Prelims
a) R23C1 = {69/78}
b) R3C34 = {29/38/47/56}, no 1
c) R34C7 = {16/25/34}, no 7,8,9
d) R34C9 = {39/48/57}, no 1,2,6
e) R5C16 = {15/24}
f) R9C34 = {17/26/35}, no 4,8,9
g) 6(3) cage at R1C8 = {123}
h) 21(3) cage at R2C7 = {489/579/678}, no 1,2,3
i) 10(3) cage at R7C7 = {127/136/145/235}, no 8,9
j) 10(4) cage at R2C3 = {1234}
k) 14(4) cage at R2C4 = {1238/1247/1256/1346/2345}, no 9
l) 27(4) cage at R4C2 = {3789/4689/5679}, no 1,2
m) 27(4) cage at R6C1 = {3789/4689/5679}, no 1,2
1a. 45 rule on R1 2 outies R2C29 = 4 = {13}, locked for R2
1b. 6(3) cage at R1C8 = {123}, locked for N3, 2 locked for R1, clean-up: no 4,5,6 in R4C7, no 9 in R4C9
1c. 10(4) cage at R2C3 = {1234}, CPE no 3 in R4C2
1d. 27(4) cage at R4C2 = {3789/4689/5679}, 9 locked for R4
1e. 27(4) cage at R6C1 = {3789/4689/5679}, CPE no 9 in R789C1
2a. 2 in N1 only in R2C3 + R3C23
2b. 45 rule on N1 3 innies R2C3 + R3C23 = 12 = {129/237/246} -> R3C3 = {679}, R3C4 = {245}
2c. 5 in N1 only in R1C123, locked for R1
2d. 2 in N1 only in R2C3 + R3C2, locked for 10(4) cage, no 2 in R4C1 + R5C2
2e. R35C2 must contain one of 1,3 (because no 1,3 in R2C3) but not both because R2C2 = {13}) -> R4C1 = {13}
2f. Killer pair 1,3 in R2C2 and R35C2, locked for C2
2g. 10(4) cage = {1234}, CPE no 4 in R1C2
2h. 45 rule on N9 2(1+1) outies R6C8 + R9C6 = 5 = {14/23}
2i. 45 rule on C789 1 innie R1C7 = 1 outie R9C6 + 5 -> R1C7 = {6789}
2j. 45 rule on N6 3 innies R4C79 + R6C8 = 11 = {128/137/245} -> R4C9 = {578}, R3C9 = {457}
2k. Consider combinations for R4C79 + R6C8
R4C79 + R6C8 = {128} => R3C9 = 4, R3C7 = {56} => R3C34 = [92] (cannot be [65] which clashes with R3C7
or R4C79 + R6C8 = {137} => R3C9 = 5 => R3C34 = [74/92]
or R4C79 + R6C8 = {245} => R3C7 = 5 => R3C34 = [74/92]
-> R3C34 = [74/92], no 5,6
2l. R2C3 + R3C23 = {129/237}, no 4
2m. 10(4) cage = {1234} -> R2C3 = 2, R5C2 = 4, clean-up: no 2 in R6C16, no 6 in R9C4
2n. Naked pair {13} in R23C2, locked for N1
2o. Killer pair 7,9 in R23C1 and R3C3, locked for N1
2p. 18(4) cage at R1C1 = {1458/3456}, 4 locked for R1
2q. Naked pair {15} in R5C16, locked for R5
2r. 7,9 in R1 only in 25(4) cage at R1C4 = {1789/3679}
2s. Min R2C4 = 4 -> max R35C5 + R4C6 = 10, no 8 in R35C5 + R4C6
2t. 45 rule on R1234 1 innie R4C8 = 1 remaining outie R5C5 + 2 -> R4C8 = {458}, R5C5 = {236}
3a. R4C79 + R6C8 (step 2j) = {128/137} (cannot be {245} because R4C79 + R6C8 + R4C8 = {245}8 clashes with 27(4) cage at R4C2), no 4,5, 1 locked for N6, clean-up: no 7 in R3C9, no 1 in R9C6 (step 2h), no 6 in R1C7 (step 2i)
3b. 27(4) cage at R4C2 = {4689/5679} (cannot be {3789} which clashes with R4C9), no 3
3c. R4C167 = {123} (hidden triple in R4)
3d. 45 rule on N4578 4(1+2+1) remaining innies R4C1 + R4C6 + R5C5 + R9C6 = 10
3e. Min R4C1 + R49C6 = 6 -> no 6 in R5C5, clean-up: no 8 in R4C8 (step 2t)
[Or, more simply, killer pair 7,8 in 27(4) cage and R4C9, locked for R4. I’d seen that 45 earlier, so wanted to use it, and it helps with the continuation]
3f. Max R4C1 + R4C6 + R5C5 = 8 but only as [323] -> no 2 in R9C6, clean-up: no 7 in R1C7 (step 2i), no 3 in R6C8 (step 2h)
3g. 21(3) cage at R2C7 = {579/678} (cannot be {489} which clashes with R1C7), no 4
3h. 4 in N3 only in R3C79, locked for R3 -> R3C4 = 2, R3C3 = 9, clean-up: no 6 in R23C1, no 6 in R9C3
3i. Naked pair {78} in R23C1, locked for C1, 8 locked for N1
3j. Naked triple {456} in R1C123, 6 locked for R1
3k. R1C123 = {456} -> R2C2 = 3 (cage sum), R2C9 = 1, R3C2 = 1 -> R4C1 = 3, clean-up: no 4 in R3C7
3l. R3C9 = 4 (hidden single in N3) -> R4C9 = 8
3m. 27(4) cage at R4C2 = {5679}, 5 locked for R4
3n. 25(4) cage at R1C4 = {1789} (only remaining combination), no 3, 7 locked for N2
4a. R4C8 = 4 -> R5C5 = 2 (step 2i), R4C6 = 1, R6C16 = [15], R4C7 = 2 -> R3C7 = 5, R6C8 = 1 -> R9C6 = 4 (step 2h, or 45 rule on N4578), R1C7 = 9 (step 2i)
4b. Naked triple {678} in R2C178, 6,8 locked for R2, 6 locked for N3
4c. R2C6 = 9 -> R2C5 + R3C6 = 7 = [43], R2C4 + R3C5 = [56], clean-up: no 3 in R9C3
4d. 2 in C6 only in R78C6 -> 16(3) cage at R7C6 = {268} (cannot be {259} because 5,9 only in R8C5) -> R78C6 = {26}, 6 locked for C6 and N8, R8C5 = 8
4e. 17(4) cage at R6C6 = {1358} (only remaining combination) -> naked triple {135} in R79C5 + R8C4, locked for N8, R9C4 = 7 -> R9C3 = 1
4f. R7C4 = 9, R6C4 = 4 (hidden single in N5) -> R5C4 + R6C5 = 10 = [37]
4g. Naked triple {679} in R5C789, 6,7 locked for R5, 6,9 locked for N6 -> R6C79 = [35]
4h. R56C3 = [86] -> R6C2 + R7C3 = 6 = [24]
4i. Naked triple {256} in R789C1, 5,6 locked for C1 and N7
4j. 27(4) cage at R6C1 = [9738]
4k. R9C67 = [46] -> R9C89 = 12 = {39}, locked for N9, 3 locked for R9
and the rest is naked singles.