Prelims
a) R1C12 = {39/48/57}, no 1,2,6
b) R12C5 = {19/28/37/46}, no 5
c) R12C6 = {39/48/57}, no 1,2,6
d) R3C56 = {59/68}
e) R78C3 = {49/58/67}, no 1,2,3
e) R89C4 = {39/48/57}, no 1,2,6
f) R8C56 = {19/28/37/46}, no 5
g) R9C56 = {39/48/57}, no 1,2,6
h) 9(3) cage at R2C1 = {126/135/234}, no 7,8,9
i) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
j) 38(8) cage at R1C3 = {12345689}, no 7
1a. 45 rule on N58 1 innie R4C4 = 5, clean-up: no 7 in R89C4
1b. 45 rule on C12 3 outies R569C3 = 8 = {125/134}, 1 locked for C3
1c. 7 in C3 only in R78C3 = {67}, locked for N7, 6 locked for C3
1d. 5 in C3 only in R569C3 = {125}, 2 locked for C3
1e. 38(8) cage at R1C3 = {12345689} -> R123C4 = {126}, locked for C4 and N2
1f. R12C5 = {37} (only remaining combination), locked for C5 and N2, clean-up: no 3,7 in R8C6, no 5,9 in R9C6
1g. 4 in N2 only in R12C6 = {48}, locked for C6, 8 locked for N2, clean-up: no 2,6 in R8C5, no 4,8 in R9C5
1h. Naked pair {59} in R3C56, locked for R3
1i. 45 rule on N8 1 outie R6C6 = 1 innie R7C4 = {37}
1j. Naked pair {37} in R69C6, locked for C6
1k. 11(3) cage at R6C6 = {236} (only remaining combination, cannot be {128/146//245} because R6C6 only contains 3,7, cannot be {137} because 3,7 only in R6C6) -> R6C6 = 3, R7C56 = {26}, locked for R7 and N8, R78C3 = [76], R7C4 = 3, clean-up: no 9 in R89C4
1l. Naked pair {48} in R89C4, locked for C4 and N8
1m. R9C6 = 7 -> R9C5 = 5, R3C56 = [95], R8C56 = [19]
1n. R7C4 = 3 -> R6C45 = 13 = [76/94]
1o. 5 in C3 only in R56C3, locked for N4
1p. 13(3) cage at R9C1 = {139/238} (cannot be {148} which clashes with R9C4), no 4, 3 locked for R9 and N7
1q. R9C3 = {12} -> no 1,2 in R9C12
1r. R1C12 = {57} (cannot be {39/48} which clash with R123C3 = {3489}, ALS block), locked for R1 and N1 -> R12C5 = [37]
1s. 9(3) cage at R2C1 = {126} (cannot be {234} which clashes with R123C3 = {3489}, ALS block), locked for N1
1t. Naked triple {126} in R2C124, locked for R2
1u. 9 in N1 only in R12C3, locked for C3
1v. Hidden killer triple 1,2,6 in R1C4 and R1C789 for R1, R1C4 = {126} -> R1C789 must contain two of 1,2,6
1w. 25(5) cage at R1C7 = {12589/14569/23569/24568} (cannot be {13489} which only contains one of 1,2,6), 5 locked for N3
1x. 7 in R3 only in R3C789, CPE no 7 in R4C9
2a. 33(6) cage at R3C2 contains 5 for C3 = {135789/145689/235689/245679} (cannot be {345678} because R56C3 only contain 1,2,5), 9 locked for N4
2b. R56C3 = {125} -> no 1,2 in R4C12 + R5C2
2c. 14(3) cage at R6C2 = {149/158/248} (cannot be {167} because 6,7 only in R6C2, cannot be {257} which clashes with R1C2), no 6,7
2d. 17(4) cage at R5C1 = {1349/1358/2348} (cannot be {1259/1268/1367/2456} which clash with R23C1, ALS block, cannot be {1457/2357} which clash with R1C1), no 6,7
2e. Killer triple 1,2,6 in R23C1 and 17(4) cage, locked for C1
2f. 17(4) cage = {1349/1358/2348} -> R5C1 = 3
2g. 45 rule on N7 3 outies R56C1 + R6C2 = 12, R5C1 = 3 -> R6C12 = 9 = {18}, locked for R6 and N4 -> R4C3 = 4, R3C2 = 4 (hidden single in N1)
2h. R9C3 = 1 (hidden single in C3) -> R9C12 = 12 = [93], R4C1 = 7, R1C12 = [57]
2i. 17(4) cage = {2348} (only remaining combination) -> R678C1 = [842]
2j. R2C2 = 2 (hidden single in N1)
2k. 3 in R4 only in R4C789, CPE no 3 in R3C7
3a. 13(3) cage at R8C8 = {238/247/256/346}
