Prelims
a) R1C67 = {14/23}
b) R23C1 = {13}
c) R23C6 = {14/23}
d) R34C5 = {29/38/47/56}, no 1
e) R4C23 = {13}
f) R45C4 = {17/26/35}, no 4,8,9
g) R4C67 = {89}
h) R56C6 = {19/28/37/46}, no 5
i) R6C45 = {39/48/57}, no 1,2,6
j) R6C78 = {12}
k) R78C4 = {15/24}
l) R9C23 = {15/24}
m) Disjoint 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9
Steps resulting from Prelims
1a. Naked pair {13} in R23C1, locked for C1 and N1
1b. Naked pair {13} in R4C23, locked for R4, N4 and upper-left window, clean-up: no 8 in R3C5, no 5,7 in R5C4
1c. Naked pair {89} in R4C67, locked for R4 and upper-right window, clean-up: no 2,3 in R3C5
1d. Naked pair {12} in R6C78, locked for R6, N6 and lower-right window, clean-up: no 8,9 in R5C6
1e. 8,9 in N3 only in R123C9, locked for C9
2. Naked pair {13} in R3C1 + R4C2, locked for upper-left lace, no 1,3 in R1C5
3. 9 in upper-left lace only in N1 + R2C4, CPE no 9 in R2C3
4. 9 in upper-right lace only in R13C9, locked for C9
4a. 1 in upper-right lace only in R2C6 + N3, CPE no 1 in R2C79
4b. 3 in upper-right lace only in R2C6 + R5C9 + N3, CPE no 3 in R2C9
5. 9 in lower-left lace only in R6C2 + N7, CPE no 9 in R7C2
6. 9 in lower-right lace only in R8C6 + N9, CPE no 9 in R8C7
7. 45 rule on N5 2 outies R3C5 + R4C7 = 1 innie R5C5 + 13
7a. Max R3C5 + R4C7 = 18 -> max R5C5 = 5
7b. Min R3C5 + R4C7 = 14, no 4 in R3C5, clean-up: no 7 in R4C5
8. Disjoint 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}
8a. 1 only in R9C5 -> no 6,7,8 in R9C5
9. R45C4 = {17/26/35}, R78C4 = {15/24} -> combined cage R4578C4 = {17}{24}/{26}{15}/{35}{24}, 2 locked for C4
10. Hidden killer pair 1,2 in R23C6 and R23C78 for upper-right window, R23C6 contains one of 1,2 -> R23C78 must contain one of 1,2
10a. Killer pair 1,2 in R1C78 and R23C78, locked for N3
10b. Hidden killer pair 1,3 in R23C6 and R23C78 for upper-right window, R23C6 contains one of 1,3 -> R23C78 must contain one of 1,3
10c. Killer pair 1,3 in R1C78 and R23C78, locked for N3
10d. 1,2 in C9 only in R789C9, locked for N9
11. Hidden killer pair 1,2 in R78C4 and R78C23 for lower-left window, R78C4 contains one of 1,2 -> R78C23 must contain one of 1,2
11a. Killer pair 1,2 in R78C23 and R9C23, locked for N7
12. 3 in N7 only in R78C23, locked for lower-left window, clean-up: no 9 in R6C5
13. Hidden killer pair 1,3 in R1C46 and R1C78 for R1, R1C78 contains one of 1,3 -> R1C46 must contain one of 1,3
13a. Killer pair 1,3 in R1C46 and R23C6, locked for N2
[I first saw this elimination as
The upper-left and upper-right windows contain two 45(9)s for R234 -> R234C159 must form a hidden window for R234
Naked pair {13} in R23C1, locked for hidden window R234C159, no 1,3 in R2C5
but I then saw that a conventional killer step achieves the same result.]
13b. Hidden killer pair 1,3 in R1C46 and R23C6 for N2, taken with the hidden killer pair in step 13 -> R1C78 and R23C6 must contain the same combination, which is also in R1C7 + R2C6
[With hindsight I could have done this step directly from steps 10 and 10a. Similarly steps 11 and 11a can be used to show that R78C4 and R9C23 must contain the same combination, which is also in R8C4 + R9C3.]
