Prelims
a) R12C5 = {19/28/37/46}, no 5
b) R2C23 = {14/23}
c) R56C9 = {39/48/57}, no 1,2,6
d) R67C7 = {89}
e) R8C23 = {19/28/37/46}, no 5
f) R9C89 = {16/25/34}, no 7,8,9
g) 11(3) cage at R5C4 = {128/137/146/236/245}, no 9
h) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
i) 26(4) cage at R1C1 = {2789/3689/4589/4679/5678}, no 1
j) 30(7) cage at R4C5 = {1234569/1234578}
1a. Naked pair {89} in R67C7, locked for C7
1b. 45 rule on C123 1 innie R3C3 = 1 outie R4C4 + 4 -> R3C3 = {56789}, R4C4 = {12345}
1c. 45 rule on C1234 2 outies R36C5 = 7 = {16/25/34}, no 7,8,9
1d. 45 rule on C6789 2 outies R45C5 = 13 = {49/58} (cannot be {67} because 30(7) cage at R4C5 can only contain one of 6,7)
1e. 45 rule on C6789 5 innies R4C678 + R5C78 = 17 = {12347/12356}, no 8,9
1f. R4C678 + R5C78 = {12347/12356}, CPE no 1,2,3 in R4C9
1g. 11(3) cage at R5C4 = {128/137/146/236} (cannot be {245} which clashes with R45C5), no 5, clean-up: no 2 in R3C5
1h. 45 rule on N7 3 outies R5C3 + R6C13 = 9 = {126/135/234}, no 7,8,9
1i. 45 rule on N7 3 innies R7C123 = 18 = {279/378/459/468/567} (cannot be {189} which clashes with R7C7, cannot be {369} which clashes with R5C3 + R6C13), no 1
1j. 45 rule on N8 3 innies R789C6 = 11 = {128/137/146/236/245}, no 9
1k. 45 rule on N8 1 outie R9C7 = 1 innie R7C6 + 5 -> R7C6 = {12}, R9C7 = {67}
1l. Max R7C6 = 2 -> min R56C6 = 13, no 1,2,3 in R56C6
1m. R45C5 contains one of 4,5, R56C6 contains one of 4,5,6 -> 11(3) cage = {128/137/236} (cannot be {146} killer ALS block), no 4, clean-up: no 3 in R3C5
1n. 45 rule on N5689 2 innies R4C49 = 9, no 9 in R4C9
1o. 45 rule on N47 3(2+1) outies R3C12 + R4C4 = 10 -> max R3C12 = 9, no 9 in R3C12
1p. 45 rule on N47 2 innies R45C1 = 1 outie R4C4 + 10, min R45C1 = 11, no 1 in R45C1
1q. 45 rule on N89 2 outies R6C78 = 1 innie R7C6 + 13
1r. R7C6 = {12} -> R6C78 = 14,15 = [86/87/95/96]
1s. 1,2 in N6 only in R45C78, locked for 30(7) cage, no 1,2 in R4C6
1t. 15(3) cage at R7C5 = {168/249/258/267/357} (cannot be {159/348/456} which clash with R45C5)
1u. 16(3) cage at R8C6 = {178/268/367/457} (cannot be {358} because R9C7 only contains 6,7)
1v. R789C6 = {128/137/245} (cannot be {146} because 16(3) cage doesn’t contain both of 4,6, cannot be {236} which clashes with 15(3) cage), no 6
1w. 15(3) cage = {168/249/258/357} (cannot be {267} which clashes with R789C6)
1x. 19(3) cage at R7C4 = {379/469/568} (cannot be {478} which clashes with R789C6, cannot be {289} which clashes with 15(3) cage combined with R789C6), no 2
1y. Hidden killer triple 7,8,9 in R12C5, R45C5 and 15(3) cage for C5, R45C5 and 15(3) cage both contain one of 7,8,9 -> R12C5 must contain one of 7,8,9 = {19/28/37}, no 4,6
[Alternatively R12C5 cannot be {46} which clashes with R36C5 and R45C5, killer ALS block]
1z. 7 in C5 only in R12C5 = {37} or 15(3) cage = {357}, 3 locked for C5 (locking cages), clean-up: no 4 in R3C5
[I was slow finding step 2d, realised that it didn’t work for R4C4 = 2, then quickly found step 2b, after which it came out quickly.]
