I finished A2X on Christmas Eve but only managed to go through Caida's and Afmob's walkthroughs yesterday evening.
Afmob wrote:
Seems my key moves are not much different from Caida's ones.
There seems to be a very narrow solving path around Caida's step 8, Afmob's step 8 and my step 21.
Mike wrote:
Yes, it's a toughie. Unlike several recent Assassin V1's, which consist of finding one (or at most, two) key move(s), apart from which the rest is plain sailing, this is more like a traditional V2, which (whilst having easier sections) generally involves more of a fight to dig away at the candidates. This puzzle does contain at least one key move, however, that will make your life easier if you find it.
I assume Mike was referring to the narrow solving path mentioned above. It certainly took a lot more work after that. I've a feeling that my later stages were longer than those of Caida and Afmob although I haven't tried to compare them to see where they were quicker.
I'll agree with both of them and rate A2X as 1.5.
Here is my walkthrough.
Prelims
a) R5C123 = {127/136/145/235}, no 8,9
b) 10(3) cage in N5 = {127/136/145/235}, no 8,9
c) 21(3) cage in N5 = {489/579/678}, no 1,2,3
d) 10(3) cage at R8C6 = {127/136/145/235}, no 8,9
e) 24(3) cage in N9 = {789}, locked for N9
1. 45 rule on N1 3 innies R1C3 + R3C13 = 10 = {127/136/145/235}, no 8,9
1a. Max R3C1 = 7 -> min R4C12 = 11, no 1
2. 45 rule on N9 3 innies R7C79 + R9C7 = 8 = 1{25/34}, no 6, 1 locked for N9
3. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3
4. 45 rule on R1234 3 innies R4C456 = 10 = {127/136/145/235}, no 8,9
5. 45 rule on C1234 3 innies R456C4 = 10 = {127/136/145/235}, no 8,9
6. 45 rule on C6789 3 innies R456C6 = 20 = {389/479/569/578}, no 1,2
7. 45 rule on C1234 1 outie R4C5 = 1 innie R6C4 + 4, R4C5 = {567}, R6C4 = {123}
8. 45 rule on C6789 1 outie R6C5 = 1 innie R4C6 + 1, no 9 in R6C5
9. 45 rule on R1234 1 outie R5C4 = 1 innie R4C6 + 4 -> R5C4 = 7, R4C6 = 3, locked for D/, R6C5 = 4 (step 8)
10. Naked pair {56} in R45C5, locked for C5 and N5
10a. Naked pair {12} in R46C4, locked for C4
10b. Naked pair {89} in R56C6, locked for C6
11. Killer pair 5,6 in R5C123 and R5C5, locked for R5
12. 45 rule on R12 3 outies R3C258 = 22 = 9{58/67}, 9 locked for R3
13. 45 rule on C12 3 outies R258C3 = 19 = {289/379/469/478/568}, no 1
13a. 2,3 of {289/379} must be in R5C3 -> no 2,3 in R28C3
14. 45 rule on C9 4 outies R1469C8 = 1 innie R5C9 + 7
14a. Min R1469C8 = 10 -> min R5C9 = 3
15. 17(3) cage at R6C7 = {179/269/278/359/368/458/467}
15a. 8,9 of {179/269/278/359/368/458} must be in R6C7-> no 1,2,3,5 in R6C7
15b. 1,2 of {179/269/278} must be in R7C7 -> no 1,2 in R7C6
16. 45 rule on C89 3 outies R258C7 = 17 = {179/269/278/359/368/458/467}
16a. 3,4 of {359/368/458/467} must be in R5C7 -> no 3,4 in R2C7
17. 17(3) cage in N3 = {179/269/278/458/467}
17a. 4 of {458} must be in R2C8 -> no 5 in R2C8
18. 45 rule on R89 3 outies R7C258 = 17 = {179/269/278/359/368} (cannot be {458/467} because 4,5,6 only in R7C2), no 4
18a. 3 of {359/368} must be in R7C5 -> no 3 in R7C2
19. 45 rule on N478 6 innies R4C123 + R789C6 = 36
19a. Max R89C6 = 9 (because of 10(3) cage at R8C6), max R7C6 = 7 -> max R789C6 = 16 -> min R4C123 = 20, no 1,2
20. R5C123 = {136/145/235} [1/2]
20a. Hidden killer pair 1,2 in R5C123 and R6C123 for N4 -> R6C123 must contain 1/2
