Prelims
a) R12C4 = {16/25/34}, no 7,8,9
b) R1C56 = {14/23}
c) R3C45 = {49/58/67}, no 1,2,3
d) R4C12 = {16/25/34}, no 7,8,9
e) R45C3 = {49/58/67}, no 1,2,3
f) 9(2) cage at R4C4 = {18/27/36/45}, no 9
g) R56C1 = {89}
h) 13(2) cage at R6C6 = {49/58/67}, no 1,2,3
i) 12(2) cage at R8C8 = {39/48/57}, no 1,2,6
j) 21(3) cage at R4C8 = {489/579/678}, no 1,2,3
k) 8(3) cage at R5C8 = {125/134}
l) 7(3) cage at R6C3 = {124}
m) 21(3) cage at R6C5 = {489/579/678}, no 1,2,3
n) 22(3) cage at R8C1 = {589/679}
o) 11(3) cage at R9C6 = {128/137/146/236/245}, no 9
Steps resulting from Prelims
1a. Naked pair {89} in R56C1, locked for C1 and N4, clean-up: no 4,5 in R45C3
1b. Naked pair {67} in R45C3, locked for C3 and N4, clean-up: no 1 in R4C12
1c. 22(3) cage at R8C1 contains 9 -> R9C2 = 9, R89C1 = 13 = {67}, locked for C1 and N7, clean-up: no 3 in R8C8
1d. Naked triple {124} in R6C3, locked for C3
1e. 8(3) cage at R5C8 = {125/134}, 1 locked for C8
2. 45 rule on N7 3 innies R7C23 + R8C3 = 11 = {128/245} -> R7C2 = {58}, 2 locked for C3 and N7
3. 12(3) cage at R5C2 = {138/345}, no 2, 3 locked for C2
3a. 2 in N4 only in R4C12 = {25}, locked for R4 and N4, clean-up: no 4,7 in R5C5
4. R12C4 = {16/25} (cannot be {34} which clashes with R1C56)
4a. Killer pair 1,2 in R12C4 and R1C56, locked for N2
5. Max R123C1 = 12 -> min R1C23 = 14, no 1,2,3,4 in R1C23, max R1C2 = 8 -> no 5 in R1C3
[This step would be clearer written as
26(5) cage at R1C1 requires at least two of 6,7,8,9 (because {23459} only totals 23) -> no 1,2,3,4,5 in R1C23]
5a. Hidden killer pair 6,7 in R1C2 and R23C2 for C2, R23C2 cannot be {67} (because min R23C3 = 8) -> R1C2 = {67}, R23C2 contains one of 6,7
5b. Max R1C23 = 16 -> min R123C1 = 10 must contain 5, locked for C1 and N1 -> R4C12 = [25]
5c. R7C2 = 8 -> R56C2 = 4 = {13}, locked for C2 and N4 -> R6C3 = 4, clean-up: no 5 in R6C6, no 9 in R7C7
5d. Naked pair {12} in R78C3, locked for N7 -> R8C2 = 4, R7C1 = 3, R9C3 = 5, clean-up: no 7 in R8C8, no 8 in R9C9
5e. R123C1 = {145} = 10 -> R1C23 = 16 -> R1C2 = 7, R1C3 = 9
6. 45 rule on C4 3 outies R359C5 = 11 = {128/137/146/236/245}, no 9, clean-up: no 4 in R3C4
6a. 7,8 of {128} must be in R3C5 -> no 7,8 in R59C5, clean-up: no 1 in R4C4
7. 45 rule on R89 2 remaining innies R8C39 = 11 -> R8C3 = 2, R8C9 = 9, R7C3 = 1, clean-up: no 3 in R9C9
7a. 8(3) cage at R5C8 = {125/134}, 1 locked for N6
7b. 1 in N9 only in R89C7, locked for C7
7c. R8C9 = 9 -> R67C9 = 8 = [26/35/62], no 4,7,8, no 5 in R6C9
8. 12(3) cage at R8C5 = {138/156}, no 7, 1 locked for R8
8a. Killer pair 5,8 in 12(3) cage and R8C8, locked for R8
9. 45 rule on R4 3 outies R5C359 = 18 = {378/567} (cannot be {468} because 4,8 only in R5C9), no 1,2,4, 7 locked for R5, clean-up: no 7,8 in R4C4
9a. R359C5 (step 6) = {137/146/236/245} (cannot be {128} because 1,2 only in R9C5), no 8, clean-up: no 5 in R3C4
9b. 1,2 only in R9C5 -> R9C5 = {12}
9c. 4 of {245} only in R3C5 -> no 5 in R3C5, clean-up: no 8 in R3C4
10. 45 rule on N2 3 innies R2C56 + R3C6 = 20 = {389/578} (cannot be {479/569} which clash with R3C45), no 4,6
10a. 45 rule on N2 1 innie R3C6 = 1 outie R2C7 + 2, no 2,4,8,9 in R2C7, no 3 in R3C6
10b. 18(3) cage at R2C5 = {369/567} (cannot be {378} which clashes with R2C3) -> R2C7 = 6, R3C6 = 8, R23C2 = [26], R23C3 = [83], clean-up: no 1,5 in R1C4, no 7 in R3C45
10c. R3C45 = [94]
10d. 18(3) cage = {567} (only remaining combination), locked for R2, R2C4 = 1 -> R1C4 = 6, R2C1 = 4, R2C9 = 3, R2C8 = 9, clean-up: no 3 in R5C5, no 5 in R7C9 (step 7c)
10e. R3C6 = 8 -> R3C78 = 9 = {27}, locked for N3
11. 1 in R4 only in R4C56, locked for N5
11a. 13(3) cage at R4C5 = {139/148}, no 6,7
12. 13(3) cage at R8C4 = {238/247} (cannot be {148} because 4,8 only in R9C4, cannot be {346} because R9C5 only contains 1,2) -> R9C5 = 2, R89C4 = [38/74], R1C56 = [32]
12a. 2,5 in C4 only in 14(3) cage at R5C4 = {257}, locked for C4 -> R8C4 = 3, R9C4 = 8, R4C4 = 4, R5C5 = 5, 14(3) cage = [275], R2C56 = [75]
13. Naked triple {678} in R4C389, locked for R4, 8 also locked for N6
13a. 21(3) cage at R4C8 = {678} (only remaining combination), locked for N6 -> R67C9 = [26], R45C9 = [87], R4C8 = 6
14. R9C9 = 4, R7C8 = 2 -> R56C8 = 6 = [15], R8C8 = 8, R1C8 = 4, R1C9 = 5 (cage sum)
and the rest is naked singles.