Prelims
a) 27(4) cage at R1C6 = {3789/4689/5679}, no 1,2
b) 29(4) cage at R2C1 = {5789}
c) 11(4) cage at R2C9 = {1235}
d) 13(4) cage at R5C8 = {1237/1246/1345}, no 8,9
e) 11(4) cage at R6C1 = {1235}
f) 28(4) cage at R6C5 = {4789/5689}, no 1,2,3
g) 27(4) cage at R6C9 = {3789/4689/5679}, no 1,2
h) 14(4) cage at R7C4 = {1238/1247/1256/1346/2345}, no 9
i) 27(4) cage at R8C3 = {3789/4689/5679}, no 1,2
1a. 11(4) cage at R2C9 = {1235}, CPE no 1,2,3,5 in R1C9
1b. 29(4) cage at R2C1 = {5789}, CPE no 5,7,8,9 in R1C1
1c. 11(4) cage at R6C1 = {1235}, CPE no 1,2,3,5 in R9C1
1d. 27(4) cage at R1C6 = {3789/4689/5679}, CPE no 9 in R1C9
1e. 27(4) cage at R6C9 = {3789/4689/5679}, CPE no 9 in R9C9
1f. 27(4) cage at R8C3 = {3789/4689/5679}, CPE no 9 in R9C1
1g. 28(4) cage at R6C5 = {4789/5689}, CPE no 8 in R89C5
1h. 13(4) cage at R5C8 = {1237/1246/1345}, 1 locked for N6
1i. 11(4) cage at R2C9 = {1235}, 1 locked for N3
2a. 45 rule on N1 2(1+1) outies R1C4 + R4C1 = 16 = [79/88/97]
2b. 29(4) cage at R2C1 = {5789}, 5 locked for N1
2c. 15(4) cage at R1C2 = {1239/1248/1347} (cannot be {2346} because R1C4 only contains 7,8,9)
2d. R1C4 = {789} -> R1C23 + R2C3 = {123/124/134}, no 6, 1 locked for N1
3a. 45 rule on R789 3 outies R6C159 = 21 -> R6C1 = 5, R6C59 = 16 = {79}, locked for R6
3b. Naked triple {123} in R7C12 + R8C1, locked for N7
3c. Naked triple {789}, locked for C1
3d. R3C2 = 5 (hidden single in N1)
3e. 11(4) cage at R2C9 = {1235}, 5 locked for C9
3f. 45 rule on N7 1 remaining outie R9C4 = 3
3g. R9C4 = 3 -> R8C3 + R9C23 = 24 = {789}, locked for N7
3h. R7C3 = 5 (hidden single in N7)
3i. 14(4) cage at R7C4 = {1247/1256}, no 8, 1,2 locked for N8
4a. 45 rule on N9 2(1+1) outies R6C9 + R9C6 = 16 = {79}
4b. 27(4) cage at R6C9 = {3789/4689}, 8 locked for N9
4c. 17(4) cage at R8C7, R9C6 = {79} -> no 7,9 in R8C7 + R9C78
4d. Naked triple {789} in R9C236, locked for R9, 8 locked for N7
4e. 17(3) cage at R7C7 = {179/269/467} (cannot be {359} because R9C9 only contains 1,2,4,6), no 3,5
4f. 1 of {179} must be in R9C9 -> no 1 in R7C7 + R8C8
4g. 5 in N9 only in 17(4) cage at R8C7 = {1259/1457/2357} (cannot be {2456} because R9C6 only contains 7,9), no 6
5a. 45 rule on C123 2 remaining outies R15C4 = 14 = [86/95], clean-up: no 9 in R4C1 (step 2a)
5b. 9 in C1 only in R23C1, locked for N1
5c. 15(4) cage at R1C2 = {1239/1248}, 2 locked for N1
6a. 45 rule on N3 2(1+1) outies R1C6 + R4C9 = 8 = [35/53/62]
6b. 27(4) cage at R1C6 = {3789/4689/5679}, 9 locked for N3
6c. 3 of {3789} must be in R1C6 -> no 3 in R1C78 + R2C7
6d. 5 of {5679} must be in R1C6 (cannot be 6{579} which clashes with 11(4) cage at R2C9 = {135}2), 6 of {4689} must be in R1C6 -> no 6 in R1C78 + R2C7
6e. 6 in N3 only in 15(3) cage at R1C9 = {267/456}, no 3,8
6f. 5 of {456} only in R2C8 -> no 4,6 in R2C8
6g. 8 in N3 only in 27(4) cage at R1C6 = {3789/4689}, no 5
6h. 3 in N3 only in R2C9 + R3C89, locked for 11(4) cage at R2C9
6i. 8 in C9 only in R78C9, locked for N9
7a. 45 rule on R123 3 outies R4C159 = 15
7b. R4C19 = [72/82/75/85] = 9,10,12,13 -> R4C5 = {2356}
8a. R1C5 = 5 (hidden single in R1)
8b. R1C5 = 5 -> R2C56 + R3C6 = 11 = {128/137/146} (cannot be {236} which clashes with R1C6), no 9, 1 locked for N2
8c. 5 in R9 only in R9C78, locked for N9
9a. 27(4) cage at R1C6 = {3789/4689}
9b. Hidden killer pair 8,9 in R1C4 and R1C78 for R1, R1C4 = {89} -> R1C78 must contain one of 8,9 -> R2C7 = {89}
10a. 7 in R1 only in R1C789, locked for N3
10b. 15(3) cage at R1C9 = {267/456}
10c. R2C8 = {25} -> no 2 in R3C7
10d. R1C23 = {12} (hidden pair in R1), locked for N1
[Looks like it’s time to start using forcing chains. My first try with R1C6 failed on one path, then I found step 11b.]