20b. Killer pair 1,2 in R6C123 and R6C4, locked for R6
21. Chaining steps 20a and 20b, R5C123 and R6C4 must contain the same value of 1/2
21a. 45 rule on R6789, 1 outie R5C6 = 1 innie R6C4 + 7 -> R5C6 + R6C4 = [81/92]
21b. -> R5C123 + R5C6 must contain 1,8 or 2,9
21c. R5C789 = {239} (only remaining combination, cannot be {149/248} which clash with R5C123 + R5C6), locked for R5 and N6 -> R56C6 = [89], 9 locked for D\
22. R1469C8 = R5C9 + 7 (step 14)
22a. Min R1469C8 = 11 -> no 3 in R5C9 -> R5C9 = 9
23. R5C123 = {145} (only remaining combination), locked for R5 and N4 -> R5C5 = 6, locked for both diagonals, R4C5 = 5, R4C4 = 2 (step 4), locked for D\, R6C4 = 1, locked for D/
23a. R12C9 cannot be {13} -> no 9 in R1C8
24. 17(3) cage at R6C7 (step 15) = {368/458/467}, no 1
24a. 1 on D\ locked locked in R1C1 + R2C2 + R3C3, locked for N1
25. R7C79 + R9C7 (step 2) = 1{25/34}
25a. 5 of {125} must be in R7C7 -> no 5 in R7C9 + R9C7
26. 5 in R6 locked in R6C89 for 13(3) cage at R6C8 = 5{17/26}, no 3,4,8
27. Min R4C12 = 13 -> max R3C1 = 5
28. R1C3 + R3C13 (step 1) = {127/136/145/235}
28a. 1 of {127/145} must be in R3C3 -> no 4,7 in R3C3
29. 2,3 in R6 locked in R6C123 -> at least one of 2,3 must be in R6C12
29a. 13(3) cage at R6C1 = {238/247/256/346} (cannot be {139} because 1,9 only in R7C1), no 1,9
29b. 4 of {247} must be in R7C1 -> no 7 in R7C1
29c. 6 of {256/346} must be in R6C12 -> no 6 in R7C1
30. 1,4 in R4 locked in R4C789 -> at least one of 1,4 must be in R4C89
30a. 13(3) cage at R3C9 = {148/157/247/346}
30b. 2,3,5 of {157/247/346} must be in R3C9 -> no 6,7 in R3C9
31. 45 rule on N3 3 innies R1C7 + R3C79 = 15 = {159/168/249/258/267/348/357/456}
31a. 9 of {159} must be in R1C7
31b. 8 of {168} must be in R3C7
31c. -> no 1 in R1C7
32. R258C3 (step 13) = {469/478/568}
32a. R5C3 = {45} -> no 4,5 in R28C3
33. 18(3) cage in N1 = {189/369/378/459/468/567}
33a. 1,3,4 of {189/378/468} must be in R2C2 -> no 8 in R2C2
33b. 8 on D\ locked in R1C1 + R8C8 -> no 8 in R1C8 + R8C1
34. R258C7 (step 16) = {179/269/278/359/368}
34a. 9 of {269} must be in R8C7 -> 2 of {269/278} must be in R5C7 -> no 2 in R2C7
34b. 1 of {179} must be in R2C7
34c. 9 of {269/359} must be in R8C7
34d. -> no 9 in R2C7
35. 17(3) cage in N3 (step 17) = {179/269/278/458/467}
35a. 2,4 of {278/458} must be in R2C8 -> no 8 in R2C8
36. 14(3) cage at R1C6 = {149/158/167/248/257/347/356} (cannot be {239} because 3,9 only in R1C7)
36a. 3,8,9 of {149/248/347} must be in R1C7 -> no 4 in R1C7
37. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {129/138/147/237/246/345} (cannot be {156} because 1,6 only in R9C3)
37a. 1 of {129/138} must be in R9C3 -> no 8,9 in R9C3
37b. 3 of {138} must be in R7C1 -> no 8 in R7C1
38. 2,3 in R6 locked in R6C123
38a. R6C12 cannot be {23} because max R7C1 = 5 -> R6C3 = {23}
39. 16(3) cage at R6C3 = {259/268/349/358/367} (cannot be {457} because R6C3 only contains 2,3)
39a. R6C3 = {23} -> no 2,3 in R7C34
40. 2,3 in R6 locked in R6C123 = {236/237/238}
40a. 45 rule on N7 6 outies R6C123 + R789C4 = 32
40b. R6C123 = 11,12,13 -> R789C4 = 19,20,21 = {389/469/489/568/569}
40c. Max R89C4 = 14 (because of 15(3) cage at R8C4) -> min R7C4 = 5
41. 12(3) cage at R3C6 = {147/156/246}, no 8
41a. 5 of {156} must be in R3C7 -> no 5 in R3C6
42. 9 in C8 locked in R237C8
42a. 45 rule on C89 4 innies R2378C8 = 1 outie R5C7 + 24 -> R2378C8 = 26,27
