Prelims
a) R23C4 = {29/38/47/56}, no 1
b) 11(2) cage at R5C4 = {29/38/47/56}, no 1
c) 6(2) cage at R5C5 = {15/24}
d) 12(2) cage at R6C5 = {39/48/57}, no 1,2,6
e) R6C78 = {69/78}
f) 23(3) cage at R3C1 = {689}
g) 8(3) cage at R5C2 = {125/134}
h) 24(3) cage at R8C9 = {789}
i) 10(3) cage at R9C5 = {127/136/145/235}, no 8,9
j) 13(4) disjoint cage at R1C3 = {1237/1246/1345}, no 8,9
k) 19(5) cage at R7C1 = {12349/12358/12367/12457/13456}
Steps resulting from Prelims
1a. Naked triple {689} in 23(3) cage at R3C1, locked for C1
1b. 8(3) cage at R5C2 = {125/134}, 1 locked for N4
1c. Naked triple {789} in 24(3) cage at R8C9, locked for N9
1d. 13(4) disjoint cage at R1C3 = {1237/1246/1345}, CPE no 1 in R1C9
1e. 19(5) cage at R7C1 = {12349/12358/12367/12457/13456}, 1 locked for N7
1f. 7 in N4 only in R4C2 + R456C3, CPE no 7 in R2C3
2. 45 rule on N3 1 innie R3C7 = 7, clean-up: no 4 in R2C4, no 8 in R6C8
3. 45 rule on full grid 1 innie R7C3 = 8, clean-up: no 3 in R5C4, no 4 in R6C5
3a. 45 rule on N7 3 remaining innies R7C2 + R8C23 = 18 = {279/369/459/567}
3b. 45 rule on N7 3 outies R8C45 + R9C4 = 13 = {139/148/157/238/247/346} (cannot be {256} which clashes with R7C2 + R8C23)
4. 45 rule on N236 2 outies R1C3 + R7C9 = 5 = {14/23}
4a. R1C3 + R7C9 = 5 -> R1C4 + R6C9 = 8 = {17/26/35}, no 4
5. 45 rule on N5 2 innies R5C4 + R6C5 = 14 = [59/68/95] -> R6C3 = {256}, R7C4 = {347}
6. 45 rule on N14 2 innies R16C3 = 9 = [36/45], clean-up: no 9 in R5C4, no 3,4 in R7C9 (step 4)
6a. Naked pair {56} in 11(2) cage at R5C4, CPE no 5,6 in R5C123 + R6C456, clean-up: no 1 in R5C5, no 7 in R7C4
6b. Killer pair 8,9 in R6C5 and R6C78, locked for R6
6c. R23C4 = {29/38}/[74] (cannot be {56} which clashes with R5C4), no 5,6
7. 22(4) cage at R7C8 = {2569/3469/3568/4567} (other combinations contain more than one of 7,8,9), no 1, R8C6 = {789}, 6 in R7C8 + R8C78, locked for N9
8. 45 rule on R89 3 outies R7C128 = 16 = {169/259/367/457} (cannot be {349} which clashes with R7C4)
8a. 9 of {259} must be in R7C2 -> no 2 in R7C2
9. 13(3) cage at R3C3 = {139/157/247} (cannot be {256} which clashes with R6C3, cannot be {346} which clashes with R1C3), no 6
9a. 1 of {139/157} must be in R3C3 -> no 3,5,9 in R3C3
10. R8C45 + R9C4 (step 3b) = {139/148/157/238/247} (cannot be {346} which clashes with R7C4), no 6
10a. 16(3) cage at R7C5 = {169/259/367/457} (cannot be {349} which clashes with R7C4)
10b. Killer triple 7,8,9 in 16(3) cage, R8C45 + R9C4 and R8C6, locked for N8
11. 45 rule on N1 3 innies R1C3 + R3C13 = 1 outie R4C2 + 8
11a. Max R1C3 + R3C13 = 16 -> max R4C2 = 8
12. 45 rule on C12 3 outies R289C3 = 15 = {159/249/267} (cannot be {456} which clashes with R6C3, cannot be {357} which clashes with R16C3), no 3
[Just spotted.]
13. R1C4 + R6C9 (step 4a) = {17/26}/[53] (cannot be [35] which clashes with R16C3)
13a. 5 in R6 only in R6C123, locked for N4
13b. 13(3) cage at R3C3 (step 9) = {139/247}
13c. Killer pair 3,4 in R1C3 and 13(3) cage, locked for C3
[Then, while looking for a way to also remove [53], I found …]
14. R16C3 (step 6) = [36/45], 13(3) cage at R3C3 (step 13b) = {139/247}
14a. Consider combinations for 8(3) cage at R5C2 = {125/134}
8(3) cage = {125} => R16C3 = [36] => 13(3) cage = {247}
or 8(3) cage = {134} => 13(3) cage = 4{27}
-> 13(3) cage = {247}, locked for C3, 7 also locked for N4 -> R16C3 = [36], R5C4 = 5, R7C9 = 2 (step 4), R6C5 = 9 (step 5) -> R7C4 = 3, R6C78 = [87]
[An alternative way to look at step 15a is
Combined cages R16C3 + 8(3) cage at R5C2 = [36]{125/134}/[45]{134}
13(3) cage at R3C3 = {247} (cannot be {139} = 1{39} which clashes with R16C3 + 8(3) cage), locked for C3, 7 also locked for N4 …]
14b. R1C4 + R6C9 (step 4a) = 8 = [71]
14c. 5 in R6 only in 8(3) cage at R5C2 -> R5C2 = 1, R6C12 = {25}, locked for R6 and N4 -> 6(2) cage at R5C5 = [24], R6C6 = 3
14d. R3C13 = [62] (hidden singles in C1 and C3), R23C4 = [29] (only remaining permutation)
14e. R4C2 = 3 (hidden single in N4) -> R2C23 + R3C2 = 22 = {589}, locked for N1 -> R1C12 = [14], R2C1 = 7
14f. R9C3 = 1 (hidden single in C3) -> 10(3) cage at R9C5 = [523] (only remaining permutation)
14g. R7C7 = 1 (hidden single in N7) -> R7C56 = 15 = [69]
15. 45 rule on N6 2 remaining innies R45C7 = 13 = {49}, locked for C7, N6 and 28(5) cage at R3C5
15a. R345C7 = 20 -> R3C56 = 8 = [35]
and the rest is naked singles.