And now another V2 from my Unfinished folder. They seem to be getting harder! Congratulations manu for producing a really challenging variant of your first Assassin!
In the introduction to the V2, manu wrote:
The last one might keep you busy for hours
Only one minor change in the cages at N7, but it makes really a difference !
That change made a very big difference. It took me hours, spread over several days.
I agree with Afmob's assessment of the difficulty of this variant.
I liked the killer triple in Afmob's step 9a, manu had a similar step. I wish I'd spotted that step which would have made my solving path a bit shorter.
My solving path is somewhat different than those of Afmob and manu but all three depended on interactions between N7 and N9.
Here is my walkthrough for A140 V2.
I found that I hadn’t tried the V2 when this puzzle first appeared. I’ve now started from the beginning, without looking at how I solved the V1 and V1.5, so hope I haven’t missed any easier steps which I saw then.
Prelims
a) R23C6 = {39/48/57}, no 1,2,6
b) R67C8 = {18/27/36/45}, no 9
c) R78C3 = {16/25/34}, no 7,8,9
d) R89C1 = {19/28/37/46}, no 5
e) 20(3) cage in N3 = {389/479/569/578}, no 1,2
f) 19(3) cage in N3 = {289/379/469/478/568}, no 1
g) 10(3) cage at R3C7 = {127/136/145/235}, no 8,9
h) 19(3) cage in N9 = {289/379/469/478/568}, no 1
i) 15(5) cage at R6C5 = {12345}
j) 23(6) cage in N1 = {123458/123467}, no 9, 1,2,3,4 locked for N1
1. 45 rule on N3 3 innies R2C9 + R3C79 = 6 = {123}, locked for N3
2. 45 rule on C123 3 outies R236C4 = 10 = {127/136/145/235}, no 8,9
3. 45 rule on N12 2 innies R3C35 = 13 = {58/67}/[94], no 1,2,3,9 in R3C5
4. 45 rule on N7 2 innies R7C12 = 12 = {39/48/57}, no 1,2,6
5. 45 rule on N8 2 outies R6C56 = 4 = {13}, locked for R6, N5 and 15(5) cage at R6C5, clean-up: no 6,8 in R7C8
5a. Naked triple {245} in R7C45 + R8C4, locked for N8
6. 45 rule on N9 2 outies R6C78 = 15 = [78/87/96], clean-up: R7C8 = {123}
7. 45 rule on C789 2 innies R5C78 = 5 = {14/23}
7a. 45 rule on C789 2 outies R5C46 = 14 = {59/68}
8. 45 rule on N47 2 outies R3C3 + R6C4 = 10 = [55/64/82], clean-up: no 4,6 in R3C5 (step 3)
8a. Naked triple {245} in R678C4, locked for C4, clean-up: no 9 in R5C6 (step 7a)
9. 45 rule on N1 2 outies R23C4 = 1 innie R3C3 -> R3C3 = 8 (because R23C4 cannot total 5 or 6), R3C5 = 5 (step 3), R6C4 = 2 (step 8), clean-up: no 4,7 in R2C6, no 7 in R3C6
9a. R3C3 = 8 -> R23C4 = {17}, locked for C4, N2 and 22(4) cage at R2C2, no 7 in R2C23
9b. 1 in R1 only in R1C123, locked for N1
10. R7C5 = 2 (hidden single in N8), clean-up: no 7 in R6C8, no 8 in R6C7 (step 6), no 5 in R8C3
11. R5C6 = 5 (hidden single in N5), R5C4 = 9 (step 7a)
12. 45 rule on N1 2 remaining innies R2C23 = 14 = {59}, locked for R2 and N1, clean-up: no 3 in R3C6