42b. R2378C8 = {2789/4589/4679/4689} (cannot be {5679} because 5,6 only in R3C8)
42c. 2,4 must be in R2C8 -> no 7,9 in R2C8
43. 17(3) cage in N3 (step 17) = {269/278/458/467} (cannot be {179} because R2C8 only contains 2,4), no 1
44. 9 on D/ locked in R7C3 + R8C2 + R9C1, locked for N7
45. 16(3) cage in N7 = {169/268/457} (cannot be {178} because R8C23 = {78} clashes with R8C8, cannot be {259} because R8C3 only contains 6,7,8)
45a. {457} must be [547]
45b. -> no 7 in R7C2, no 5,7 in R8C2
46. R7C258 (step 18) = {179/269/278/359/368}
46a. 1 of {179} must be in R7C2 -> no 1 in R7C5
47. R1C7 + R3C79 (step 29) = {159/348/357} (cannot be {168} because no 1,6,8 in R3C7, cannot be {249} which clashes with R2C8, cannot be {258/267/456} because there’s no place for 9 in N3), no 2,6
47a. 4 of {348} must be in R3C7 -> no 4 in R3C9
48. 12(3) cage at R3C6 (step 39) = {147/156/246}
48a. 6 of {156} must be in R4C7 (cannot be [651] which clashes with R3C258)
48b. 2 of {246} must be in R3C6
48c. -> no 6 in R3C6
49. R4C123 + R789C6 = 36 (step 19)
49a. R4C123 = 22,23,24 -> R789C6 = 12,13,14
49b. R789C6 = {147/156/246/157/247/256/167/257} [1/2]
49c. R789C5 = {129/138/237}
49d. Killer triple 1,2,3 in R789C56, locked for N8
49e. Min R89C4 = 9 -> max R9C3 = 6
50. 3 in N8 locked in R789C5, locked for C5
50a. R789C5 = {138/237}, no 9
50b. 9 in N8 locked in R789C4, locked for C4
51. R789C6 = 12,13,14 (step 47a) -> R789C4 = 19/20/21
51a. R789C4 = {469/569/489} [4/5]
51b. Hidden killer pair 4,5 in N8 -> R789C6 must contain 4/5 -> R789C6 not {167}
52. 45 rule on R89 4 innies R8C2378 = 1 outie R7C5 + 23
52a. Max R8C2378 = 30 -> no 8 in R7C5
53. R89C6 must contain 1/2 (step 49b)
53a. 10(3) cage at R8C6 = {127/136/145/235}
53b. 4 of {145} must be in R9C7 -> no 4 in R89C6
54. R7C258 (step 18) = {179/269/278/359/368} [8/9]
54a. Hidden killer pair 8,9 in R7 -> R7C34 must contain 8/9
54b. 16(3) cage at R6C3 (step 39) = {259/268/349/358} (cannot be {367}), no 7
55. R7C13 + R9C3 (step 37) = {129/138/246/345}
55a. 1,6 of {129/246} must be in R9C3 -> no 2 in R9C3
55b. R7C13 + R9C3 cannot be {246} because [246] clashes with R258C3 = {568}
55c. -> R7C13 + R9C3 = {129/138/345}, no 6
55d. 3 of {345} must be in R9C3 (cannot be in R7C1 because R79C3 = {45} clashes with R5C3) -> no 4,5 in R9C3
55e. {345} must be [453] (if [543] cannot make combination for 16(3) cage at R6C3) -> no 5 in R7C1, no 4 in R7C3
55f. R9C67 cannot be {13} -> no 6 in R8C6
56. R789C4 = {469/569/489}
56a. R9C3 = {13} -> R89C4 = {159/348} (cannot be {168} which clashes with R789C4), no 6
56b. R789C4 = {569/489} (cannot be {469} which clashes with R89C4) -> R7C4 = {69}
57. 16(3) cage at R6C3 (step 54b) = {259/268} (cannot be {358} because R7C4 only contains 6,9) -> R6C3 = 2, R7C34 = [59/86], no 9 in R7C3
58. 3 in N4 locked in R6C12, locked for 13(3) cage -> no 3 in R7C1
59. R7C13 + R9C3 = [453] (only remaining permutation), 5 locked for D/, R7C4 = 9 (step 57), R3C3 = 1, R5C3 = 4, R7C7 = 3, locked for D\, R5C78 = [23]
60. R7C79 + R9C7 (step 2) = [314] (only remaining permutation), R9C9 = 5, locked for D\
61. R2C2 = 4 (hidden single on D\), R2C8 = 2, locked for D/, R9C8 = 6, R8C9 = 2
62. Naked pair {78} in R78C8, locked for C8 and N9 -> R6C8 = 5, R8C7 = 9, R8C2 = 8, locked for D/, R8C8 = 7, locked for D\
and the rest is naked singles and cage sums, possibly only one cage sum if the right one is selected