Prelims
a) R1C67 = {18/27/36/45}, no 9
b) R1C89 = {18/27/36/45}, no 9
c) R2C78 = {16/25/34}, no 7,8,9
d) R23C9 = {29/38/47/56}, no 1
e) R3C67 = {14/23}
f) R34C8 = {39/48/57}, no 1,2,6
g) R45C7 = {17/26/35}, no 4,8,9
h) R45C9 = {17/26/35}, no 4,8,9
i) R56C8 = {49/58/67}, no 1,2,3
j) R67C1 = {17/26/35}, no 4,8,9
k) R78C2 = {29/38/47/56}, no 1
l) R89C1 = {29/38/47/56}, no 1
m) R8C34 = {17/26/35}, no 4,8,9
n) R8C56 = {39/48/57}, no 1,2,6
o) R9C23 = {16/25/34}, no 7,8,9
p) R9C45 = {19/28/37/46}, no 5
q) R9C67 = {49/58/67}, no 1,2,3
r) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
1. 45 rule on N3 3 innies R1C7 + R3C78 = 18 = {189/279/369/378/459/468} (cannot be {567} because R3C7 only contains 1,2,3,4)
1a. R3C7 = {1234} -> no 1,2,3,4 in R1C7 + R3C8, clean-up: no 5,6,7,8 in R1C6, no 8,9 in R4C8
2. 45 rule on R89 2 outies R7C27 = 9, no 9 in R7C2, no 8,9 in R7C7, clean-up: no 2 in R8C2
3. 45 rule on N9 2(1+1) outies R6C9 + R9C6 = 10, min R9C6 = 4 -> max R6C9 = 6
4. Hidden killer pair 8,9 in R56C8 and R6C7 for N6, each can only contain one of 8,9 -> R6C7 = {89}, R56C8 = {49/58}, no 6,7
4a. 16(3) cage at R6C6 cannot contain both of 8,9, R6C7 = {89} -> no 8,9 in R67C6
4b. R34C8 = {57}/[93] (cannot be [84] which clashes with R56C8), no 8 in R3C8, no 4 in R4C8
5. Hidden killer pair 2,6 in R45C7, R45C9 and R6C9 for N6, R45C7 and R45C9 must both contain both or neither of 2,6, R6C9 cannot contain both of 2,6 -> no 2,6 in R6C9, clean-up: no 4,8 in R9C6 (step 3), no 5,9 in R9C7
6. R1C7 + R3C78 (step 1) = {189/279/369/378/459} (cannot be {468} because R3C8 only contains 5,7,9)
6a. 9 of {459} must be in R3C8 -> no 5 in R3C8, clean-up: no 7 in R4C8
6b. Killer pair 5,9 in R34C8 and R56C8, locked for C8, 5 also locked for N6, clean-up: no 4 in R1C9, no 2 in R2C7, no 3 in R45C7, no 3 in R45C9, no 5 in R9C6 (step 3), no 8 in R9C7
7. Naked quad {1267} in R45C79, locked for N6, clean-up: no 9 in R9C6 (step 3), no 4 in R9C7
7a. Naked pair {67} in R9C67, locked for R9, clean-up: no 4,5 in R8C1, no 1 in R9C23, no 3,4 in R9C45
8. 45 rule on C89 3 outies R278C7 = 12 = {138/147/246/345} (cannot be {129/156/237} which clash with R45C7), no 9
9. R6C7 = 9 (hidden single in C7), clean-up: no 4 in R56C8
9a. Naked pair {58} in R56C8, locked for C8 -> R4C8 = 3, R3C8 = 9, R6C9 = 4, R9C6 = 6 (step 3), R9C7 = 7, clean-up: no 2 in R1C6, no 1,6 in R1C9, no 4 in R2C7, no 2,7 in R23C9, no 1 in R45C7, no 2 in R8C3
9b. Naked pair {26} in R45C7, locked for C7 and N6, clean-up: no 3 in R1C6, no 1 in R2C8, no 3 in R3C6
9c. Naked pair {17} in R45C9, locked for C9, clean-up: no 2 in R1C8
10. R1C7 + R3C78 (step 6) = {189/459}, no 3, clean-up: no 2 in R3C6
10a. Naked pair {14} in R3C67, locked for R3
10b. Naked pair {14} in R13C6, locked for C6 and N2, clean-up: no 8 in R8C5
10c. R1C89 = [18/45/72] (cannot be [63] which clashes with R23C9), no 3,6
11. R6C7 = 9 -> R67C6 = 7 = {25}, locked for C6, clean-up: no 7 in R8C5
12. Killer triple 1,2,4 in R9C23, R9C45 and R9C8, locked for R9, clean-up: no 7,9 in R8C1
13. 1 in N7 only in R7C13 + R8C3
13a. 45 rule on N7 3 innies R7C13 + R8C3 = 16 = {169/178}, no 2,3,4,5, clean-up: no 3,5,6 in R6C1, no 3,5 in R8C4
13b. 8,9 only in R7C3 -> R7C3 = {89}
14. R6C9 = 4 -> R7C89 = 11 = [29/65]
14a. Killer pair 2,5 in R7C6 and R7C89, locked for R7, clean-up: no 6,9 in R8C2
[Only just spotted …]
15. 45 rule on R12 3 innies R2C239 = 24 = {789} -> R2C9 = 8, R2C23 = {79}, locked for R2, N1 and 36(6) cage at R2C2, R3C9 = 3, R1C7 = 5 -> R1C6 = 4, R3C67 = [14], R1C9 = 2 -> R1C8 = 7, R2C678 = [316], R78C7 = [38], R7C8 = 2, R67C6 = [25], R7C9 = 9, R89C9 = [65], R7C3 = 8
15a. R8C34 = {17} (only remaining combination), locked for R8, R8C6 = 9 -> R8C5 = 3, R89C8 = [41], R8C1 = 2 -> R9C1 = 9, R8C2 = 5 -> R7C2 = 6
16. R2C1 = 4 (hidden single in R2) -> R1C12 = 11 = {38}, locked for R1 and N1, R3C2 = 2
16a. R1C3 = 1 (hidden single in R1), R8C34 = [71]
16b. R7C345 = 8{47} -> R6C3 = 5 (cage sum)
17. R3C1 = 5 (hidden single in N1) -> R4C12 = 14 = [68]
and the rest is naked singles.