13. 19(3) cage in N3 = {469/478}, 4 locked for N3
13a. 9 of {469} must be in R3C8 -> no 6 in R3C8
13b. 6 in R3 only in R3C12, locked for N1
14. R1C6 = 2 (hidden single in C6)
14a. 20(4) cage in R1C4 = {2369/2468}
14b. 9 of {2369} must be in R1C5 -> no 3 in R1C5
14c. 20(3) cage in N3 = {569/578}
14d. Hidden killer pair 8,9 in R1C45 and 20(3) cage at R1C7 for R1, 20(3) cage contains one of 8,9 -> R1C45 must contain one of 8,9
14e. 8,9 of 20(4) cage in R1C4 must be in R1C45 -> no 8 in R2C5
15. 45 rule on N9 3 innies R7C78 + R8C7 = 10 = {127/136/145/235}, no 8,9
16. 16(3) cage at R6C7 cannot contain both of 7,9, R6C7 = {79} -> no 7 in R78C7
17. 9 in R3 only in R3C68
17a. R3C6 = 9 => R2C6 = 3
or R3C8 = 9 => R2C78 = {46} (step 13) => R2C5 = 3
-> 3 must be in R2C56, locked for R2 and N2
17b. 3 in N3 only in R3C79, locked for R3
18. Killer pair 6,8 in R1C4 and 20(3) cage at R1C7, locked for R1
18a. Naked pair {49} in R1C5 + R2C6, locked for N2
19. R9C4 = 3 (hidden single in C4), clean-up: no 7 in R8C1
20. Hidden killer triple 7,8,9 in R7C12, R7C6 and R7C9 for R7, R7C12 contains one of 7,8,9 -> R7C6 = {789}, R7C9 = {789}
21. 45 rule on C6 2 remaining outies R89C5 = 2 innies R46C6 + 5
21a. 1 in N5 only in R6C56, 1 in N8 only in R89C56
21b. R46C6 = [41] = 5 => R89C5 = 10 = {19}, R46C6 cannot be [61/71/81] because R89C5 containing 1 cannot total more than 10
R46C6 cannot be [43/83] which clash with R23C6
-> R46C6 = [41/63/73], no 8 in R4C6
22. R6C4 = 2 -> R5C3 + R6C23 + R7C2 = 20 = {1469/1478/1568/3458/3467} (cannot be {1379} which clashes with R6C7) contains 1 in R5C3 or 3 in R5C3 + R7C2
22a. R5C3 = 1 => R5C78 = {23} (step 7)
22b. -> 3 in R5C3 + R7C2 or R5C78, CPE no 3 in R5C2
23. Max R3C7 = 3 -> min R4C78 = 7
23a. R3C3 = 8 -> R4C123 = 14
23b. 45 rule on R4 3 remaining innies R4C789 = 1 outie R5C5 + 6
23c. Max R5C5 = 8 -> max R4C789 = 14 -> max R4C9 = 7
23d. 8 in R4 only in R4C45, locked for N5
24. 9 in R4 only in R4C123, locked for N4
24a. R4C123 = 14 (step 23a) = {149/239}, no 5,6,7
25. 5 in R4 only in R4C789, locked for N6
25a. R4C789 = R5C5 + 6 (step 23b)
25b. R5C5 = {467} -> R4C789 = 10,12,13 = {145/235/156/157} (cannot be {345} which clashes with R4C123, cannot be {256} because 7 must be in R4C789 = 13 when R5C5 = 7)
25c. 1,2 of {145/235} must be in R4C9 (because min R4C78 = 7, step 23) -> no 3,4 in R4C9
25d. 5 of {156/157} must be in R4C9 (because min R4C78 = 7, max R4C78 = 9) -> no 6,7 in R4C9
26. Hidden killer pair 8,9 in R56C9 and R6C78 for N6, R6C78 contains one of 8,9 -> R56C9 must contain one of 8,9
26a. 21(5) cage at R2C9 = {12369/12378/12459/13458} (cannot be {12468} which clashes with R6C8, cannot be {12567/13467/23457} which don’t contain 8 or 9), 1 locked for C9
26b. R234C9 contain three of 1,2,3,5 -> no 1,2,3 in R5C9
