Cages are ordered increasing from top to bottom and left to right.
The cages are digital, the last digit of the sum is in one of the cells.
Two cells have consecutive values, with the other non-consecutive so either C C NC or NC C C
R1C1 and R1C9 are each in two cages.
1. Each cage must contain the last digit of the cage sum, with the other two digits totalling 10, so cage sums must be in the range 11 to 19.
11 = [128]
12 = [129/237]
13 = [238/346]
14 = [347]
No possible permutations for 15, since [456] would have three consecutive values
16 = [367]
17 = [278/467]
18 = [189/378]
19 = [289]
2a. The two cages at R1C1 share the same cell and are in the same nonet so must contain five different values. Only possibilities are [237/289] and [346/378]
2b. Similarly for the two cages at R1C9; they can only be [237/289] and [346/378]
2c. The two diagonal cages at R1C1 and R1C9 are both in the top snake so cannot share the same values so must be [289/346] with the vertical cages at R1C1 and R1C9 [237/378] -> R1C19 = {23}, R2C1 and R2C9 = {37}, R3C1 and R3C9 = {78}, R2C2 and R2C8 = {48}, R3C3 and R3C7 = {69}, all locked for their rows, also 3,7 locked for C1 and C9 and 7,8 locked for N1 and N3
2d. Remaining values in top snake = 1,5,7, 7 can only be in R1 -> R1C5 = 7, R2C46 = {15}, locked for R2 and N2
2e. Naked triple {234} in R3C456, locked for R3 and N2
3. Only possibility for cage at R1C3 = [189] -> R1C3 = 1, R1C4 = 8, R2C5 = 9 -> R1C6 = 6, R3C2 = 5, R3C8 = 1
3a. 4 in N1 only in R12C2, locked for C2
3b. 6 in N1 only in R23C3, locked for C3
3c. 6 in N3 only in R23C7, locked for C7
4a. All cages must start with 1,2,3 or 4 -> R5C6 = {1234}, R6C1 = {124}, R6C7 = {1234}, R7C5 = {1234}, R8C1 = {124}, R9C4 = {1234}
4b. Second cells of cages cannot be 1,5 or 9 -> no 1,5,9 in R4C5, R5C7, R6C9, R7C2, R8C2, R8C5 and R9C5
4c. Last cells of cages can only be one of 6,7,8 or 9 -> R4C6 = {789}, R5C8 = {6789}, R7C8 = {6789}, R8C3 = {789}, R8C6 = {789}, R9C3 = {789}, R9C6 = {789}
4d. Naked triple {789} in R489C6, locked for C6
4e. 5 in C5 only in R56C5, locked for N5
5. Old Lace property R37C5 must exactly equal R5C46 and R5C37 must exactly equal R46C5
5a. R37C5 only contain 1,2,3,4 -> no 6,7,9 in R5C4
5b. No 1,6 in R5C37 -> no 1,6 in R46C5
5c. No 7,9 in R46C5 -> no 7,9 in R5C37
6. 5 in C5 only in R56C5 -> 5 must be in R5C35 (Old Lace property), locked for R5
6a. 5 in left-hand snake only in R7C3 + R9C1, locked for N7
6b. 5 in R7C3 + R9C1, locked for bottom snake
6c. 5 in N8 only in R7C46, locked for R7
6d. R9C1 = 5 (hidden single in N7)
7. 5 in right-hand snake only in R46C8, locked for C8 and N6
7a. R8C9 = 5 (hidden single in C9)
7b. R1C7 = 5 (hidden single in R1)
7c. 4 in N3 only in R12C8, locked for C8
8. 1 in C5 only in R57C5, locked for Old Lace
8a. 1 in N5 only in R5C456, locked for R5
9. 1 in left-hand snake only in R46C2, locked for C2 and N4
9a. No 1 in cage at R6C1 -> no 2 in R7C2
10. 1 in right-hand snake only in R7C7 + R9C9, locked for N9
10a. 1 in R7C7 + R9C9, locked for bottom snake
11. R8C1 = 1 (hidden single in R8) -> cage at R8C1 = [128/129/189] -> R8C2 = {28}, R9C3 = {89}
11a. 4 in N7 only in R7C13, locked for R7
12. Cage at R6C1 = [237/238/278/467] (cannot be [289] which clashes with R9C3) -> no 8 in R7C2, no 9 in R8C3
13. Cage at R3C5 = [237/238/289/347], no 4 in R3C5, no 2 in R4C5
13a. No 4 in R37C5 -> no 4 in R5C46 (Old Lace property)
14. 7 in left-hand snake only in R46C2 + R7C3, CPE no 7 in R46C3 + R79C2
14a. 9 in left-hand snake only in R3C3 + R46C2 + R5C1 + R7C3, CPE no 9 in R46C3
15. 3 in C3 only in R4567C3, CPE no 3 in R46C2 using left-hand snake
16. 7 in C3 only in R78C3, CPE no 7 in R8C468 using bottom snake
17. Cage at R7C5 = [129/189/238] (cannot be [128] which clashes with R8C2) -> R7C5 = {12}, R8C5 = {238}
17a. Killer pair 2,8 in R8C2 and R8C56, locked for R8 -> R8C3 = 7
18. R7C7 = 7 (hidden single in bottom snake), placed for right-hand snake -> R9C9 = 1 (hidden single in N9)
18a. R46C2 = {17} (hidden pair in left-hand snake), 7 locked for N4
19. 4 in C9 only in R456C9, locked for N6
19a. R5C8 = 7 (hidden single in R5) -> cage at R5C6 = [237] -> R5C6 = 2, R5C7 = 3, placed for Old Lace
19b. R5C4 = 1, R2C46 = [51]
19c. R36C6 = [34], 4 placed for Old Lace, R37C5 = [21], R3C4 = 4, R7C6 = 5
20. R7C5 = 1 -> cage at R7C5 = [189], R8C5 = 8, R8C6 = 9, R9C6 = 7
21. R8C2 = 2, placed for left-hand snake and bottom snake -> vertical cage at R1C1 = [378], 3 placed for left-hand snake, R12C2 = [94], 4 placed for left-hand snake, R23C3 = [26], vertical cage at R1C9 = [237], 2 placed for right-hand snake, R12C8 = [48], 8 placed for right-hand snake, R23C7 = [69], 9 placed for right-hand snake
22. Naked pair {56} in R46C8, locked for C8 and N6 -> R456C9 = [948]
23. R6C9 = 8, R7C8 = 9 -> cage at R6C7 = [189] -> R6C7 = 1
and the rest is naked singles, without using cages, snakes or Old Lace.