Thanks for a really challenging puzzle
HATMAN. I couldn't solve it so of course, it wasn't suitable as an Assassin.
But seriously, when I see what I missed it seems a perfect v2,
not a v1 Assassin.
Mike's way is incredible! Well done Mike!
Andrew has some really, really nice moves too. Love the ALS blocks especially and the nice "45" work in r1. Some of the other steps are quite complicated. I had no chance of finding HATMAN's way either. I love fish moves so don't really understand what HATMAN (seems) to have against them.
To try and justify my contrarian views about this puzzle, I decided to have a go at optimising Andrew's walkthrough to see how many of the first 32 steps were actually necessary. Exactly 5...weren't needed.
But it reads a lot easier without most of the permutation-placement work that I always struggle with. But the chains/multi-element steps are still needed. BTW - SS's key was to eliminate 2 from r5c9 using all sorts of blocks.
You guys are incredible solvers but I hope that this level of puzzle doesn't get posted again as the V1 Assassin.
Optimised version of Andrew's WT.[Thanks to Andrew for some corrections.]Prelims
a) 9(3) cage in N1 = {126/135/234}, no 7,8,9
b) 22(3) cage at R1C4= {589/679}
c) 9(3) cage in N3 = {126/135/234}, no 7,8,9
d) 21(3) cage at R6C7 = {489/579/678}, no 1,2,3
e) 9(3) cage in N7 = {126/135/234}, no 7,8,9
f) 19(3) cage in N8 = {289/379/469/478/568}, no 1
g) 9(3) cage in N9 = {126/135/234}, no 7,8,9
h) 19(5) cage at R5C3 = {12349/12358/12367/12457/13456}
Steps resulting from Prelims
1a. 22(3) cage at R1C4= {589/679}, 9 locked for R1 and N2
1b. 19(5) cage at R5C3 = {12349/12358/12367/12457/13456}, 1 locked for R5
2. 45 rule on N1 1 innie R3C2 = 1 outie R4C3 + 8 -> R3C2 = 9, R4C3 = 1
2a. R4C3 = 1 -> R23C3 = 12 = {48/57}, no 2,3,6
3. 45 rule on N3 1 innie R3C8 = 1 outie R4C7 + 5, R3C8 = {78}, R4C7 = {23}
4. 45 rule on C7 3 innies R159C7 = 8 = {125/134}, 1 locked for C7
4. Killer pair 2,3 in R159C7 and R4C7, locked for C7
5. Hidden killer pair 7,8 in R1C3 and 22(3) cage at R1C4 for R1, 22(3) cage contains one of 7,8 -> R1C3 = {78}
5a. Killer pair 7,8 in R1C3 and R23C3, locked for C3 and N1
6. 45 rule on N7 1 innie R7C2 = 1 outie R6C3 + 6 -> R7C2 = 8, R6C3 = 2
6a. R6C3 = 2 -> R78C3 = 12 = {39}(only remaining combination), locked for C3 and N7
7. 9(3) cage in N7 = {126} (only remaining combination), locked for N7
8. R5C3 = 6 (hidden single in C3)
8a. 19(5) cage at R5C3 = {12367/13456}, no 8,9, 3 locked for R5
9. 9(3) cage in N1 = {135/234} (cannot be {126} which clashes with 9(3) cage in N7, ALS block), no 6, 3 locked for N1
9a. Killer pair 4,5 in 9(3) cage and R23C3, locked for N1
9b. Naked triple {126} in R389C1, locked for C1
9c. 1,2 of 9(3) cage only in R1C2 -> R1C2 = {12}
9d. 3 in N1 only in R12C1, locked for C1
Step numbering changes from here.
