Assassin 50

[Glyn]

Thanks to Para and Cathy. Both much more elegant offerings than the hodge/podge of T&E that I have been using on the other one.

[Andrew]

Para hasn't solved Assassin 50 V1 yet, Andrew is stuck! Better hurry up guys A51 is coming soon (I might have to wait until Monday to tackle it though).

I'm honoured/flattered that Cathy mentioned me, even though it is because I was stuck. I know that my solving has improved a lot from doing Assassins and being active on this forum.

It's several days since I looked at Assassin 50V1 after going as far as I could with normal killer moves; I hadn't yet tried any others such as contradiction moves.

Mike's one that he has recently posted seems to be what I was looking for. I've looked at the position I reached and it seems to work.

In the last few days I've been working on one of Ed's puzzles in my backlog and hope to post a walkthrough for that one next week.

[Para]

In case anyone's interested, I found a variation on Para's step 45 (the move that finally broke the puzzle), which only involves a single loop, and which does not require using the 25/4 cage at R2C2

Yeah i tend to only use chains i can visualize. I used the 25(4) cage because it was set for me as needs either 3 or 7(so kinda like a bivalue cell). Also i used this chain because i rather not use a chain that ends in a contradiction but rather chains going 2 ways and both making the same elimination at the end (like in xy-chains or medusa colouring)
I was mostly annoyed that it kept stalling. Well 51 is hopefully a bit less annoying. I took 3 looks to finally finish. First run was till about step 30. Second run created step 33 and associates. The 3rd look finally grasped the chain.

greetings

Para

[Andrew]

A tough challenge, as was to be expected for Assassin 50. It needed a lot of combination work as can be seen in Cathy's and Para's walkthroughs.

I must admit that I missed the pointing pairs and pointing triple in Cathy's walkthrough. I must train myself to look out for them. Clearly any nonet with two outies totalling 3, 4, 16 or 17 must give either naked or pointing pairs. In this particular puzzle I don't think it matter that I missed them but I'm still annoyed with myself that I did.

The second pointing pair and the pointing triple were neat. She made good use of the shape of the 45 cage.

As I said in my previous message I was stuck (after step 42) and went off to work on other puzzles until I happened to see Mike's contradiction move.

Here is my walkthrough

1. R1C34 = {49/58/67}, no 1,2,3

2. R1C67 = {17/26/35}, no 4,8,9

3. R34C1 = {13}, locked for C1

4. R34C9 = {39/48/57}, no 1,2,6

5. R67C1 = {49/58/67}, no 1,2,3

6. R67C9 = {59/68}

7. R9C34 = {19/28/37/46}, no 5

8. R9C67 = {49/58/67}, no 1,2,3

9. 11(3) cage in N458 = {128/137/146/236/245}, no 9

10. 19(3) cage in N7 = {289/379/469/478/568}, no 1

11. 11(3) cage in N9 = {128/137/146/236/245}, no 9

12. 45 rule on N1 2 innies R1C3 + R3C1 = 7 -> R1C3 = {46}, clean-up: R1C4 = {79}

13. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = [39]/{57}, clean-up: R1C6 = {135}, R4C9 = {357}

14. 45 rule on N7 2 innies R7C1 + R9C3 = 6 -> R7C1 = {45}, R9C3 = {12}, clean-up: R6C1 = {89}, R9C4 = {89}

15. 45 rule on N9 2 innies R7C9 + R9C7 = 17 = {89}, locked for N9, clean-up: R6C9 = {56}, R9C6 = {45}
15a. Killer pair 8/9 in R9C47, locked for R9

16. 45 rule on N9 2 outies R6C9 + R9C6 = 10 = [64] -> R7C9 = 8, R9C7 = 9, R9C4 = 8, R9C3 = 2, R7C1 = 4, R6C1 = 9

17. 19(3) cage in N7 = {568} (only remaining combination) -> R8C1 = 8
17a. R9C12 = 11 = {56}, locked for R9 and N7

18. 11(3) cage in N9 R9C89 = {137} -> R8C9 = {137} -> 17(4) cage = {2456}
18a. R89C9 = {13/17} ({37} clashes with R34C9) -> 1 locked in R89C9 for C9 and N9
18b. Killer pair 3/7 in R34C9 and R89C9, locked for C9

