be {26} which clashes with R9C8), no 5 in R4C9
4h. 14(3) cage at R5C9 (step 3f) = {257/347/356}
4i. Consider combinations for 21(4) cage = {2478/2568/3468}
21(4) cage = {2478} => 5 in R4 only in R4C56, locked for N5 => R56C6 = {49}, 4 locked for N5
or 21(4) cage = {2568/3468}, 6 locked for N6 => R6C4 = 6 (hidden single in R6) => R45C5 = {34}, 4 locked for N5
-> 25(5) cage at R4C5 = {12679/23578}, no 4
4j. 6 of {12679} must be in R6C4 -> no 9 in R6C4
4k. 6 of {12679} in R6C4 -> R45C4 = {34}, 4 locked for N5, R56C6 = {58}, locked for C6, R37C6 = {24}, locked for C6 -> 9 of {12679} only in R4C6 = 9 -> no 9 in R456C5
4l. 9 in C4 only in R89C4, locked for N8
4m. R2C5 = 9 (hidden single in C5) -> R2C6 = 3
4n. R1C2 = 7 (hidden single in R1)
[Step 5b took me a while to find as a clean forcing chain]
5a. 12(3) cage at R4C1 (step 3a) = {129/138}, 14(3) cage at R5C9 (step 3f) = {257/347/356}
5b. Consider combinations for R56C6 = {49/58}
R56C6 = {49}, 9 locked for N5 => R4C1 = 9 (hidden single in R4), R4C2 + R5C1 = [21]
or R56C6 = {58}, 5 locked for N5 => R4C8 = 5 (hidden single in R4), 14(3) cage = {347}, 4 locked for N6 => R4C7 = 8
-> R4C2 = {23}, R45C1 = {18/19}
[Cracked, at last.]
5c. R1C1 = 3 (hidden single in C1) -> R1C3 = 9, R9C345 = [391]
5d. 1 in N5 only in R45C4 = {16}, 6 locked for N5
5e. 4 in N5 only in R56C6 = {49}, 4 locked for C6, 9 locked for N5
5f. R4C1 = 9 (hidden single in R4) -> R4C2 + R5C1 = [21], R45C4 = [16], R45C3 = [67], R56C7 = [91], R56C7 = [49]
5g. 4 in R4 only in R4C789, locked for N6
5h. 21(4) cage at R4C7 (step 4f) = {2478} (only remaining combination) -> R4C789 = [874], R5C8 = 2
and the rest is naked singles.