13c. R1C78 = {14}, locked for N3
or R1C78 = {23}, R1C7 + R2C6 = {23} => 1 in upper-right lace only in R2C8 + R3C7, locked for N3
-> no 1 in R3C8
14. 1,2 in C9 only in R789C9
14a. Hidden killer pair 1,2 in R6C8 and R79C9 for lower-right lace, R79C9 must contain at least one of 1,2, R6C8 = {12} -> R79C9 must contain one of 1,2 -> R8C9 = {12}
14b. Killer pair {12} in R6C8 and R79C9, locked for lower-right lace, no 1,2 in R9C5
15. Disjoint 14(4) cage at R1C5 = {2345} (only remaining combination), CPE no 2,3,4,5 in R5C5 -> R5C1 = 1, clean-up: no 7 in R4C4, no 9 in R6C6
15a. 2 in 14(4) cage only in R1C5 + R5C1, locked for upper-left lace
15b. 3 in 14(4) cage only in R5C9 + R9C5, locked for lower-right lace
16. 7 in N5 only in R56C6 = {37} or R6C45 = {57} -> R6C45 = {48/57} (cannot be [93], locking-out cages)
17. R4C6 = 9 (hidden single in N5), R4C7 = 8
17a. 45 rule on N5 one remaining innie R4C5 = 5, R3C5 = 6, clean-up: no 3 in R5C4, no 7 in R6C45
18. Naked pair {26} in R45C4, locked for C4 and N5, clean-up: no 4 in R5C6, no 4,8 in R6C6, no 4 in R78C4
18a. Naked pair {48} in R6C45, locked for R6
18b. Naked pair {37} in R56C6, locked for C6, clean-up: no 2 in R23C6
18c. Naked pair {14} in R23C6, locked for C6, N2 and upper-right window -> R1C5 = 2, clean-up: no 3 in R1C78
18d. Naked pair {14} in R1C78, locked for R1 and N3
18e. Naked pair {14} in R1C7 + R2C6, locked for upper-right lace
19. Naked pair {15} in R78C4, locked for C4, N8 and lower-left window
19a. Naked pair {68} in R78C6, locked for C6, N8 and lower-right window -> R1C6 = 5, R9C6 = 2, clean-up: no 4 in R9C23
19b. Naked pair {15} in R9C23, locked for R9 and N7
20. R1C4 = 3 (hidden single in N2)
21. 5 in disjoint 14(4) cage at R1C5 only in R5C19, locked for R5
21a. 5 in N6 only in R56C9, locked for C9
22. R4C1 = 2 (hidden single in C1), R45C4 = [62], R4C8 = 7, R4C9 = 4
23. Naked quad {6789} in R1239C9, locked for C9
23a. Naked pair {35} in R56C9, locked for N6
23b. Naked pair {69} in R5C78, locked for R5
24. Naked pair {35} in R3C7 + R5C9, locked for upper-right lace -> R2C8 = 6, R5C78 = [69]
24a. Naked pair {89} in R13C9, locked for C9 -> R2C9 = 7, R9C9 = 6, R8C6 = 8, R7C6 = 6
24b. Naked pair {89} in R2C45, locked for R2 and N2 -> R3C4 = 7
25. Naked triple {345} in R5C9 + R8C8 + R9C5, locked for lower-right lace
25a. Naked pair {79} in R79C7, locked for C7
25b. R9C8 = 8 (hidden single in N9)
26. Naked pair {45} in R2C2 + R5C1, locked for upper-left lace
26a. Naked pair {89} in R2C4 + R3C3, locked for upper-left lace
26b. Naked pair {67} in R1C13, locked for R1
26c. Naked pair {89} in R1C2 + R3C3, locked for N1
27. R7C1 = 8 (hidden single in C1)
28. R6C4 = 8 (hidden single in lower-left window)
and the rest is naked singles.