Having caught up with my backlog of unfinished V1s (A161 and A165) last month, I had a look to see if there were any other of Ronnie's puzzles that I hadn't yet done. I found that I'd got stuck on A154 V1.5 and hadn't yet started A150 V2 so I had a go at both of them in the last few days.
I'd got as far as step 21 and had a note of the innies in step 23 (I'd also used 45 rule on N58 for A154) but until this week I hadn't worked out how I could use them. Then after steps 24, 25 and 28 the puzzle was cracked.
Afmob wrote:
I used lots of combo clashes to solve this Killer, so maybe someone can find a neater way to crack it.
Maybe manu's step 2d is that way? It's a neat way, combining a "clone" and a short forcing chain. Many of my steps are similar to those used by Afmob but my breakthrough is different.
Here is my walkthrough for A154 V1.5.
Prelims
a) 7(2) cage in N4 = {16/25/34}, no 7,8,9
b) 11(2) cage in N6 = {29/38/47/56}, no 1
c) R67C3 = {13}
d) R67C7 = {15/24}
e) 20(3) cage at R5C4 = {389/479/569/578}, no 1,2
f) 20(3) cage at R5C5 = {389/479/569/578}, no 1,2
g) 19(3) cage in N7 = {289/379/469/478/568}, no 1
h) 20(3) cage in N9 = {389/479/569/578}, no 1,2
i) 28(4) cage at R1C6 = {4789/5689}, no 1,2,3
j) 14(4) cage at R1C9 = {1238/1247/1256/1346/2345}, no 9
1. Immediate follow-up steps
1a. Naked pair {13} in R67C3, locked for C3, clean-up: no 4,6 in R6C2
1b. 28(4) cage at R1C6 = {4789/5689}, CPE no 8 in R1C9
2. 45 rule on C123 3 outies R149C4 = 11 = {128/137/146/236/245}, no 9
3. 45 rule on C789 3 outies R149C6 = 9 = {126/135/234}, no 7,8,9
3a. R1C6 = {456} -> no 4,5,6 in R49C6
3b. 8,9 of 28(4) cage at R1C6 only in R2C7 + R3C8 + R4C9, CPE no 8,9 in R23C9
4. 45 rule on N7 3 innies R7C23 + R8C3 = 9 = {126/135/234}, no 7,8,9
4a. 45 rule on N7 3(2+1) outies R6C13 + R9C4 = 17
4b. Max R6C13 = 12 -> min R9C4 = 5
4c. Max R9C4 = 8 -> min R6C13 = 9, min R6C1 = 6
5. R149C4 (step 2) = {128/137/146/236/245}
5a. R9C4 = {5678} -> no 5,6,7,8 in R14C4
6. 45 rule on N9 3(2+1) outies R6C79 + R9C6 = 12
6a. Max R6C7 + R9C6 = 8 -> min R6C9 = 4
7. 45 rule on R1234 4 outies R5C1289 = 14 = {1238/1247/1256/1346/2345}, no 9
8. 45 rule on R9 3 innies R9C456 = 13
8a. Max R9C46 = 11 -> min R9C5 = 2
8b. Min R9C46 = 6 -> max R9C5 = 7
8c. 1 in R9 only in R9C6789, CPE no 1 in R7C8 + R8C7
9. 45 rule on N47 1 outie R9C4 = 1 innie R4C1 + 1 -> R4C1 = {4567}
10. 45 rule on N69 1 innie R4C9 = 1 outie R9C6 + 5 -> R4C9 = {678}
