Red border cages contain consecutive numbers, not necessarily in order; black border cages cannot contain consecutive numbers.
1. 20(3) cage at R1C3 = {479} (only combination without consecutive numbers), locked for N1
1a. 11(3) cage at R1C5 = {137/146} (other combinations contain consecutive numbers), 1 locked for C5 and N2
1b. 12(3) cage at R1C3 = {246} (only remaining combination without consecutive numbers) -> R1C3 = 4, placed for D\ at R1C3, R12C4 = {26}, locked for C4 and N2
1c. 11(3) cage at R1C5 = {137}, locked for C5 and N2
2. Remban group at R1C1 = {567/678} (cannot be {789} which clashes with 20(3) cage at R1C23) -> R2C2 = 7, placed for D\, R1C1 + R3C3 = {56/68}, 6 locked for N1 and D\ at R1C1, R3C1 = 9, placed for D\ at R3C1
2a. 9 in N2 only in R12C6, locked for C6
3. Remban group at R7C7 = {123/234/345}, no 8,9, 3 locked for D\ and N9
4. 10(3) cage at R6C6 = {136} (only combination without consecutive numbers) -> R7C5 = 6, placed for D\ at R3C1, D/ at R3C9 and Old Lace, R8C6 = 3, placed for D\ at R3C1, R6C6 = 1, placed for D\ at R1C1, D/ at R3C9 and Old Lace
4a. R5C6 = 6 (hidden single in C6)
5. Remban group at R7C7 (step 3) = {234/345}, 4 locked for D\ and N9
6. 9 on D\ at R1C1 only in R4C4 + R5C5, locked for N5 and Old Lace
6a. Killer cage at R4C4 cannot contain both of 1,2 and both of 8,9 -> R4C4 + R5C5 = {59}, locked for N5, D\ at R1C1 and Old Lace
6b. Naked pair {68} in R1C1 + R3C3, locked for N1
6c. Naked triple {234} in Remban group at R7C7, locked for N9
7. R5C4 = 3 (hidden single in N5)
7a. R3C5 = 3 (hidden single in Old Lace), placed for D\ at R1C3 and D/ at R1C7, R12C5 = [71]
7b. R6C4 = 4 (hidden single in Old Lace), placed for D/ at R1C9 and D\ at R3C1
7c. Naked pair {28} in R46C5, locked for C5 and N5 -> R4C6 = 7, placed for D\ at R1C3, D/ at R1C9 and Old Lace
7d. Naked pair {28} in R5C37, locked for R5
7e. Naked pair {28} in R5C37, CPE no 2,8 in R1C7 using D/ at R1C7, no 2,8 in R9C3 using D/ at R3C9
7e. 1 in N1 only in R13C2, locked for C2
7f. 4 in C5 only in R89C5, locked for N8
8. The only numbers missing from all the short diagonals are 2,5,8
8a. D\ at R3C1 contains two of 2,5,8 in R4C2 and R5C3 -> no 5,8 in R9C7
[I was forgetting about this cage …]
9. R1C3 = 4 -> Remban group at R1C2 = {234/345}, no 1, 3 locked for N1
9a. R3C2 = 1 (hidden single in N1)
9b. 2 in R3 only in R3C789, locked for N3
[Then I was a bit slow to spot …]
10. R5C37 = {28} are both on short diagonals so the only number which can be missing from all the short diagonals is 5 -> no 5 in R1C7, R2C6, R3C9, R4C248, R6C28, R7C19, R8C4 and R9C3
10a. Naked pair {28} in R4C2 + R5C3, locked for N4
10b. Naked pair {28} in R4C25, locked for R4
11. R4C4 = 9, placed for D/ at R1C7, R5C5 = 5, placed for D/ at R1C9, R6C2 = 6, placed for D/ at R1C7, R1C7 = 1, placed for D/ at R1C7, R9C7 = 7
11a. R1C6 = 9 (hidden single in C6)
11b. 5 in N2 only in R3C46, locked for R3
12. 1 on D/ at R1C9 only in R7C3 + R9C1, locked for N7
12a. R8C9 = 1 (hidden single in R8)
12b. R5C8 = 1 (hidden single in N6)
13. Naked triple {289} in R5C7 + R6C8 + R7C9, locked for D\ at R1C3, 2 also locked for N6 -> R2C4 = 6, R1C4 = 2
13a. Naked triple {289} in R5C7 + R6C8 + R7C9, CPE no 8,9 in R56C9
14. R5C2 = 9 (hidden single in R5)
14a. R5C1 = 4 (hidden single in N4), R5C9 = 7
14b. R3C8 = 7 (hidden single in N3)
14c. Naked pair {28} in R48C2, locked for C2
14d. Naked triple {357} in R6C139, locked for R6
15. 9 on D/ at R1C9 only in R2C8 + R7C3, CPE no 9 in R7C8
At this stage I looked at placements for R9C3 but I’ve optimised slightly, omitting those steps, since the next step results in a placement for R9C3
16. Consider placements for R5C3
R5C3 = 2 => R4C2 = 8, R8C2 = 2, placed for D/ at R1C9
or R5C3 = 8 => R5C7 = 2
-> no 2 in R3C7
[Maybe this step is a finned X-Wing?]
16a. Naked pair {68} in R3C37, locked for R3 -> R3C46 = [54], R3C9 = 2, R2C6 = 8, placed for D/ at R1C7, R5C3 = 2, placed for D/ at R1C7, R4C2 = 8, R7C1 = 7, R8C2 = 2, R8C8 = 4, R4C8 = 3, placed for D/ at R3C9, R9C3 = 9
and the rest is naked singles.
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