In the A154 thread I wrote:
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.
Now that I've gone through Afmob's walkthrough, here is my one. The critical area was N9 and the 27(5) cage which we looked at in different ways. Afmob first looked at the 27(5) and then outies for N9. I found innies-outies for N9 easier to think about although now that I've gone through Afmob's walkthrough his way seems to be more direct, particularly in finding the critical 9 locked in R6C68 for R6.
Afmob wrote:
That was a tough Killer! Like V1 I hope that someone finds an easier way to solve it. Maybe by using a small forcing chain?
It certainly was tough! I don't think my way was any easier; I didn't spot any forcing chains.
Rating Comment. I'll also rate A150 V2 at (Easy?) 1.75 because I think Afmob's solving path and my one have similar levels of difficulty. My hardest steps were 28b, 29a and 30a.
Here is my walkthrough for A150 V2. Thanks Afmob for the clarification to step 24b.
Prelims
a) R12C1 = {16/25/34}, no 7,8,9
b) R1C23 = {79}
c) R1C78 = {18/27/36/45}, no 9
d) R12C9 = {49/58/67}, no 1,2,3
e) R2C34 = {29/38/47/56}, no 1
f) R2C67 = {29/38/47/56}, no 1
g) R8C12 = {19/28/37/46}, no 5
h) R89C5 = {49/58/67}, no 1,2,3
i) R8C89 = {15/24}
j) 11(3) cage in N1 = {128/137/146/236/245}, no 9
k) 11(3) cage in N3 = {128/137/146/236/245}, no 9
1. 45 rule on R9 1 innie R9C5 = 4, R8C5 = 9, clean-up: no 1 in R8C12
2. Naked pair {79} in R1C23, locked for R1 and N1, clean-up: no 2 in R1C78, no 2,4 in R2C4, no 4,6 in R2C9
3. 45 rule on C1234 2 innies R17C4 = 12 = [48/57]
3a. R1C78 = {18/36} (cannot be {45} which clashes with R1C4)
3b. 16(4) cage at R6C5 cannot contain both of 7,8 -> no 7,8 in R6C5 + R7C56
4. 45 rule on C6789 2 innies R17C6 = 4 = {13}, locked for C6, clean-up: no 8 in R2C7
4a. Killer pair 1,3 in R1C6 and R1C78, locked for R1, clean-up: no 4,6 in R2C1
5. 45 rule on R12 2 innies R2C28 = 7 = {16/25/34}, no 7,8
6. 45 rule on R6789 2 innies R6C19 = 12 = {39/48/57}, no 1,2,6
7. 45 rule on N1 2 innies R2C3 + R3C1 = 11 = {38/56}, no 1,2,4, clean-up: no 7,9 in R2C4
8. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = {39/57}/[48], no 1,2,6, no 4 in R3C9, clean-up: no 5,9 in R2C6
9. 11(3) cage in N1 = {128/146/245} (cannot be {236} which clashes with R2C3 + R3C1), no 3, clean-up: no 4 in R2C8 (step 5)
10. 2 in N3 only in 11(3) cage = {128/236/245}, no 7
11. 7,9 in N3 only in R2C9 and R2C7 + R3C9
11a. Hidden killer pair 7,9 in R2C9 and R2C7 + R3C9 for N3, R2C7 + R3C9 cannot contain both of 7,9 -> R2C9 = {79} and R2C7 + R3C9 must contain one of 7,9 -> R2C7 + R3C9 = {39/57}, no 4,8, clean-up: no 5,8 in R1C9, no 7 in R2C6
12. 45 rule on R1 3 outies R2C159 = 16 = {169/178/259} (cannot be {268/358} because R2C9 only contains 7,9, cannot be {367} which clashes with R2C34), no 3, clean-up: no 4 in R1C1
12a. 1 of {169/178} must be in R2C1 -> no 1 in R2C5
12b. 7 of {178} must be in R2C9 -> no 7 in R2C5
13. R2C79 = {79} (hidden pair in R2), locked for N3, clean-up: no 6,8 in R2C6
14. 16(4) cage in N2 = {1258/1348/1456/2356}
14a. Killer pair 2,4 in 16(4) cage and R2C6, locked for N2
15. 3 in N1 only in R2C3 + R3C1 (step 7) = {38} (only remaining combination), locked for N1, clean-up: no 5,6 in R2C4
15a. Naked pair {38} in R2C34, locked for R2, clean-up: no 4 in R2C2 (step 5)