3b. 3,5,7 only in R8C8 -> R8C8 = {357}
3c. 45 rule on N9 2 innies R78C7 = 1 outie R6C9 + 1
3d. R78C7 cannot total 3,7,10 (because no 2 in R78C7, 3,4 only in R8C7, 1,9 only in R7C7, 3,7 only in R8C7) -> R6C9 = {457}, R78C7 = 5,6,8 = [14/15/17/53], no 8,9
3e. 15(4) cage at R5C7 = {1248/1257/1356} (cannot be {1239/2346} which don’t fit with R78C7, cannot be {1347} = {34}[17] because no 3 in R56C7), no 9, 1 locked for C7
3f. 4 of {1248} must be in R8C7 -> no 4 in R56C7
3g. {1356} = [1653] -> no 6 in R5C7
3h. 9 in C7 only in R124C7, CPE no 9 in R2C9
3i. Consider placement for 7 in N9
R8C7 = 7 => 15(4) cage = {1257}
or R8C8 = 7 => R9C78 = {24}, 4 locked for N9
or R8C9 = 7 => R6C9 = {45} => R78C7 = [14/15], R8C8 = 3 (hidden single in N9) => R9C78 = {28/46} => 15(4) cage = {1257/1356} (cannot be {1248} which clashes with R9C7 = {28} or is eliminated by {46}, 4 locked for N9)
-> 15(4) cage = {1257/1356}, no 4,8, 5 locked for C7
3j. R78C7 = [15/17/35] = 6,8 -> R6C9 = {57}
3k. R2C8 = 5 (hidden single in R2)
4a. 45 rule on N9 3 outies R56C7 + R6C9 = 14 = {167/257}
4b. 1 of {167} must be in R5C7, 7 of {257} must be in R6C79 (R6C79 cannot be {25} which clashes with R6C3) -> 7 in R6C79, locked for R6 and N6, R6C4 = 9 -> R6C5 = 4 (cage sum)
4c. 6 in R6 only in R6C78, locked for N6
4d. 28(5) disjoint cage at R2C9 = {14689/23689/24589/34678} (cannot be {13789/34579} because R6C5 only contains 2,6, cannot be {15679} because R2C9 only contains 3,4,8, cannot be {24679/25678} = [47]{269}/[87]{256} which clash with R56C7 + R6C9)
4e. Consider combinations for R56C7 + R6C9 = {167/257}
R56C7 + R6C9 = {167} = [167] => 1 in N9 only in 31(5) cage at R6C9 = {16789} = 7{19}[86], 8 locked for C9 => 28(5) disjoint cage = {14689/23689/34678} (cannot be {24589} = [48952])
or R56C7 + R6C9 = {257}, 5 locked for N6
-> 28(5) disjoint cage = {14689/23689/34678}, no 5
4f. 5 in N6 only in R56C7 + R6C9 = {257}, 2 locked for N6 -> R6C8 = 6
4g. 15(4) cage at R5C7 = {1257} (only remaining combination) -> R7C7 = 1, R568C7 = {257}, 2,7 locked for C7
5a. 9 in N3 only in 25(5) cage at R1C7 (step 1w) = {12589/14569/23569}
5b. 23(5) cage at R3C7 = {12389/13469/13478} (cannot be {12479} because R3C7 only contains 6,8, cannot be {23468} = [62]{38}4 which clashes with 25(5) cage)
5c. R3C7 = {68} -> no 8 in R345C8 + R4C9)
5d. 8 in N6 only in R4C7 + R5C9, locked for 28(5) disjoint cage at R2C9, no 8 in R23C9
5e. 28(5) disjoint cage at R2C9 (step 4e) = {14689/23689/34678}
5f. 1 of {14689} must be in R3C9 -> no 1 in R5C9
5g. 1 in N6 only in R4C78 + R5C8, locked for 23(5) cage, no 1 in R3C8
5h. Consider placement for 7 in C8
R3C8 = 7 => 23(5) cage = {13478}
or R8C8 = 7, R9C78 = 6 = [42] => 23(5) cage = {13469/13478}
-> 23(5) cage = {13469/13478}, no 2
5i. 23(5) cage = {13469/13478} -> R5C8 = 4
5j. Naked pair {37} in R38C8, locked for C8
5k. 13(3) cage at R8C8 (step 3a) = {238/247} (cannot be {346} because 4,6 only in R9C7) -> R9C8 = 2, R9C7 = {48}
5l. R9C9 = 6 (hidden single in R9)
5m. Hidden killer pair 3,4 in 13(3) cage and R8C9 for N9, 13(3) cage contains one of 3,4 -> R8C9 = {34}
5n. Naked pair {34} in R28C9, locked for C9
5o. Naked pair {19} in R4C78, locked for R4 and N6
5p. R4C7 + R5C9 = [38], R6C8 = 6, R2C9 = 4 -> R3C9 = 7 (cage sum)
and the rest is naked singles.