2a. 11(3) cage at R5C4 (step 1m) = {128/137/236}, R3C3 = R4C4 + 4 (step 1b)
2b. Consider permutations for R36C5 = 7 (step 1c) = [16/52/61]
R36C5 = [16] => 11(3) cage = {236}
or R36C5 = [52] => 11(3) cage = {128/236}
or R36C5 = [61], no 6 in R3C3 => no 2 in R4C4 => 2 in N5 in R45C4 => 11(3) cage = {128}
-> 11(3) cage = {128/236}, no 7, 2 locked for N5, clean-up: no 6 in R3C3, no 7 in R4C9 (step 1n)
2c. 15(3) cage at R5C6 = {49}2/{58}2/{67}2/{68}1 (cannot be {59}1 which clashes with R45C5)
2d. Consider placements for R4C4 = {1345}
R4C1 = 1 => 11(3) cage = {236}, 6 locked for N5 => 15(3) cage = {49}2/{58}2
or R4C1 = {345}, 1,2 in N5 only in 11(3) cage = {128}, 8 locked for N5 => 15(3) cage = {49}2/{67}2
-> R7C6 = 2, R56C6 = {49/58/67}, R9C7 = 7 (step 1k), R89C6 = 9 = {18/45}, no 3, R56C6 = {49/67} (cannot be {58} which clashes with R89C6, no 5,8
[Cracked. The rest is fairly straightforward.]
2e. R7C6 = 2 -> R6C78 = 15 (step 1r) = [87/96]
2f. 19(3) cage at R7C4 (step 1x) = {379/469} (cannot be {568} which clashes with R89C6), no 5,8, 9 locked for C4 and N8
2g. 15(3) cage at R7C5 (step 1w) = {168/357}, no 4
2h. 4 in C5 only in R45C5 = 13 = {49}, locked for N5, 9 locked for C5, 4 locked for 30(7) cage at R4C5, clean-up: no 1 in R12C5, no 5 in R4C9 (step 1n)
2i. Naked pair {67} in R56C6, locked for C6 and N6, clean-up: no 8 in R3C3 (step 1b), no 1 in R3C5
2j. 11(3) cage = {128} (only remaining combination), 1 locked for N5, 8 locked for C4, clean-up: no 8 in R4C9 (step 1n)
2k. R45C5 = {49} -> 30(7) cage = {1234569}, 6 locked for N6 -> R4C9 = 4, R6C8 = 7, R56C9 = {39}, locked for C9 and N6 -> R4C6 = 3, R4C4 = 5, R3C3 = 9 (step 1b), R45C5 = [94], R56C6 = [76], R67C7 = [89], clean-up: no 1 in R8C2, no 3,4 in R9C8
2l. Naked pair 1,2 in R6C45, locked for R6 and N5 -> R5C4 = 8
2m. Naked quad {1256} in R45C78, 5 locked for R5
2n. R5C3 + R6C13 (step 1h) = {135/234} (cannot be {126} because 1,2,6 only in R5C3) -> R5C3 = {12}, R6C13 = {34/35}, 3 locked for R6 and N4 -> R56C9 = [39], R6C2 = 4, R6C13 = {35}, 3,5 locked for 27(6) cage, R5C3 = 1, clean-up: no 9 in R8C2, no 6 in R8C3
2o. R5C3 + R6C13 = 1{35} = 9 -> R7C123 = 18 = {468} (only remaining combination), locked for R7 and N7, clean-up: no 2 in R8C23
2p. Naked pair {37} in R8C23, locked for R8 and N7
2q. 45 rule on N47 2 remaining innies R45C1 = 15 = [69] (cannot be {78} because 7,8 only in R4C1), R5C2 = 2, clean-up: no 3 in R2C3
2r. R45C1 = 15 -> R3C12 = 5 = [23/41]
2s. Naked quad {1234} in R2C23 + R3C12, 1,3 locked for C2, 2,3,4 locked for N1 -> R8C23 = [73], R4C23 = [87]
2t. 19(3) cage at R7C4 = {379} (only remaining combination, cannot be {469} because R7C4 only contains 3,7) = [793]
2u. 15(3) cage = {168} (only remaining combination) -> R7C5 = 1, R89C5 = {68}, locked for C5, 8 locked for N8, R36C5 = [52], R6C4 = 1, R7C89 = [35], clean-up: no 2 in R9C89
2v. Naked pair {16} in R9C89, locked for R9 and N9
2w. Naked pair {25} in R9C13, locked for N7, 5 locked for R9 -> R9C6 = 4
3a. Naked triple {189} in R123C6, 1 locked for 25(5) cage at R1C4
3b. R123C6 = 18 -> R13C7 = 7 = {34}/[52]
3c. Killer pair 2,4 in R13C7 and R8C7, locked for C7 -> R4C78 = [12]
3d. R17C2 = [56], naked pair {78} in R12C1, 8 locked for C1 and N1, R1C3 = 6, clean-up: no 2 in R3C7
3e. Naked pair {34} in R13C7, locked for N3, 4 locked for C7
3f. R3C9 = 7 (hidden single in R3) -> 17(3) cage at R1C8 = {269} (only remaining combination) = [926]
and the rest is naked singles.