Prelims. Eliminations made for givens, including along short diagonals.
1. 1 in C1 only in R89C1, locked for N7
2. 8 in C9 only in R12C9, locked for N3
3. 2 in R1 only in R1C12, locked for N1
4. 7 in R9 only in R9C89, locked for N9
5. 1 in window at R1C3 only in R1C45678, locked for R1
6. 7 in window at R2C1 only in R23456C1, locked for C1
7. 2 in window at R3C9 only in R45678C9, locked for C9
8. 8 in window at R8C2 only in R9C23456, locked for R9
9. Grouped X-Wing for 8 in window at R1C3 and R12C9, no other 8 in R12
9a. 8 in C1 only in R34567C1, locked for window at R2C1, no 8 in R34C2
10. Grouped X-Wing for 2 in R1C12 and window at R2C1, no other 2 in C12
10a. 2 in R9 only in R9C34567, locked for window at R8C2, no 2 in R8C34
11. Grouped X-Wing for 1 in R89C1 and window at R8C2, no other 1 in R89
11a. 1 in C9 only in R34567C9, locked for window at R3C9, no 1 in R67C8
12. Grouped X-Wing for 7 in window at R3C9 and R9C89, no other 7 in C89
12a. 7 in R1 only in R1C34567, locked for window at R1C3, no 7 in R2C67
13. There are eight 45(9) windows -> R1C12 + R12C9 + R5C5 + R89C1 + R9C89 must form a hidden 45(9) window
13a. 2 in R1 only in R1C12, 8 in C9 only in R12C9, 1 in C1 only in R89C1 and 7 in R9 only in R9C89 -> no 1,2,7,8 in R5C5
14. 3,8 in window at R1C3 only in R1C3456 + R2C6, no 3 in R2C4, no 8 in R3C5 using short diagonal
15. 2 in window at R2C1 only in R4567C1 + R4C2, no 2 in R5C3 using short diagonal
16. 7 in window at R3C9 only in R3456C9 + R6C8, no 7 in R5C7 using short diagonal
17. 1,6 in window at R8C2 only in R8C4 + R9C4567, no 1 in R7C5, no 6 in R8C6 using short diagonal
[I ought to have spotted the next two steps earlier. Steps 18a and 19a have since been re-written, after I realised that they were hidden pairs. Also it took me a long time to spot that they eliminated 3,6 from R5C5 although I’d done similar eliminations in step 13.]
18. 6 in N4 only in R456C1 + R4C2, locked for window at R2C1, no 6 in R23C1 + R3C2
18a. R1C12 = {26} (hidden pair for N1), locked for R1 and hidden 45(9) window, no 6 in R12C9 + R5C5 + R9C89
18b. 6 in window at R1C3 only in R2C67, locked for R2
18c. 6 in C9 only in R34568C9, locked for window at R3C9, no 6 in R6C8
18d. 6 in C8 only in R345C8, locked for window at R3C6, no 6 in R3C6 + R4C7 + R5C67
18e. 6 in R9 only in R9C4567, locked for window at R8C2, no 6 in R8C4
19. 3 in N6 only in R456C9 + R6C8, locked for window at R3C9, no 3 in R7C89 + R8C9
19a. R9C89 = {37} (hidden single in N9), locked for R9 and hidden 45(9) window, no 3 in R5C5 + R89C1
19b. 3 in window at R8C2 only in R8C34, locked for R8
19c. 3 in C1 only in R24567C1, locked for window at R2C1, no 3 in R4C2
19d. 3 in C2 only in R567C2, locked for window at R5C2, no 3 in R5C34 + R6C3 + R7C4
19e. 3 in R1 only in R1C3456, locked for window at R1C3, no 3 in R2C6
20. R5C5 = 9 (naked single), locked for hidden 45(9) window, no 9 in R12C9 + R89C1
20a. 9 in R1 only in R1C345678, locked for window at R1C3, no 9 in R2C67
20b. 9 in C1 only in R234567C1, locked for window at R2C1, no 9 in R34C2
20c. 9 in C9 only in R345678C9, locked for window at R3C9, no 9 in R67C8
20d. 9 in R9 only in R9C234567, locked for window at R8C2, no 9 in R8C34
21. R14C2 = {26} (hidden pair in C2)
21a. R69C8 = {37} (hidden pair in C8)
22. Consider the placement of 5 in C1
5 in C1 of window at R2C1 => no 5 in R3C2 => R9C2 = 5 (hidden single in C2)
or 5 in R89C1
-> 5 must be in R89C1 + R9C2, locked for N7
