Prelims
a) R12C7 = {18/27/36/45}, no 9
b) R12C8 = {39/48/57}, no 1,2,6
c) R89C4 = {17/26/35}, no 4,8,9
d) R89C5 = {17/26/35}, no 4,8,9
e) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
f) 13(4) cage at R1C2 = {1237/1246/1345}, no 8,9
g) 37(6) cage at R5C8 = {256789/346789}, no 1
h) 41(7) cage at R3C3 = {2456789}, no 1,3
i) 36(8) cage at R6C9 = {12345678}, no 9
1a. 13(4) cage at R1C2 = {1237/1246/1345}, 1 locked for R1, clean-up: no 8 in R2C7
1b. 45 rule on N2 2 outies R1C23 = 5 = {14/23}
1c. R1C23 = 5 -> R1C45 = 8 = {17/26/35}, no 4
1d. 45 rule on N3 2 innies R3C78 = 7 = {16/25/34}, no 7,8,9
1e. 45 rule on N12 1 innie R3C3 = 1 outie R4C1 + 4, R3C3 = {56789}, R4C1 = {12345}
1f. 2,4 in 41(7) cage at R3C3 only in R4C2345 + R5C45, CPE no 2,4 in R4C6
2a. 9 in N9 only in R79C7, locked for C7
2b. 9 in N6 only in R5C89 + R6C8, locked for 37(6) cage at R5C8
2c. R9C7 = 9 (hidden single in C7) -> R89C6 = 6 = {15/24}
2d. 45 rule on N8 3 remaining innies R7C456 = 23 = {689}, locked for R7, 6 locked for N8, clean-up: no 2 in R78C45
2e. 9 in R7 only in R7C45, CPE no 9 in R6C4
2f. R78C6 = {24} (hidden pair in N8), locked for C6
2g. 45 rule on N9 1 outie R6C9 = 1 remaining innie R7C7 -> R6C9 = {23457}
2h. 37(6) cage at R5C8 = {256789/346789}, CPE no 7 in R45C7
2i. 1 in N6 only in R4C789 + R5C7, CPE no 1 in R4C6
2j. 7,9 in R4 only in R4C23456, CPE no 7,9 in R5C45
3. 45 rule on C789 3 remaining outies R457C6 = 16 = {169/178/358/367}
3a. R7C6 = {68} -> no 6,8 in R45C6
3b. R45C6 = {35/37}/[71/91], no 9 in R5C6
3c. Consider placement for 8 in N6
8 in R45C7 => R7C6 = 8 (because 37(6) cage at R5C8 contains 8) => R45C6 = 8 = {35}/[71] => R345C7 = 14 = {248} (cannot be {158} which clashes with R45C6)
or 8 in R5C89 + R6C78 => R7C6 = 6, R45C6 = 10 = {37}/[91], R345C7 = 12 = {156/246/345}
-> R345C7 = {156/246/248/345}
3d. 45 rule on R1234 4 outies R5C4567 = 16 = {1258/1267/1348/1456/2356} (cannot be {1357} because R5C45 only contain one odd number, cannot be {2347} = {24}[73] which clashes with R45C6)
4. 45 rule on C6789 2 innies R36C6 = 1 outie R2C4 + 6, IOU no 6 in R6C6
[Only just spotted what seems to be a key step; it proves to be the key step. With hindsight it could have been used immediately after step 2d.]
