Prelims
a) R12C1 = {89}
b) R23C4 = {29/38/47/56}, no 1
c) R2C67 = {17/26/35}, no 4,8,9
d) R45C4 = {39/48/57}, no 1,2,6
e) R78C4 = {16/25/34}, no 7,8,9
f) R78C8 = {15/24}
g) R78C9 = {69/78}
h) R8C23 = {29/38/47/56}, no 1
i) R8C67 = {15/24}
j) 10(3) cage at R2C9 = {127/136/145/235}, no 8,9
1a. Naked pair {89} in R12C1, locked for C1 and N1
1b. 45 rule on R1 4 outies R2C1258 = 28 = {4789/5689}, no 1,2,3, 8,9 locked for R2, clean-up: no 2,3 in R3C4
1c. 45 rule on R12 3 innies R2C349 = 9 = {126/135/234}, no 7, clean-up: no 4 in R3C4
2a. 45 rule on N9 2 innies R78C7 = 7 = {16/34} (cannot be {25} which clashes with R78C8) = [34/61], clean-up: no 1,4 in R8C6
2b. Killer pair 1,4 in R78C7 and R78C8, locked for N9
2c. R78C4 = {16/34} (cannot be {25} which clashes with R8C6), no 2,5
2d. 45 rule on R9 2 outies R8C15 = 13 = [49/58]/{67}, no 1,2,3, no 4,5 in R8C5
2e. Combined cage R8C15 + R8C67 = [49][51]/[58][24]/{67}[24]/{67}[51]
2f. R8C23 = {29/38} (cannot be {47/56} which clash with combined cage)
2g. 16(3) cage at R7C1 = {169/178/259/358/457} (cannot be {268/349} which clash with R8C23, cannot be {367} which clashes with R7C7)
3a. 45 rule on N5 3 innies R4C56 + R6C4 = 8 = {125/134}, 1 locked for N5
3b. 45 rule on N5 1 outie R3C5 = 1 innie R6C4 + 5 -> R3C6 = {6789}, R6C4 {1234}
3c. Combined cage R45C4 = {39/48/57} and R4C56 + R6C4 = {125/134} must contain 5, locked for N5
3d. 45 rule on C4 3 innies R169C4 = 15
3e. Max R6C4 = 4 -> min R19C4 = 11, no 1 in R19C4
3f. Hidden killer triple 7,8,9 in R169C4, R3C4 and R45C4 for C4, R169C4 = 15 cannot contain more than one of 7,8,9, R45C4 contains one of 7,8,9 -> R169C4 must contain one of 7,8,9 and R3C4 = {789}, clean-up: no 5,6 in R2C4
4. 45 rule on N8 3 innies R7C56 + R8C6 = 15 = {159/249/258/267/357} (cannot be {168/348} because R8C6 only contains 2,5, cannot be {456} which clashes with R78C4)
5. 45 rule on R89 2 innies R8C48 = 1 outie R7C9
5a. R7C9 = {6789} -> R8C48 = 6,7,8,9 = [42/34/61/35/62] (cannot be [15] because R78C4 = [61] clashes with R7C9 = 6, cannot be [45] which clashes with R8C67), no 1 in R8C4, clean-up: no 6 in R7C4
5b. R8C48 = 6,7,8 -> R7C9 = {678}, clean-up: no 6 in R8C9
5c. 1 in R8 only in R8C78, locked for N9, clean-up: no 5 in R8C8
5d. 45 rule on R89 3 innies R8C489 = 15 and doesn’t contain 5 = {168/249/267/348}
5e. Consider placements for 1 in R8
R8C7 = 1 => R7C7 = 6 (step 2a) => no 9 in R8C9
or R8C8 = 1 => R8C489 = {168}
-> no 9 in R8C9, clean-up: no 6 in R7C9
[After going through Ed’s walkthrough I realised that if I’d used R7C489 = 13 sooner, to eliminate 6 from R7C9, this short forcing chain would have been avoided.]
5f. R8C489 = {168/267/348}
5g. 3 of {348} must be in R8C4 -> no 4 in R8C4, clean-up: no 3 in R7C4
5h. Naked pair {78} in R78C9, locked for C9 and N9
5i. 16(3) cage at R7C1 (step 2g) = {169/178/259/358/457}
5j. 45 rule on R89 3 outies R7C489 = 13 = {148/247} (cannot be {157} which clashes with 16(3) cage at R6C1), no 5, 4 locked for R8, clean-up: no 1 in R8C8
5k. Naked pair {24} in R78C8, locked for C8 and N9, R8C7 = 1 -> R8C6 = 5, R7C7 = 6 (step 2a), clean-up: no 2,7 in R2C6, no 3 in R2C7, no 8 in R8C5 (step 2d)
5l. Naked triple {359} in 17(3) cage at R9C7, locked for R9
5m. 5 in N7 only in 16(3) cage at R7C1 = {259/358}, no 1,7
5n. 18(4) cage in N7 = {1467} (hidden quad in N7), 1 locked for R9
5o. 2,8 in R9 only in R9C456, locked for N8
6. Consider placement for 1 in R67C4
R6C4 = 1 => R3C5 = 6 (step 3b)
or R7C4 = 1 => R8C4 = 6
-> no 6 in R8C5, clean-up: no 7 in R8C1 (step 2d)
[Ed pointed out that I’d overlooked further eliminations. I’d missed that it also removes 6 from R9C5 and from R1C4, which would have simplified step 7f.]