26c. 9 of {12369} must be in R6C9 -> no 6 in R6C9
27. 5 in R6 only in R6C123
27a. R5C3 + R6C23 + R7C2 (step 22) = {1469/1478/1568/3458/3467}
27b. 7 of {1478/3467} cannot be in R7C2 (because R7C12 = [57] (step 4) clashes with R6C1 = 5, hidden single in R6) -> no 7 in R7C2, clean-up: no 5 in R7C1 (step 4)
28. R6C1 = 5 (hidden single in C1)
28a. R5C3 + R6C23 + R7C2 (step 22) = {1469/1478/3458/3467} (cannot be {1568} which clashes with R6C8), CPE no 4 in R5C2
28b. 1 of {1469/1478} must be in R5C3, 3 of {3458} must be in R5C3, 6 or 7 of {3467} must be in R5C3 (R6C23 cannot be {67} which clashes with R6C78) -> no 4 in R5C3
29. 23(4) cage at R5C1 contains 5 = {1589/2579/3569/3578/4568}
29a. 6 of {3569} must be in R5C2, {4568} = [4658/8654] (cannot be [6854] because R5C2 + R7C1 = 12 clashes with R7C12 = 12 (step 4), CCC) -> no 6 in R5C1
30. 23(4) cage at R5C1 cannot be {2579}, here’s how
{2579} => R7C1 = 9 => R7C2 = 3 (step 4) => {2579} clashes with R5C3 + R6C23 + R7C2 (step 22) = {3467} (only combination with 3 in R7C2)
30a. 23(4) cage at R5C1 (step 29) = {1589/3569/3578/4568}, no 2
31. 2 in R5 only in R5C78 = {23} (step 7), locked for R5 and N6
31a. R4C123 = {239} (hidden triple in N4)
32. 23(4) cage at R5C1 (step 30a) = {1589/3578/4568} (cannot be {3569} because 3,9 only in R7C1)
32a. 3 of {3578} must be in R7C1 -> no 7 in R7C1, clean-up: no 5 in R7C2 (step 4)
33. R7C12 (step 4) = 12 = {39/48}
33a. R78C3 = [16/52/61] (cannot be {34} which clashes with R7C12), no 3,4
34. 16(3) cage at R9C7 = {169/178/259/268/457}
34a. 16(3) cage in N7 = {169/178/259/367/457} (cannot be {268} which clashes with R78C3, cannot be {349/358} which clash with R7C12)
34b. 16(3) cage in N7 cannot be {367}, here’s how
{367} = 3{67} => 16(3) cage at R9C7 = {259} => R9C1 = 4 (hidden single in R9) => R8C1 = 6 clashes with {367}
34c. -> 16(3) cage in N7 = {169/178/259/457}, no 3
34d. {169/259} => no 9 in R89C1
{178/457} => R7C12 (step 4) = {39} => no 9 in R89C1
34e. -> no 9 in R89C1, clean-up no 1 in R89C1
[Steps 34d and 34e can be expressed as a combined cage R7C12 + 16(3) cage, if preferred. Alternatively the same result can be obtained from combining the 7(2) and 16(3) cages; in that case the combined cage must contain 1.]
35. 19(3) cage in N9 = {289/379/469/478} (cannot be {568} which clashes with R7C78 + R8C7), no 5
35a. 2 of {289} must be in R8C9 (R78C9 cannot be {89} which clashes with 21(5) cage at R2C9), no 2 in R8C8
[It looks like R7C78 + R8C7 (step 15) cannot be {145} because of UR for R78C47, although I know one has to be careful about URs for killers. However I don’t use URs because they rely on there being a unique solution and seem to bypass part of the solving path. Then I found a contradiction move.]
