Congratulations Frank for solving it so quickly!
You finished it before I started.
Fairly straightforward but I did need some hidden killers, expressed directly or indirectly so I can't rate it lower than 1.0.
Here is my walkthrough for A72. There could be quicker routes near the end but it was getting late so I may have missed some.
Edit. I've now checked through my walkthrough (it was too late to do that on Thursday evening, well actually the "wee sma' hours" of Friday morning), tidying up the later steps and correcting an error near the end. Hope I've got it right now.
1. R12C1 = {49/58/67}, no 1,2,3
2. R12C5 = {29/38/47/56}, no 1
3. R12C9 = {59/68}
4. R89C1 = {59/68}
5. R89C5 = {{29/38/47/56}, no 1
6. R89C9 = {14/23}
7. 9(3) cage at R2C3 = {126/135/234}, no 7,8,9
8. 10(3) cage at R3C1 = {127/136/145/235}, no 8,9
9. R5C123 = {128/137/146/236/245}, no 9
10. R5C789 = {127/136/145/235}, no 8,9
11. 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
12. 10(3) cage at R6C8 = {127/136/145/235}, no 8,9
13. 10(3) cage at R7C6 = {127/136/145/235}, no 8,9
14. 32(5) cage at R2C8 = {26789/35789/45689} = 89{267/357/456}, no 1
15. 32(5) cage at R6C6 = {26789/35789/45689} = 89{267/357/456}, no 1
16. 39(7) cage at R3C5 = {1356789/2346789} = 36789{15/24}
"It starts with a little present"
17. 45 rule on R5 and C5, R5C5 counts toward both row and column, total 82 -> R5C5 = 8, clean-up: no 3 in R12C5, no 3 in R89C5
"There are in fact two more little presents"
18. 45 rule on C1234 1 innie R5C4 = 9
19. 45 rule on C6789 1 innie R5C6 = 7
20. 9 in C5 locked in R12C5 or R89C5 -> one of these must be {29} -> 2 in C5 locked in R12C5 or R89C5
21. 45 rule on R1234 2 innies R34C5 = 6 = {15} (only remaining combination)
21a. Naked pair {15} in R34C5, locked for C5, clean-up: no 4 in 39(7) cage (step 16), no 6 in R12C5, no 6 in R89C5
22. 45 rule on R1 3 innies R1C159 = 16 = {259/268/457}
22a. 2 of {259} must be in R1C5 -> no 9 in R1C5, clean-up: no 2 in R2C5
23. 45 rule on R1 3 outies R2C159 = 22 = {589/679} = 9{58/67}, no 4, 9 locked for R2, clean-up: no 9 in R1C1, no 7 in R1C5
24. R1C159 (step 22) = {259/268/457}
24a. 4 of {457} must be in R1C5 -> no 4 in R1C1, clean-up: no 9 in R2C1
25. Killer pair 5,6 in R12C1 and R89C1, locked for C1
[I missed the clash between R12C1 and R89C1. However that allowed the interesting step 36.]
