Prelims
a) R3C78 = {13}
b) R7C23 = {39/48/57}, no 1,2,6
c) 20(3) cage at R1C3 = {389/479/569/578}, no 1,2
d) 22(3) cage at R4C1 = {589/679}
e) 21(3) cage at R5C9 = {489/579/678}, no 1,2,3
f) 20(3) cage at R6C4 = {389/479/569/578}, no 1,2
g) 14(4) cage at R1C1 = {1238/1247/1256/1346/2345}, no 9
h) 27(4) cage at R2C3 = {3789/4689/5679}, no 1,2
i) 18(5) cage in R5C2 = {12348/12357/12456}, no 9
Steps resulting from Prelims
1a. R3C78 = {13}, locked for R3 and N3
1b. 22(3) cage at R4C1 = {589/679}, 9 locked for N4
1c. 27(4) cage at R2C3 = {3789/4689/5679}, 9 locked for N1
[Immediate placements.]
2a. 45 rule on N1 1 innie R1C3 = 4 -> R12C4 = 16 = {79}, locked for C4 and N2, clean-up: no 8 in R7C2
2b. 45 rule on N9 1 innie R9C7 = 6 -> R89C6 = 10 = {19/28/37}, no 4,5
2c. 45 rule on R12 1 innies R2C3 = 7, R12C4 = [79], R3C123 = 20 = {569}, locked for R3 and N1, clean-up: no 5 in R7C2
2d. Naked triple {248} in R3C456, locked for R3 and N2 -> R3C9 = 7
2e. 45 rule on N3 1 outie R2C6 = 3 -> R2C78 = 12 = {48}, locked for R2 and N3, clean-up: no 7 in R89C6
2f. Naked pair {12} in R2C12, locked for R2 and N1
2g. 45 rule on R89 1 innie R8C7 = 8, R2C78 = [48], R7C789 = 10 = {127/145/235}, no 9, clean-up: no 2 in R9C6
2h. R7C23 = {39}/[48] (cannot be [75] which clashes with R7C789), no 5,7
3a. R3C9 = 7 -> R4C789 + R5C8 = 14 = {1238/1256/1346/2345}, no 9
3b. 45 rule on N6 using R4C789 + R5C8 = 14, 2 innies R56C7 = 10 = {19/37}, no 2,5
3c. R4C789 + R5C8 = {1256/2345} (cannot be {1238/1346} which clash with R56C7, no 8, 5 locked for N6
3d. Killer pair 1,3 in R3C7 and R56C7, locked for C7
4. 13(3) cage at R3C4 = {28}3/{48}1, 8 locked for R3, R4C4 = {13}
4a. 13(3) cage at R3C6 = {148/238/247/256/346} (cannot be {139/157} because R3C6 only contains 2,4), no 9
4b. 9 in R4 only in R4C12, locked for N4
5. 4 in N4 only in 18(5) cage at R5C2 -> no 4 in R7C1
5a. 18(5) cage = {12348/12456}, no 7
5b. 7 in N4 only in 22(3) cage at R4C1 = {679}, 6 locked for N4
6. 6 in R7 only in R7C1456
6a. 45 rule on R789 4 innies R7C1456 = 23 = {1679/2678/3569/4568}
6b. 45 rule on N7 1 innie R7C1 = 1 outie R8C4 = {12356}
6c. R7C1 = R8C4 -> R7C1456 = R7C456 + R8C4 = {1679/2678/3569/4568}, 6 locked for N8
6d. Killer pair 8,9 in R7C456 + R8C4 and R89C6, locked for N8
[Ed pointed out that I’d missed 9 in N8 only in R7C56 + R89C6, CPE no 9 in R6C6]
7. 20(3) cage at R6C4 = {389/569/578} (cannot be {479} because 7,9 only in R6C5), no 4
7a. 7,9 only in R6C5 = {79}
8. 45 rule on R1234 2 outies R5C18 = 1 innie R4C3 + 3
8a. Min R5C18 = 7 -> no 1,2,3 in R4C3
8b. R4C3 = {58} -> R5C18 = 8,11 = [62/71/65/74], no 3,6 in R5C8
9. 45 rule on R6789 2 outies R5C29 = 1 innie R5C7 + 8, IOU no 8 in R5C2
9a. Max R5C29 = 14 -> no 7,9 in R6C7, clean-up: no 1,3 in R5C7 (step 3b)
9b. R6C7 = {13} -> R5C29 = 9,11 = [18/36/54/29/38/56], no 4 in R5C2
9c. 4 in N4 only in R6C12, locked for R6
9d. 21(3) cage at R5C9 = {489/678} = [498/678/876] -> R5C9 = {468}, R6C8 = {79}, R6C9 = {68}
9e. R5C29 = [18/36/54/38/56], no 2
9f. Naked pair {79} in R6C58, locked for R6
9g. R4C789 + R5C8 (step 3c) = {1256/2345}
9h. R5C29 + R6C7 = [181/361/383] (cannot be [541/563] because R5C9 + R6C7 = [41/63] clash with R4C789 + R5C8), no 5 in R5C2, no 4 in R5C9
[Cracked; the rest is fairly straightforward.]
9i. Naked pair {68} in R56C9, locked for C9 and N6, R6C8 = 7 (cage sum), R5C7 = 9 -> R6C7 = 1 (step 3b), R2C9 = 5, R1C789 = [269], R3C78 = [31], R4C7 = 5
9j. R78C7 = [78] = 15 -> R7C89 = 3 = [21], R5C8 = 4, R4C89 = [32], R4C4 = 1 -> R3C45 = 12 = {48}, clean-up: no 2 in R8C4 (step 6b)
9k. R3C6 = 2 (hidden single in N2) -> R4C56 = 11 = {47}, 7 locked for R4 and N5, clean-up: no 8 in R9C6 (step 2b)
9l. Naked pair {19} in R89C6, locked for C6 and N8
9m. R4C3 = 8, clean-up: no 4 in R7C2
9n. Naked pair {39} in R7C23, locked for R7 and N7, clean-up: no 3 in R8C4 (step 6b)
10. 18(5) cage at R5C2 (step 5a) = {12456} -> R5C2 = 1, R6C123 = {245}, locked for R6 and N4, R7C1 = 6, R8C4 = 6 (step 6b), R2C12 = [12]
10a. R6C4 = 3 (hidden single in R6), R6C5 = 9 -> R7C4 = 8 (cage sum)
10b. R47C6 = [74] (hidden pair in C6), R7C5 = 5 -> R6C6 = 8 (cage sum)
10c. R8C4 = 6 -> R8C23 = 7 = [52]
and the rest is naked singles.