16. R2C6 = 4 (hidden single in R2), R2C7 = 7, R2C9 = 9, R1C9 = 4, R1C4 = 5, R7C4 = 7 (step 3), clean-up: no 2 in R2C1, no 3,8 in R6C1 (step 6), no 2 in R8C8
16a. 2 in N2 only in R12C5, locked for C5
16b. 16(4) cage in N2 (step 14) = {1258/2356}
16c. Killer pair 3,8 in 16(4) cage and R2C4, locked for N2
17. 45 rule on N3 1 remaining innie R3C9 = 5, clean-up: no 2 in R2C2 (step 5), no 7 in R6C1 (step 6), no 1 in R8C8
18. 16(4) cage at R6C5 = {1357} (only remaining combination), no 6, 5 locked for C5
19. 18(4) cage at R3C9 = {2358} (only remaining combination), locked for C9 -> R8C9 = 1, R8C8 = 5, R7C9 = 6, R9C9 = 7, clean-up: no 5 in R6C1 (step 6)
19a. Naked triple {238} in R456C9, locked for N6
20. R7C9 = 6 -> R67C8 = 11 = [74/92]
21. 24(4) cage at R9C6 = {2679/3579/3678}
21a. 5,6 only in R9C6 -> R9C6 = {56}
22. 16(3) cage in N6 = {169/457}
22a. 5 of {457} must be in R5C7 -> no 4 in R5C7
22b. Killer pair 7,9 in 16(3) cage and R6C8, locked for N6
23. 45 rule on C1 3 innies R789C1 = 17 = {179/278/359/458/467} (cannot be {269} which clashes with R1C1, cannot be {368} which clashes with R3C1)
23a. 7 of {278/467} must be in R8C1 -> no 2,6 in R8C1, clean-up: no 4,8 in R8C2
23b. 3 of {359} must be in R8C1 -> no 3 in R79C1
24. 45 rule on N9 2 outies R6C8 + R9C6 = 2 innies R78C7 + 2, R6C8 + R9C6 = 12,13,14,15 -> R78C7 = 10,11,12,13 = {28/29/38/39/48/49}
[After going through Afmob’s walkthrough I realised that this should have been R78C7 = {28/29/38/48/49} (cannot be {39} which clashes with 24(4) cage at R9C6). As a result some of the steps after this may be a bit longer than necessary.]
24a. 27(5) cage at R6C6 = {12789/13689/14589/14679/23589/23679/24579/24678} (cannot be {15678} because R78C7 must contain one of 2,3,4, cannot be {34569} because {39} must be in R78C7 and {456} clashes with R9C6, cannot be {34578} because {38} must be in R78C7 and R8C6 doesn’t contain 4,5 or 7)
24b. {49} of {14589/14679} must be in R78C7, {49} of {24579} must be in R78C7 (because 2 must be in R8C6), {48} of {24678} must be in R78C7 (R78C7 cannot be {28} because
R6C67 = [74] clashes with R6C18, ALS block) -> no 4 in R6C7
25. 45 rule on N6 3 innies R4C7 + R6C78 = 16 = {169/457}
25a. 4 of {457} must be in R4C7 -> no 5 in R4C7
26. 45 rule on C789 3 remaining outies R689C6 = 1 innie R4C7 + 13
26a. R4C7 = {146} -> R689C6 = 14/17/19 = {257/269/289/568}(cannot be {278} because R9C6 only contains 5,6)
26b. 7,9 of {257/269/289} must be in R6C6 -> no 2 in R6C6
27. 45 rule on R8 4 innies R8C3467 = 20 = {2378/2468/3467}
27a. 7 of {2378/3467} must be in R8C3 -> no 3 in R8C3
28. 24(4) cage at R3C6 = {1689/2679/4578} (cannot be {2589} because R4C7 only contains 1,4,6, cannot be {4569} which clashes with R9C6)
28a. R689C6 (step 26a) = {257/269/568} (cannot be {289} which clashes with 24(4) cage)
28b. 7 in C6 only in 24(4) cage at R3C6 or in R6C6 -> 24(4) cage = {2679/4578} or 24(4) cage = {1689}, R6C6 = 7, R4C7 = 1, R6C7 = 6 (step 25) -> either R6C67 = [76] or R6C6 not 7 and R6C7 = {15} (step 25, because R4C7 = {46} when 7 in 24(4) cage at R3C6) -> 27(5) cage at R6C6 must contain both of 6,7 or not contain 7
28c. 27(5) cage at R6C6 (step 24a) = {13689/14589/23589/23679/24678} (cannot be {12789/24579} which contain 7 but not 6, cannot be {14679} because R6C67 cannot be [76] and also contain 1)