10a. 9 of 28(4) cage at R1C6 only in R2C7 + R3C8, locked for N3
11. 45 rule on N1 3(2+1) outies R1C4 + R4C14 = 10 = {127/136/145/235} (normal combinations apply because all three cells are common peers)
11a. 5 of {145} must be in R4C1 -> no 4 in R4C1, clean-up: no 5 in R9C4 (step 9)
12. 45 rule on N3 2 innies R2C7 + R3C8 = 1 outie R4C6 + 14
12a. Min R2C7 + R3C8 = 15, no 4,5
12b. 28(4) cage at R1C6 = {4789/5689}
12c. 4,5 only in R1C6 -> R1C6 = {45}
13. R149C6 (step 3) = {135/234}, 3 locked for C6
14. 45 rule on N2 2 innies R1C46 = 1 outie R4C5 + 4
14a. Max R1C46 = 9 -> max R4C5 = 5
15. 45 rule on N5 3 outies R7C456 = 3 innies R4C456 + 13
15a. Min R4C456 = 6 -> min R7C456 = 19, no 1
16. 45 rule on N7 2 outies R6C1 + R9C4 = 1 innie R7C3 + 13
16a. R7C3 = {13} -> R6C1 + R9C4 = 14,16 = [68/86/97], no 7 in R6C1
16b. R6C1 + R9C4 = 14,16 -> R7C2 + R8C3 = 6,8
16c. 22(4) cage at R6C1 = {68}[35]/[97][15]/[97]{24} -> no 5,6 in R7C2, no 6 in R8C3
16d. R7C23 + R8C3 (step 4) = {135/234}, 3 only in R7C23, locked for R7 and N7
17. 45 rule on N1 2 innies R2C3 + R3C2 = 1 outie R4C4 + 6
17a. Max R4C4 = 4 -> max R2C3 + R3C2 = 10, no 9 in R3C2
18. 45 rule on R4C14569 = 20 = {12368/12458/12467/13457/23456}
18a. 5 of {12458/13457/23456} must be in R4C1 -> no 5 in R4C5
18b. R1C46 (step 14) = R4C5 + 4
18c. Max R4C5 = 4 -> max R1C46 = 8, no 4 in R1C4
19. R9C456 = 13 (step 8) = {148/157/238/247/256/346}
19a. R9C4 = {678} -> no 6,7 in R9C5
20. 19(3) cage in N7 = {289/469/478/568}
20a. 17(3) cage in N7 = {179/269/278/467} (cannot be {458} which clashes with 19(3) cage), no 5
20b. R9C456 = (step 19) = {157/238/247/256/346} (cannot be {148} which clashes with 19(3) cage)
21. 13(3) cage at R9C7 = {139/157/238/346} (cannot be {148} which clashes with 19(3) cage at R9C1, cannot be {247/256} which clash with R9C456)
21a. 45 rule on N9 3 innies R7C78 + R8C7 = 12 = {129/147/156/246} (cannot be {138/237/345} which clash with 13(3) cage), no 3,8
21b. 1 of {156} must be in R7C7 -> no 5 in R7C7, clean-up: no 1 in R6C7
21c. 18(4) cage at R6C9 = {1269/1359/1467/2349/2367/2457/3456} cannot be {1368} because 1,3 only in R9C6, cannot be {1278/1458/2358} because R7C8 + R8C7 = {25/27/45} aren’t consistent with any combinations for R7C78 + R8C7 -> no 8 in R6C9
[This is how far I’d got when this puzzle first appeared. I had a note for the innies in step 23, which I’d used for A154, but at that time hadn’t worked out how to use them for this puzzle.]