10. 9(3) cage in N3 = {126/135/234}
10a. 6 of {126} must be in R1C89 (R1C89 cannot be {12} which clashes with R1C2), no 6 in R2C9
11. 45 rule on R1 2 innies R1C37 = 2 outies R2C19 + 5
11a. Min R2C19 = [31] = 4 -> min R1C37 = 9 = [72] (cannot be [81] which clashes with R2C19 = [31]) -> no 1 in R1C7
11b. Max R1C37 = [85] = 13 -> max R2C19 = 8 = [53] (cannot be [35] which clashes with R1C37 = [85]) -> no 5 in R2C9
11c. R1C3 = 8 is not possible at the same time as R2C1 = 5 (because they would clash with R23C3) -> max R2C19 = 7 -> min R1C1289 = 11
12. Min R1C1289 = 11 -> R1C1289 must contain one of 5,6
12a. Killer pair 5,6 in R12C89 and 22(3) cage at R1C4, locked for R1
13. 45 rule on N3 3 innies R2C7 + R3C78 = 21 = {489/579/678}
14. 15(3) cage in N3 = {249/267/348/357} (cannot be {159/168} because R1C7 only contains 2,3,4; cannot be {258/456} which clash with R2C7 + R3C78), no 1
15. R159C7 (step 4) = {125/134}
15a. 2 of {125} must be in R1C7 -> no 2 in R59C7
16. 9(3) cage in N9 = {135/234} (cannot be {126} which clashes with 9(3) cage in N7, ALS block), no 6, 3 locked for N9
17. R9C456 = {789} (hidden triple in R9), locked for N8
17a. 19(3) cage in N8 = {469/568} (cannot be {289/379/478} because 7,8,9 only in R9C6), no 2,3,7; 6 locked for R8 and N8
17b. 3 in R9 only in R9C89, locked for N9
18. 45 rule on R9 2 remaining innies R9C37 = 2 outies R8C19 + 3
18a. Min R8C19 = 3 -> min R9C37 = 6 -> R9C37 = {15/45}, 5 locked for R9
18b. 9(3) cage in N9 = {135/234}
18c. 5 of {135} must be in R8C9 -> no 1 in R8C9
19. 15(3) cage in N9 = {159/168/249} (cannot be {267/258} because R9C7 only contains 1,4,5; cannot be {456} which clashes with 9(3) cage in N9 step 18b), no 7
20. 45 rule on N9 3 innies R7C78 + R8C7 = 21 and must have 7 = {579/678}, no 1,2,4
21. 45 rule on N9 1 outie R6C7 = 1 innie R7C8, no 4,8 in R6C7
22. deleted
23. 45 rule on R5 4 innies R5C1289 = 26 = {2789/4589}
23a. 7 of {2789} must be in R5C2 -> no 7 in R5C189
24. 18(3) cage in N4 = {378/459}
24a. 8,9 only in R5C1 -> R5C1 = {89}
24b. 3 of {378} must be in R6C2 -> no 7 in R6C2
25. 45 rule on R5 2 innies R5C89 = 1 outie R6C2 + 8
25a. R6C2 = {345} -> R5C89 = 11,12,13 = {29/48/58} (cannot be {49} because R5C12 = [85] (step 23) clashes with the combinations for the 18(3) cage in N4 step 24)
25b. 18(3) cage in N6 = {369/378/459/468/567} (cannot be {279} which clashes with R5C89, CCC, because there’s no 7 in R5C8), no 2
26. R8C2 cannot be 5, here’s how
26a. R8C9 = 2 => R9C89 = {34} => R9C3 = 5 => no 5 in R8C2
R8C9 = {45} => naked triple {456} in R8C569, locked for R8 => R8C2 = 7
26b. -> no 5 in R8C2
27. 5 in C2 only in R456C2, locked for N4
27a. Killer pair 4,7 in 18(3) cage at R5C1 (in R56C2) and R8C2, locked for C2
28. Only one remaining combination for R5C1289, here’s how
28a. R8C9 = 2 => no 2 in R5C9
28b. R8C9 = {45} => naked triple {456} in R8C569, locked for R8 => R8C2 => 7 => no 7 in R5C2
28c. -> R5C1289 (step 23) = {4589} (only remaining combination, cannot be {2789} because no 2 in R5C9 or no 7 in R5C2), no 2,7
28d. R8C2 = 7 (hidden single in C2), placed for D/
Back to Andrew's step 33
Cheers
Ed