26. 1 in C1 locked in R345C1
26a. CPE no 1 in R4C2
27. 45 rule on R9 3 innies R9C159 = {169/178/259/349/367/457} (cannot be {268} because 6,8 only in R9C1, cannot be {358} because no 3,5,8 in R9C5)
27a. 2 of {259} must be in R9C9 -> no 2 in R9C5, clean-up: no 9 in R8C5
28. 9 in N8 locked in R9C56, locked for R9, clean-up: no 5 in R8C1
29. R9C159 (step 27) = {169/178/259/367/457} (cannot be {349} because no 3,4,9 in R9C1)
29a. 4 of {457} must be in R9C9 -> no 4 in R9C5, clean-up: no 7 in R8C5
30. R12C9 contains 8/9
30a. 32(5) cage at R2C8 (step 14) = 89{267/357/456} so must contain 8/9 in N3 -> R4C7 = {89}
30b. Killer pair 8,9 in R12C9 and 32(5) cage, locked for N3
31. Hidden killer pair 8,9 in R12C9 and R4C9 -> R4C9 = {89}
32. Killer pair 8,9 in R4C79, locked for R4 and N6
33. 32(5) cage at R6C6 (step 15) = 89{267/357/456}, 8,9 locked for N9
34. 10(3) cage at R3C1 (step 8) = {127/136/145/235}
34a. No 4 in R3C1 because R4C12 = [15] clashes with R4C5
35. 4 in C1 locked in R4567C1
35a. CPE no 4 in R6C2
36. R12C1 contains 7/8, R89C1 contains 8/9 -> R67C1 cannot contain more than one of 7,8,9 -> max R67C1 = 13 -> min R6C2 = 6
36a. Max R6C2 = 9 -> min R67C1 = 10 -> R67C1 must contain one of 7,8,9
36b. Killer triple 7,8,9 in R12C1, R67C1 and R89C1, locked for C1
37. 10(3) cage at R3C1 (step 8) = {127/136/145/235}
37a. 5,6,7 only in R4C2 -> R4C2 = {567}
38. 45 rule on C9 4 outies R4C8 + R5C78 + R6C8 = 11 = {1235}, locked for N6
38a. 7 in N6 locked in R6C79, locked for R6
39. R5C789 (step 10) = {136/145} (cannot be {127/235} because R5C9 only contains 4,6), no 2, 1 locked for R5 and N6
39a. 2 in N6 locked in R46C8, locked for C8
40. 2 in R5 locked in R5C123, locked for N4
40a. R5C123 (step 9) = {236/245}
41. 7 in R4 only in R4C23
41a. CPE no 7 in R23C2
42. 19(3) cage at R6C1 (step 11) = {289/379/469/478}
42a. 7 of {379} must be in R7C1 -> no 3 in R7C1
42b. 2 of {289} and 7 of {478} must be in R7C1 -> no 8 in R7C1
43. 10(3) cage at R6C8 (step 12) = {127/145} (cannot be {136} because R6C89 = [36] clashes with R6C5, cannot be {235} because R6C9 only contains 4,6,7) -> R7C9 = 1, R6C89 = [27/54], clean-up: no 4 in R89C9
44. Naked pair {23} in R89C9, locked for C9 and N9
45. 10(3) cage at R7C6 (step 13) = {127/136/145/235}
45a. Min R8C7 = 4 -> max R78C6 = 6, no 6
45b. 1 of {145} must be in R8C6
45c. 5 of {235} must be in R8C7
45d. -> no 4,5 in R8C6
46. R9C159 (step 29) = {259/367}, no 8, clean-up: no 6 in R8C1
47. R9C678 = {367/457} (cannot be {169/178/259/268/349/358} because 1,2,3,8,9 only in R9C6), no 1,2,8,9 in R9C6, 7 locked in R9C78 for R9 and N9
47a. 3 of {367} must be in R9C6 -> no 6 in R9C6
48. R9C5 = 9 (naked single), R8C5 = 2, R12C5 = [47], R89C9 = [32], R8C6 = 1, clean-up: no 6 in R1C1
[Could now have fixed R12C19 using step 22. This also applies after step 50.]
49. 1 in R9 locked in R9C23
49a. R9C234 = {148} (only remaining combination), locked for R9, clean-up: no 5 in R9C678 (step 47) -> R9C6 = 3, R67C6 = [36], clean-up: no 6 in R8C7 (step 13)
50. Naked pair {67} in R9C78, locked for R9 and N9 -> R9C1 = 5, R8C1 = 9, clean-up: no 8 in R12C1 -> R12C1 = [76], clean-up: no 8 in R1C9
51. 7 in N8 locked in R78C4, locked for 18(3) cage -> no 7 in R8C3
51a. 18(3) cage at R7C4 = {567} (only remaining combination), no 4,8 -> R8C3 = 6
52. Naked pair {57} in R78C4, locked for C4 and N8 -> R7C6 = 4, R7C1 = 2, R8C7 = 5, R78C4 = [57], R9C4 = 8
52a. Naked pair {14} in R9C23, locked for N7 -> R8C2 = 8, R8C8 = 4
53. R6C1 = 8 (hidden single in C1), R6C2 = 9
54. 4 in C1 locked in R45C1, locked for N4
55. 23(5) cage at R6C3, R7C23 = {37}, R8C2 = 8 -> R6C34 = 5 = [14]
I seem to have deleted too much when editing this walkthrough so the rest is straightforward but not quite down to naked singles.