Afmob wrote:
To be honest, this one was easier than V1. SudokuSolver missed my step 3a and thereby made this Killer look harder than it really is.
I'll agree with that. I haven't yet finished A164 but managed to finish the "V1.5" is one evening, which had a 2 hour break to watch TV; that's faster than I manage to solve most Assassins.
Here is my walkthrough for A164 "V1.5". As soon as I started looking at Afmob's walkthrough I realised that I'd missed one of the prelims
so I haven't looked at the rest of it. That sort of thing can happen when one does one's own prelims but, even so, I'm happy to continue solving using an Excel worksheet. I haven't time at the moment to re-work my walkthrough so I'm posting it as I did it; I'll be watching the Saturday and Sunday stages of the Tour de France and also the Hungarian GP before I have time to re-work it.
Edit. I've had another look at my walkthrough, see comment after Prelims. Then I went through Afmob's walkthrough, which has a very different solving path than mine.
Prelims
a) R1C23 = {18/27/36/45}, no 9
b) R12C9 = {59/68}
c) R34C9 = {29/38/47/56} (cannot be {56} which clashes with R12C9), no 1,5,6
d) R67C1 = {49/58/67}, no 1,2,3
e) R89C1 = {14/23}
f) R9C78 = {17/26/35}, no 4,8,9
g) 11(3) cage in N1 = {128/137/146/236/245}, no 9
h) R1C456 = {389/479/569/578}, no 1,2
i) 10(3) cage at R2C7 = {127/136/145/235}, no 8,9
j) 19(3) cage in N4 = {289/379/469/478/568}, no 1
k) 6(3) cage at R6C9 = {123}, CPE no 1,2,3 in R89C9
l) 21(3) cage at R7C3 = {489/579/678}, no 1,2,3
m) 19(3) cage in N9 = {289/379/469/478/568}, no 1
n) 14(4) cage at R4C3 = {1238/1247/1256/1346/2345}, no 9
o) 29(4) cage at R4C6 = {5789}
[I missed 18(5) cage in N5 = {12348/12357/12456}, no 9, 1,2 locked for N5. However apart for locking 9 in R45C6 it doesn’t seem to make much difference to my walkthrough so I haven’t re-worked it.]
1. Killer triple 1,2,3 in R7C89 and R9C78, locked for N9
2. 45 rule on N89 1 innie R7C4 = 1 outie R6C9 + 3 -> R7C4 = {456}
2a. 21(3) cage at R7C3 = {489/579/678}
2b. R7C4 = {456} -> no 4,5,6 in R78C3
3. 45 rule on N12 1 innie R3C6 = 1 outie R4C1 + 1, no 1 in R3C6, no 7,8,9 in R4C1
4. 45 rule on N36 3 outies R345C6 = 1 innie R6C9 + 21
4a. R6C9 = {123} -> R345C6 = 22,23,24 = {589/679/689/789} -> R3C6 = {567}, R45C6 = {79/89}, no 5, 9 locked for C6, N5 and 29(4) cage at R4C6, clean-up: no 1,2,3 in R4C1 (step 3)
4b. 5 in 29(4) cage at R4C6 locked in R56C7, locked for C7 and N6, clean-up: no 3 in R9C8
5. 10(3) cage at R2C7 = {127/136/145/235}
5a. R3C6 = {567} -> no 6,7 in R23C7
6. 45 rule on N8 3 innies R7C4 + R78C6 = 10 = {136/145/235} (cannot be {127} because R7C6 only contains 4,5,6), no 7,8
6a. 6 of {136} must be in R7C4 -> no 6 in R78C6
7. 45 rule on R123 2 innies R3C89 = 1 outie R4C1 + 10
7a. Min R4C1 = 4 -> min R3C89 = 14, no 1,2,3,4 in R3C89, clean-up: no 7,8,9 in R4C9
8. 45 rule on N2 3 innies R23C4 + R3C6 = 11 = {137/146/236/245} (cannot be {128} because R3C6 only contains 5,6,7), no 8,9
8a. R3C6 = {567} -> no 5,6,7 in R23C4
9. 45 rule on N2 2 outies R23C3 = 1 innie R3C6 + 6
9a. Min R3C6 = 5 -> min R23C3 = 11, no 1 in R23C3
10. 45 rule on N9 2 innies R78C7 = 1 outie R6C9 + 12
10a. R6C9 = {123} -> R78C7 = 13,14,15 = {49/68/69} (cannot be {67} which clashes with 19(3) cage, cannot be {78} which clashes with R56C7, ALS block), no 7
11. 19(3) cage in N9 = {478/568} (cannot be {469} which clashes with R78C7), no 9, 8 locked for N9