11a. R1C4 + R4C1 (step 2a) = [88/97], R1C6 + R4C9 (step 6a) = [35/62], R2C56 + R3C6 (step 8b) = {128/137/146}, R4C159 (step 7b) = [762/735/825]
11b. Consider placement for 2 in N2
R2C4 = 2 => R2C8 = 5 => R4C9 = 5 (hidden single in 11(4) cage at R2C9) => R4C15 = [73] => R1C4 = 9
or 2 in R2C56 + R3C6 = {128}, 8 locked for N2 => R1C4 = 9
or 2 in R3C45 => 20(4) cage at R2C4 = {2378/2468} (cannot be {2369} because R1C6 + R2C4 + R3C45 = {2369} clashes with R2C56 + R3C6), 8 locked for N2 => R1C4 = 9
-> R1C4 = 9, R4C1 = 7, R4C5 = {36}
[Cracked. The rest is fairly straightforward.]
11c. R2C7 = 9 (hidden single in N3) -> R23C1 = [89]
11d. R1C23 = {12}, R1C4 = 9 -> R2C3 = 3 (cage sum)
11e. R1C6 = 3 (hidden single in R1), R2C7 = 9 -> R1C78 = 15 = {78}, 7 locked for N3
11f. Naked pair {46} in R1C9 + R3C7 -> R2C8 = 5 (cage sum)
11g. R2C9 + R3C89 = {123} -> R4C9 = 5 (cage sum)
11h. R4C19 = [75] -> R4C5 = 3
11i. R9C7 = 5 (hidden single in N9)
12a. R1C4 = 9 -> R5C4 = 5 (step 5a)
12b. R8C6 = 5 (hidden single in N8) -> R6C5 + R7C56 = 23 = 9{68}, locked for R7, 6 locked for N8)
12c. R6C9 = 7, R8C9 = [98] (hidden pair in C9) -> R7C8 = 3 (cage sum)
12d. R9C6 = 9 (hidden single in N8) -> R8C3 = 9 (hidden single in N7)
12e. R3C9 = 3 (hidden single in N3)
12f. Naked pair {12} in R7C12, locked for R7 and N7 -> R8C1 = 3
12g. R9C67 = [95] = 14 -> R8C7 + R9C8 = 3 = {12}, locked for N9
12h. Naked pair {46} in R19C1, locked for C1
12i. Naked pair {46} in R19C9, locked for C9
12j. Naked pair {46} in R9C19, locked for R9
12k. Naked pair {12} in R17C2, locked for C2
12l. Naked pair {12} in R5C19, locked for R5
13a. 13(4) cage at R5C8 = {1246} (only remaining combination), locked for N6 -> R4C78 = [89], R5C7 = 3
13b. R1C78 = [78] -> 17(3) cage at R7C7 = [476], R1C9 + R3C7 = [46], R1C1 = 6, R8C2 + R9C1 = [64], R4C2 = 4, R2C2 + R3C3 = [74], R9C23 = [87]
13c. R56C2 = [93] = 12 -> R5C1 + R6C3 = 3 = {12}, locked for N4
13d. Naked pair {12} in R6C37, locked for R6
14. R2C56 + R3C6 (step 8b) = {146} (cannot be {128} which clashes with R3C45) -> R3C6 = 1, R2C56 = {46}, locked for N2
and the rest is naked singles.