6a. 7 in N7 only in R9C123, locked for R9
7. 5 in C4 only in R1C4 or in R45C4
7a. R169C4 = 15 (step 3d) cannot contain 5 (cannot be {159/357} because R9C4 only contains even numbers, cannot be {456} which clashes with R78C4, cannot be {258} = [528] which, combined with R3C5 + R6C4 (step 3b) = [72] clashes with R23C4), no 5 in R1C4
7b. 5 in C4 only in R45C4 = {57}, locked for N5, 7 also locked for C4, clean-up: no 4 in R2C4
7c. R4C56 + R6C4 (step 3a) = {134} (only remaining combination), 3,4 locked for N5, clean-up: no 7 in R3C5 (step 3b)
7d. R169C4 = {168/348} (cannot be {249} = [942] which clashes with R3C5 + R6C4 (step 3b) = [94]), no 2,9, 8 locked for C4
7e. R3C4 = 9 -> R2C4 = 2, clean-up: no 6 in R2C6, no 4 in R6C4 (step 3b)
7f. R169C4 = {168/348} = [816/438] (cannot be [618] which clashes with R3C5 + R6C4 (step 3b) = [61], cannot be [834] which clashes with R3C6 + R6C4 (step 3b) = [83]) -> R1C4 = {48}, R9C4 = {68}
7g. Combined cage R169C4 + R3C5 (using step 3b) = [816]6/[438]8 -> 8 in R1C4 + R3C5, locked for N2
7h. 4 in N5 only in R4C56, locked for R4
7i. 6 in C4 only in R89C4, locked for N8
7j. R2C349 (step 1c) contains 2 = {126/234}, no 5
8a. R2C18 = {89} (hidden pair in R2)
8b. 5 in N2 only in R12C5, locked for 27(6) cage at R1C2
8c. R2C1258 (step 1b) = {4789/5689} -> R2C25 = [47/65/74], no 6 in R2C5
8d. 27(6) cage = {124578/134568/234567}
8e. 5,6 of {134568} must be in R2C25, 5,6 of {234567} must be in R2C25 (because 4 of this combination is in R1C4) -> no 6 in R1C235
8f. 6 in R1 only in 29(5) cage at R1C6
8g. 9 in R12 only in R12C1 and 29(5) cage -> 29(5) cage must contain 9 = {15689/25679/34679} (cannot be {24689} which clashes with R12C1 + R1C4, Killer ALS block)
8h. 5 in N1 only in R3C123, locked for R3
8i. 10(3) cage at R2C9 = {127/136}, no 4, 1 locked for N3
8j. 29(5) cage = {25679/34679} (cannot be {15689} = 1{5689} which clashes with R2C67), no 1,8, 7 locked for R1
[Cracked. The rest is fairly straightforward.]
8k. R2C8 = 9 -> R12C1 = [98]
8l. R3C7 = 8 (hidden single in N3), R3C5 = 6 -> R4C56 = 7 = {34}, 3 locked for R4 and N5, R6C4 = 1, R7C4 = 4 -> R8C4 = 3, R1C4 = 8, R9C4 = 6, R78C8 = [24], R8C1 = 6 -> R8C5 =7 (step 2d), R78C9 = [78]
8m. Naked pair {29} in R8C23, 9 locked for N7
9. 45 rule on N3 2 outies R12C6 = 10 = [73] -> R2C7 = 5, R4C56 = [34], R3C6 = 1, R7C56 = [19], R12C5 = [54]
9a. R2C2 = 7 (hidden single in R2)
9b. R1C45 = [85] + R2C25 = [74] = 24 -> R1C23 = 3 = {12}, locked for N1, 2 locked for R1
9c. R2C39 = [61]
9d. R3C89 = [72] (hidden pair in R3)
9e. R3C67 = [18] = 9 -> R456C7 = 12 = {237} (only remaining combination), 3 locked for C7 and N6
10. 2 in C1 only in R456C1, locked for N4
10a. 27(6) at R2C6 = {134568} (only remaining combination), no 7,9, 1,8 locked for N4
10b. R6C4 = 1 -> R6C23 = 11 = [47/65]
10c. R4C2 = 9 (hidden single in N4) -> R34C1 = 5 = [32], R7C1 = 5
10d. Naked pair {47} in R56C1, locked for C1 and N4
and the rest is naked singles.