22. 45 rule on N9 3 innies R7C78 + R8C7 (step 21a) = {129/147/156/246}
22a. 6 of {156/246} must be in R8C7 (R78C7 cannot be {15/24} because of CCC with R67C6), no 6 in R7C8
22b. 5 of {156} must be in R7C8 -> no 5 in R8C7
23. 45 rule on N58 5(3+2) innies R4C456 + R9C46 = 16 must contain at least one 1 in R4C456 + R9C6 (if R4C456 = {234} = 9 -> R9C46 = 7 can only be [61]), CPE no 1 in R56C6
23a. 1 in N5 only in R4C456, locked for R4
23b. 1 in R6 only in R6C23, locked for N4
24. Hidden killer triple 1,2,3 in 22(4) cage, 7(2) cage and R6C6 for N4, 7(2) cage contains one of 1,2,3, R6C6 = {13} -> 22(4) cage must contain one of 2,3
24a. 22(4) cage in N4 = {2479/2569/2578/3469/3478} (cannot be {3568/4567} which clash with 7(2) cage, cannot be {2389} which contains two of 2,3)
25. 45 rule on N4 3 innies R4C1 + R6C13 = 16 = {169/178/358} (cannot be {367} which clashes with 22(4) cage)
25a. 8,9 only in R6C1 -> R6C1 = {89}
25b. R6C1 + R9C4 (step 16a) = [86/97] -> R9C4 = {67}, clean-up: no 7 in R4C1 (step 9)
[Alternatively hidden killer pair 8,9 in 22(4) cage and R6C1 for N4, 22(4) cage contains one of 8,9 -> R6C1 must contain one of 8,9 -> R6C1 = {89}]
25c. R4C1 + R6C13 = {169/358}
25d. R4C1 + R9C4 = [56/67], CPE no 6 in R9C1
26. 7 in N4 only in 22(4) cage (step 24a) = {2479/2578/3478}, no 6
26a. 6 in N4 only in R4C1 + R5C3, CPE no 6 in R2C3
27. R9C456 (step 19) = {157/247/256/346}
27a. 4,5 only in R9C5 -> R9C5 = {45}
28. 1 in R4 only in R4C456
28a. R4C14569 (step 18) = {12368/12458/12467/13457}
28b. 7,8 only in R4C9 -> R4C9 = {78}, clean-up: no 1 in R9C6 (step 10)
29. 1 in R9 only in R9C789, locked for N9, clean-up: no 5 in R6C7
30. R7C78 + R8C7 (step 21a) = {246} (only remaining combination) -> R8C7 = 6, R7C78 = {24} (locked for R7 and N9), clean-up: no 5 in R6C8
31. Naked pair {13} in R7C23, locked for N7, R8C3 = 5 (step 4), clean-up: no 2 in R6C2
32. Naked pair {24} in R67C7, locked for C7, clean-up: no 7,9 in R6C8
33. 18(4) cage at R6C9 (step 21c) = {2367/3456} -> R9C6 = 3, R4C9 = 8 (step 10), clean-up: no 3 in 11(2) cage in N6
33a. 5,7 of 18(4) cage only in R6C9 -> R6C9 = {57}
34. 3 in N9 only in 20(3) cage = {389} (only remaining combination) -> R7C9 = 9, R8C89 = [83]
35. Naked triple {157} in R9C789, locked for R9 -> R9C5 = 4, R9C4 = 6, R4C1 = 5 (step 9), clean-up: no 2 in R5C3
36. Naked triple {578} in R7C456, locked for R7 and N8 -> R7C1 = 6
36a. R4C14569 (step 28a) = {12458} (only remaining combination) -> R4C456 = {124} -> R4C4 = 4, R1C4 = 1 (step 2), R4C56 = {12}, locked for R4 and N5, CPE no 2 in R3C6
37. R4C8 = 6 (hidden single in R4), clean-up: no 5 in R5C7
37a. Naked pair {24} in R6C78, locked for N6
37b. Naked pair {24} in R67C8, locked for C8
38. Naked pair {79} in R25C7, locked for C7 -> R4C7 = 3
39. Naked pair {79} in R4C23, locked for N4 -> R6C1 = 8, R6C3 = 3 (step 25), R7C23 = [31], R6C2 = 1, R5C3 = 6
40. R4C78 = [36] = 9 -> R5C89 = 8 = {17}, locked for R5 and N6 -> R5C7 = 9, R6C8 = 2, R67C7 = [42], R7C8 = 4, R6C9 = 5, R2C7 = 7, R3C8 = 9, R1C6 = 4 (cage sum)
41. R4C6 = 2 (step 3), R1C9 = 6 -> R2C8 + R3C7 = 6 = {15}, locked for N3 -> R1C78 = [83], R4C5 = 1
42. Naked pair {29} in R8C45, locked for R8 -> R8C6 = 1
43. R23C1 = {13} (hidden pair in C1) = 4 -> R1C23 = 14 = [59], R4C23 = [97]
44. R2C3 = 4 (hidden single in C3), R3C2 = 6 (cage sum), R23C9 = [24], R2C2 = 8, R3C3 = 2, R1C1 = 7, R1C5 = 2, R8C45 = [29]
45. 22(4) cage in N2 = {2569} (only remaining combination) -> R2C456 = {569}, locked for R2 and N2
46. 45 rule on C6 2 remaining innies R23C6 = 17 = [98]
and the rest is naked singles.