28d. 3,4 of {23589/23679/24678} must be in R78C7 = {38/39/48}, no 2 in R78C7
29. 4 in C7 only in R4C7 and R78C7, R46C7 = {16/45} (step 25) -> R6C7 can only contain 1 or 6 when R78C7 contains 4 (a sort of variable hidden killer pair)
29a. 27(5) cage at R6C6 (step 28c) = {14589/23589/24678} (cannot be {13689/23679} which must have 1 or 6 in R6C7 but don’t contain 4)
29b. 7 of {24678} must be in R6C6 -> no 6 in R6C6
30. 27(5) cage at R6C6 (step 29a) = {14589/23589/24678}
30aa. {14589} => R6C7 = 1, R4C7 + R6C8 = [69] (step 25)
30ab. {23589} => R8C6 = 2 => R6C6 = 9 (step 28a)
30ac. {24678} => R6C6 = 7 => R6C8 = 9
30b. -> 9 must be in R6C68, locked for R6 -> R6C1 = 4, R6C9 = 8 (step 6), clean-up: no 6 in R8C2
31. R789C1 (step 23) = {179/278/359}, no 6
31a. 3,7 only in R8C1 -> R8C1 = {37} -> R8C12 = {37}, locked for R8 and N7
32. 21(4) cage at R3C1 = {2478/3459/3468} (cannot be {1479/2469} because R3C1 only contains 3,8), no 1
33. 9 in C4 only in R345C4, locked for 22(4) cage at R3C4, no 9 in R4C3
33a. 4,9 in C4 only in 22(4) cage at R3C4 = {1489/2479/3469}, no 5
33b. 7 of {2479} must be in R4C3 -> no 2 in R4C3
34. 15(3) cage at R6C2 = {159/168/249/258/348/456} (cannot be {267/357} because 3,6,7 only in R6C2), no 7
35. R689C6 (step 28a) = {257/269/568}
35a. 2,8 only in R8C6 -> R8C6 = {28}
36. 6 in R8 only in R8C34, locked for 23(5) cage at R6C3, no 6 in R6C34
36a. 23(5) cage at R6C3 = {12569/13469/13568/14567/23468/23567}
36b. 2,6 of {12569/23567} must be in R8C34, 2,3 of {23468} must be in R6C34 -> no 2 in R7C3
37. 45 rule on N4 3 innies R4C3 + R6C23 = 1 outie R3C1 + 9
37a. R3C1 = {38} -> R4C3 + R6C23 = 12,17 = {138/156/237/278/368}
37b. 15(3) cage at R4C2 = {159/168/267} (cannot be {258/357} which clash with R4C3 + R6C23), no 3
37c. R4C3 + R6C23 = {138/237/278/368} (cannot be {156} which clashes with 15(3) cage), no 5
38. 15(3) cage at R6C2 (step 34) = {159/168/249/258/348/456}
38a. 2 of {249/258} must be in R6C2 -> no 2 in R7C12
39. R7C8 = 2 (hidden single in R7), R6C8 = 9 (step 20), clean-up: no 1,6 in 16(3) cage in N6 (step 22)
39a. R5C7 = 5, R45C8 = {47}, locked for N6
39b. Naked pair {16} in R46C7, locked for C7, clean-up: no 3,8 in R1C8
40. Naked pair {16} in R12C8, locked for N3
40a. R3C7 = 2 (hidden single in N3)
41. R1C1 = 2 (hidden single in N1), R2C1 = 5
41a. R2C5 = 2 (hidden single in N2)
42. 21(4) cage at R3C1 (step 32) = {3468} (only remaining combination), locked for C1, 6 locked for N4 -> R8C12 = [73]
42a. Naked pair {19} in R79C1, locked for N7
43. 15(3) cage at R6C2 (step 34) = {159/249} (cannot be {258/348} because R7C1 only contains 1,9) -> R7C1 = 9, R67C2 = [15/24], R9C1 = 1
43a. Killer triple 1,4,6 in R23C2 and R67C2, locked for C2
43b. 6 in C2 only in R23C2, locked for N1
44. R9C7 = 9 (hidden single in R9)
44a. 24(4) cage at R9C6 (step 21) = {3579} (only remaining combination) -> R9C6 = 5, R9C8 = 3
45. Naked pair {48} in R78C7, locked for C7 and 27(5) cage at R6C6 -> R8C6 = 2, R1C7 = 3, R1C6 = 1, R12C8 = [61], R3C8 = 8, R1C5 = 8, R2C2 = 6, R2C34 = [83], R3C1 = 3, R7C56 = [13], R6C5 = 5, R6C6 = 7, R6C7 = 6 (step 28b, or hidden single in R6), R4C7 = 1
46. R6C3 = 3 (hidden single in R6), R4C3 = 7, R1C23 = [79], R45C8 = [47]
47. Naked pair {68} in R89C4, locked for C4 -> R3C4 = 9
and the rest is naked singles.