22a. 5 in window at R8C2 only in R9C256, locked for R9
22b. 5 in C3 only in R1234C3, CPE no 5 in R3C5 using short diagonal
23. Consider the placement for 4 in C9
4 in R12C9
or 4 in C9 of window at R3C9 => no 4 in R7C8 => R1C8 = 4 (hidden single in C8)
-> 4 must be in R1C8 + R12C9, locked for N3
23a. 4 in window at R1C3 only in R1C458, locked for R1
23b. 4 in C7 only in R6789C7, CPE no 4 in R7C5 using short diagonal
24. 4 in hidden 45(9) cage only in R2C9 + R89C1, CPE no 4 in R2C1
24a. 5 in hidden 45(9) cage only in R12C9 + R8C1, CPE no 5 in R8C9
25. Consider combinations for R12C9
R12C9 = [84] => R2C6 = 8 (hidden single in R2) => R2C7 = 6 (hidden single in R2)
R12C9 = {58}, locked for N3 => R2C7 = 6
-> R2C7 = 6
25a. 6 in C8 only in R45C8, locked for N6
25b. R8C9 = 6 (hidden single in C9)
25c. 6 in window at R6C5 only in R6C56, locked for R6 and N5
26. Consider combinations for R89C1
R89C1 = {14}, locked for N7 => R8C3 = 3
R89C1 = [51] => R8C4 = 1 (hidden single in R8) => R8C3 = 3 (hidden single in R8)
-> R8C3 = 3
26a. 3 in C2 only in R56C2, locked for N4
26b. R2C1 = 3 (hidden single in C1)
26c. 3 in window at R2C3 only in R4C45, locked for R4 and N5
27. 7,9 in R2 only in R2C345, locked for window at R2C3, no 7,9 in R34C345, CPE no 9 in R1C3 using short diagonal
27a. 2,9 in R8 only in R8C567, locked for window at R6C5, no 2,9 in R67C567, CPE no 9 in R9C7 using short diagonal
28. 4 in N1 only in R2C3 + R3C123, CPE no 4 in R3C4
28a. 5 in N9 only in R7C789 + R8C7, CPE no 5 in R7C6
29. 4 in R3 only in R3C123, locked for N1
29a. 5 in R7 only in R7C789, locked for N9
30. R89C1 = {14}/[51] cannot be [51], here’s how
R89C1 = [51], locked for hidden 45(9) cage => R1C9 = 8, R3C2 = 5 (hidden single in C2), R2C34 = {79}, R1C3 = 7 clashes with R2C34 using short diagonal
30a. -> R89C1 = {14}, locked for C1, N7 and hidden 45(9) cage, no 4 in R2C9
30b. R9C2 = 5 (hidden single in N7), R3C2 = 4
30c. Naked pair {58} in R12C9, locked for C9 and N3
30d. Naked pair {58} in R2C69, locked for R2
30e. Naked pair {79} in R2C34, locked for R2, CPE no 7 in R1C3 using short diagonal
30f. R2C5 = 4
30g. Naked pair {58} in R1C3 + R2C6, locked for window at R1C3, no 5,8 in R1C456
30h. Naked triple {389} in R567C2, locked for window at R5C2, no 8,9 in R5C34 + R6C3 + R7C4
30i. 9 in C2 only in R67C2, CPE no 9 in R7C1 using short diagonal
30j. Naked quad {1379} in R1C456 + R2C4, locked for N2
30k. 1 in window at R2C3 only in R4C345, locked for R4
31. Naked pair {14} in R8C14, locked for R8
31a. Naked pair {29} in R8C67, locked for R8, CPE no 2 in R9C7 using short diagonal
31b. R8C5 = 5
31c. Naked pair {14} in R79C7, locked for C7 and N9 -> R7C8 = 5
32. R1C8 = 4 (hidden single in C8)
32a. Naked triple {169} in R345C8, locked for window at R3C6, no 9 in R4C7, no 1 in R5C6
32b. 9 in C8 only in R34C8, CPE no 9 in R3C9 using short diagonal
33. R7C7 = 4 (hidden single in window at R6C5), R9C7 = 1, R9C1 = 4, R8C1 = 1, R8C4 = 4
33a. Naked quad {2689} in R8C6 + R9C456, locked for N8
33b. 8 in window at R6C5 only in R6C567, locked for R6
34. Naked pair {58} in R13C3, locked for C3 and N1
34a. R3C3 = 5 (hidden single in window at R2C3), R1C3 = 8, R1C9 = 5, R2C9 = 8, R2C6 = 5
35. Consider placements for R3C8
R3C8 = 1 => R3C9 = 7, R4C8 = 9 (hidden single in C8) => R4C9 = 2
R3C8 = 9 => R8C7 = 7 (hidden single in C7) => R7C9 = 2
-> 2 must be in R4C9 + R7C9, locked for C9
36. 2 in R6 only in R6C13, locked for N4 -> R4C2 = 6, R4C3 = 1
and the rest is naked singles.