5. R89C4 and R89C5 are both {17/35}, preventing R1C45 being {17/35} -> R1C45 = {26}, locked for R1 and N2, clean-up: no 3 in R1C23 (step 1b), no 3,7 in R2C7
5a. Naked pair {14} in R1C23, locked for N1, 4 locked for R1, clean-up: no 5 in R2C7, no 8 in R2C8
5b. R7C6 = 6 (hidden single in C6) -> R45C6 (step 3) = 10 = {37}/[91], no 5
5c. 37(6) cage at R5C8 = {256789/346789}, 8 locked for N6
5d. Naked pair {89} in R7C45, CPE no 8 in R6C4
5e. Hidden killer pair 1,3 in R45C6 and 23(4) cage at R6C4 for N5, R45C6 contains one of 1,3 -> 23(4) cage must contain one of 1,3 = {1589/3479/3569/3578} (cannot be {1679} which clashes with R45C6, other combinations don’t contain 1 or 3), no 2
5f. 2 in N5 only in R45C45, locked for 41(7) cage in R3C3
5g. 12(3) cage at R3C1 = {129/138/237/246/345} (cannot be {147} because 1,4 only in R4C1, cannot be {156} which clashes with R3C3 + R4C1 = [51], step 1e)
5h. 4 of {345} must be in R4C1 -> no 5 in R4C1, clean-up: no 9 in R3C3 (step 1e)
5i. 41(7) cage at R3C3 = {2456789}, 9 locked for R4, clean-up: no 1 in R5C6 (step 5b)
5j. Naked pair {37} in R45C6, locked for C6, 7 locked for N5, 3 locked for 22(5) cage at R3C7, clean-up: no 4 in R3C8 (step 1d)
5k. R345C7 (step 3c) = {156/246}, 6 locked for C6, clean-up: no 3 in R1C7
5l. R12C7 = [72/81] (cannot be [54] which clashes with R345C7), no 4,5
5m. Killer pair 1,2 in R2C7 and R345C7, locked for C7, clean-up: no 2 in R6C9 (step 2g)
5n. 23(4) cage at R6C4 = {1589}, 1,5 locked for R6, 5 locked for N5, clean-up: no 5 in R7C7 (step 2g)
5o. Killer pair 1,5 in R6C4 and R89C4, locked for C4
5p. 41(7) cage = {2456789}, CPE no 5,7 in R56C3
5q. 4,6 in N5 only in R45C45, locked for 41(7) cage, clean-up: no 2 in R4C1 (step 1e)
5r. 17(3) disjoint cage at R1C6 = {179/359/458}
5s. 3,4,7 of {179/359/458} only in R2C4 -> R2C4 = {347}
5t. 45 rule on N1 3 remaining innies R3C123 = 16 = {259/268/358} (cannot be {367} because 12(3) cage at R3C1 cannot contain both of 3,6), no 7, clean-up: no 3 in R4C1 (step 1e)
5u. 41(7) cage = {2456789}, 7 locked for R4 and N4 -> R4C6 = 3, placed for D/, R5C6 = 7, clean-up: no 9 in R1C8
6a. 1,6 in N6 only in R4C789 + R5C7
6b. 45 rule on N69 4 remaining innies R4C789 + R5C7 = 14 = {1256}, 2,5 locked for N6
6c. R5C6 = 7 -> R5C4567 = {1267} (step 3d) -> R5C7 = 1, R5C45 = {26}, locked for R5 and N5, R2C7 = 2 -> R1C7 = 7, clean-up: no 5 in R12C8, no 5 in R3C7, no 5,6 in R3C8 (both step 1d), no 7 in R6C9 (step 2g)
6d. R45C6 = [37], R5C7 = 1 -> R34C7 = 11 = [65], 6 placed for D/, R3C8 = 1 (step 1d), R5C5 = 2, placed for both diagonals
6e. Naked quad {4789} in R4C2345, 4 locked for R4, 8 locked for 41(7) cage at R3C3 -> R4C1 = 1, R3C3 = 5, placed for D\
6f. 2 in R3 only in R3C12, R4C1 = 1 -> R3C12 = 11 = {29}, 9 locked for R3 and N1 -> R3C6 = 8
6g. 7 in R3 only in R3C45, locked for N2
6h. 17(3) disjoint cage at R1C6 (step 5r) = {359} (only remaining combination) -> R2C4 = 3, R12C6 = {59}, locked for N2, 9 locked for C6
6i. R6C6 = 1, placed for D\, R6C4 = 5, placed for D/
6j. Naked pair {17} in R89C4, locked for N8, 7 locked for C4 -> R3C45 = [47]
6k. R2C9 = 5 (hidden single in N3), R12C6 = [59], R2C8 = 4, placed for D/, R1C8 = 8, R1C9 = 9, placed for D/, R3C9 = 3, R56C9 = [84], R67C7 = [34], R56C8 = [97], R8C7 = 8
6l. R1C1 = 3, placed for D\, R8C8 = 6, R9C9 = 7, both placed for D\, R2C2 = 8, placed for D\, R89C4 = [71], R9C1 = 8, R8C2 = 1, R7C3 = 7, R1C2 = 4, R8C9 = 2, R89C6 = [42]
6m. R9C23 = [64] (hidden pair in R9)
and the rest is naked singles, without using the diagonals.