11a. 9 in N9 locked in R78C7, locked for C7
12. 9 locked in R78C7 for 19(4) cage at R7C7 = 9{136/145} (cannot be 9{235} because R78C7 only contain 4,6,9), no 2, 1 locked in R78C6, locked for C6 and N8
12a. 4 of 9{145} must be in R78C7 -> no 4 in R78C6
13. R7C4 + R78C6 (step 6) = {136/145}
13a. 4,6 only in R7C4 -> R7C4 = {46}, clean-up: no 2 in R6C9 (step 2)
13b. 21(3) cage at R7C3 = {489/678} (only remaining combinations), 8 locked in R78C3, locked for C3 and N7, clean-up: no 1 in R1C2, no 5 in R6C1
14. 2 in 6(3) cage at R6C9 locked in R6C89, locked for R6 and N9, clean-up: no 6 in R9C78
15. 45 rule on R789 2 innies R7C12 = 1 outie R6C9 + 6
15a. Max R6C9 = 3 -> max R7C12 = 9, no 7,9 in R7C1, no 6,7,9 in R7C2, clean-up: no 4,6 in R6C1
16. R7C35 = {78} (hidden pair in R7), R7C7 = 9 (hidden single in R7)
17. 45 rule on N7 2 innies R7C12 = 1 outie R7C4 + 3, IOU no 3 in R7C2
18. 45 rule on N3 2 innie R3C89 = 1 outie R3C6 + 9, IOU no 9 in R3C89, clean-up: no 2 in R4C9
[Steps 17 and 18 are better than steps 7 and 15 because they give the same results plus IOUs. However I didn’t spot the IOU steps until now.]
19. R7C12 = R7C4 + 3 (step 17), R7C4 = {46} -> R7C12 = 7,9 = {16/45} (only remaining combinations)
19a. R89C9 = {23} (cannot be {14} which clashes with R7C12), locked for C9 and N9
20. 17(3) cage in N8 = {278/368/458} (cannot be {269/359} because R7C5 only contains 7,8, cannot be {467} which clashes with R7C4), no 9, 8 locked for N8
20a. 9 in N8 locked in R9C456, locked for R9
21. R9C9 = 8 (hidden single in R9), R3C9 = 7, R4C9 = 4, clean-up: no 6 in R12C9
21a. Naked pair {59} in R12C9, locked for C9 and N3 -> R8C9 = 6, R8C8 = 5 (step 11), R8C7 = 4, clean-up: no 3 in R9C7
[At this stage I noticed R3C6 = {56}, R4C1 = {56}, R3C6 = R4C1 + 1 (step 3)… However the placements for R3C6 and R4C1 came slightly more easily in step 22.]
22. 19(4) cage at R7C7 (step 12) = 9{145} (only remaining combination) -> R78C6 = [51], R3C6 = 6, R3C8 = 8, R4C1 = 5 (step 3), clean-up: no 8 in R6C1
22a. R3C6 = 6 -> R23C7 = 4 = {13}, locked for C7 and N3 -> R9C78 = [71]
22b. Naked pair {23} in R7C89, locked for 6(3) cage at R6C9 -> R6C9 = 1
23. Naked pair {46} in R7C14, locked for R7 -> R7C2 = 1, R7C1 = 6 (step 19), R6C1 = 7, R7C4 = 4
23a. 21(3) cage at R7C3 (step 13b) = {489} (only remaining combination) -> R78C3 = [89], R8C2 = 7, R7C5 = 7, clean-up: no 2 in R1C3
23b. 17(3) cage in N8 (step 20) = {278} (only remaining combination) -> R8C45 = {28}, locked for R8 and N8 -> R89C1 = [32], R9C6 = 3
24. R3C8 = 8 -> R4C78 = 9 = [27/63]
24a. Killer pair 2,3 in R4C78 and R5C9, locked for N6
25. Naked pair {58} in R56C7, locked for 29(4) cage at R4C6 -> R45C6 = {79}, locked for C6 and N5
26. 45 rule on N5 2 remaining innies R56C4 = 11 = {38/56}, no 1,2
26a. 45 rule on N5 2 remaining outies R45C3 = 3 = {12}, locked for C3 and N4, clean-up: no 8 in R1C2
27. R4C1 = 5 -> R3C12 = 13 = {49} (only remaining combination), locked for R3 and N1, clean-up: no 5 in R1C23
27a. Naked pair {18} in R12C1, locked for C1 and N1, R2C2 = 2 (cage sum), clean-up: no 7 in R1C3
27b. Naked pair {36} in R1C23, locked for R1 and N1
28. R7C2 = 1 -> R6C23 = 11 = [83], clean-up: no 3,8 in R5C4 (step 26)
29. R23C3 = [75] = 12 -> R23C4 = 5 = [32]
30. R1C78 = [24], R12C6 = [84], R12C1 = [18]
30a. 45 rule on R1 1 remaining innie R1C9 = 9
and the rest is naked singles.