36. 16(3) cage at R9C7 cannot be {268} here’s how
{268} => 5 in R9 must be in R9C23 => 16(3) cage in N7 (step 34a) = {259} (cannot be {457} because no remaining candidates in R9C1) = 2{59} => R78C3 = {16} => cannot place 4 in R9
36a. -> 16(3) cage at R9C7 (step 34) = {169/178/259/457}
37. 19(3) cage in N9 = {289/469/478} (cannot be {379} which clashes with 16(3) cage), no 3
37a. 2 of {289} must be in R8C9, 9 of {469} must be in R8C9 -> no 9 in R8C9
38. 3 in N9 must be in R7C78 + R8C7 -> R7C78 + R8C7 (step 15) = {136/235}, no 4
39. 16(3) cage at R6C7 = {169/259/367}
39a. 2 of {259} must be in R8C7 -> no 5 in R8C7
40. R7C12 (step 33) = {39/48}
40a. R7C12 = {39} => R7C8 = 1 => R7C78 + R8C7 (step 38) = {136}
R7C12 = {48} => R7C4 = 5
-> no 5 in R7C7
41. R7C78 + R8C7 (step 38) = {136} (only remaining combination), locked for N9, 6 also locked for C7
41a. Killer triple 1,2,3 in R3C7, R5C7 and R78C7, locked for C7
42. 5 in N9 only in 16(3) cage at R9C7, locked for R9
42a. 16(3) cage at R9C7 (step 36a) = {259/457}, no 8
42b. 8 in C7 only in R12C7, locked for N3
43. R3C9 = 3 (hidden single in C9)
43a. 10(3) cage at R3C7 = {127/145}, no 6
43b. 6 in R4 only in R4C456, locked for N5
44. 19(3) cage in N9 (step 37) = {289/478}
44a. 21(5) cage at R2C9 (step 26a) = {12369/13458} (cannot be {12378} which clashes with 19(3) cage, ALS block for one permutation), no 7
45. 19(3) cage in N9 (step 44) = {289/478}
45a. 9 of {289} must be in R7C9 (R78C9 cannot be [82] which clashes with 21(5) cage at R2C9) -> no 9 in R8C8
45b. Killer pair 2,9 in 21(5) cage at R2C9 and 19(3) cage in N9 (2,9 must be in one or other cage, not the usual killer pair; maybe this is really a combined cage but I saw it as a killer pair), locked for C9
46. 10(3) cage at R3C7 (step 43a) = {127/145}
46a. 7 of {127} must be in R4C7 -> no 7 in R4C8
46b. 7 in N6 only in R46C7, locked for C7
47. 16(3) cage at R9C7 (step 42a) = {259/457}
47a. 2 of {259} must be in R9C8 -> no 9 in R9C8
47b. 9 in C8 only in R13C8, locked for N3
48. 20(3) cage in N3 (step 14c) = {569/578}
48a. 9 of {569} must be in R1C8 -> no 6 in R1C8
49. 16(3) cage in N7 (step 34c) = {169/178/259/457}
49a. Cannot be {259}, here’s how
{259} = 5{29} => 16(3) cage at R9C7 = {457}, R78C3 = {16} => R9C1 = 8, R8C1 = 2 clashes with 16(3) cage
49b. -> 16(3) cage in N7 = {169/178/457}, no 2
49c. 5 of {457} must be in R8C2 -> no 4 in R8C2
50. 21(5) cage at R2C9 (step 44a) = {12369/13458}
50a. 19(3) cage in N9 (step 37) = {289/478}
50b. 19(3) cage = {289} => 21(5) cage = {13458}, 4 locked for C9
or 19(3) cage = {478}, 4 locked for N9
-> no 4 in R9C9
50c. Hidden killer pair 2,4 in 21(5) cage at R2C9 and R8C9 for C9, 21(5) cage contains one of 2,4 -> R8C9 = {24}
50d. 19(3) cage in N9 = {289/478}
50e. R8C9 = {24} -> no 4 in R8C8
51. Hidden killer pair 8,9 in 21(5) cage at R2C9 and R7C9 for C9, 21(5) cage contains one of 8,9 -> R7C9 = {89}
52. R7C6 = 7 (hidden single in R7)
53. R7C12 (step 33) = {39/48}
R7C12 = {39} => R7C78 = [61] => R7C3 = 5 => 16(3) cage in N7 (step 49b) = {178}
or R7C12 = {48}
-> 8 must be in R7C12 or 16(3) cage, locked for N7, clean-up: no 2 in R89C1
54. R8C3 = 2 (hidden single in N7), R7C3 = 5, R78C4 = [45], R8C9 = 4, clean-up: no 8 in R7C12 (step 33), other clean-ups omitted
55. Naked pair {39} in R7C12, locked for R7 and N7 -> R7C78 = [61], R8C7 = 3, R7C9 = 8, R8C8 = 7, R56C9 = [69], R6C78 = [78], R8C1 = 6, R9C1 = 4, R9C789 = [925], R4C9 = 1, R4C78 = {45}, locked for R4 -> R4C6 = 6
56. R2C23 = [59], R2C9 = 2, R23C1 = [72], R4C3 = 3, R4C1 = 9, R7C1 = 3, R1C1 = 1, R5C1 = 8, R5C2 = 7 (cage sum from step 30a)
and the rest is naked singles.