19. 13(3) cage in N1 min R12C1 = 7 -> max R1C2 = 6

20. 8,9 in N1 locked in 25(5) cage = 89{17/26/35}, no 4

21. 4 in N1 locked in R1C23, locked for R1

22. 45 rule on R12 4 outies R3C2378 = 26 = {2789/3689/4589/4679/5678}, no 1

23. 13(3) cage in N1 = {157/247/256} (cannot be {346} because 3,4 only in R1C2), no 3
23a. No 2 in R1C2 because R12C1 = {56} clashes with R9C1

24. 45 rule on R789 3 innies R7C456 = 18 = {279/369/567}, no 1

25. 1 in R7 locked in R7C23, locked for N7

26. 45 rule on R89 4 outies R7C2378 = 15 with 1 locked in R7C23 = 1{257/356} (cannot be {1239} because 1,3,9 only in R7C23) = 15{27/36}, no 9
26a. 5 in R7C2378 locked in R7C78, locked for R7 and N9
26b. 9 in N7 locked in R8C23, locked for R8
26c. R7C456 (step 24) = 9{27/36}, 15(4) cage in N8 = 15{27/36}

27. 18(3) cage in N658 max R6C67 = 15 -> min R7C6 = 3

28. 45 rule on C789 4 innies R1456C7 = 17 = {1358/1457/2348/2357}

29. 2 in N4 locked in 16(4) cage = 2{158/167/347/356} [1/3]
29a. Killer pair 1/3 in R4C1 and 16(4) cage for N4

30. 45 rule on C123 4 innies R1456C3 = 23 = {4568} (only remaining combination), locked for C3
30a. 5,8 in C3 locked in R456C3, locked for N4
30b. 16(4) cage (step 29) = 27{16/34}

31. 8 in C2 locked in R23C2 and must be the only even number in the 25(4) cage (because R23C3 only contain odd numbers) = 89{17/35} [1/3], no 2,6
[The combinations for the 25(4) cage would have given the same result but spotting this even/odd case, a type of move that I like, saved me having to work them out this time.]
31a. Killer pair 1/3 in R3C1 and 25(4) cage for N1

32. 2 in C2 locked in R456C2 -> no 2 in R5C1
32a. 13(3) cage in N1 = 2{47/56}

33. 11(3) cage in N458 (step 9) = {128/146/245} (cannot be {137/236} because no 1,2,3,6,7 in R6C3), no 3,7
33a. All combinations require 2 or 6 in R7C4 -> no 2 in R6C4

34. R7C456 (step 26c) = 9{27/36}, R7C4 = {26} -> no 2,6 in R7C56

35. 18(3) cage in N658 = {189/279/378/459}
35a. 4 only in R6C7 -> no 5 in R6C7

36. 13(3) cage in N254 = {148/157/238/247/256/346} (cannot be {139) because no 1,3,9 in R4C3), no 9

37. 45 rule on C89 4 innies R2378C8 = 17 = {1259/1268/1457/2348/2357/2456} (cannot be {1349/1358/1367} because no 1,3,7,8,9 in R78C8)
37a. 1 only in R2C8 -> no 9 in R2C8

38. 14(3) cage in N3 = {149/239/248/257} (cannot be {158/167/347/356} because no 1,3,6,7,8 in R12C9), no 6
38a. 1,3 only in R1C8 -> no 9 in R1C8
38b. 7 only in R1C8 -> no 5 in R1C8
38c. 3,7,8 only in R1C8 -> no 2 in R1C8
38d. {239} can only be [329] ([392] clashes with R1C467), {257} can only be [725] ([752] clashes with R1C67) -> no 5 in R1C9, no 2 in R2C9
38e. 6 in N3 locked in 19(4) cage = 6{139/148/157/238} (cannot be {2467} which clashes with the 14(3) cage)

39. 45 rule on R1 2 outies R2C19 – 3 = 1 innie R1C5, min R2C19 = 6 -> min R1C5 = 3
39a. R2C19 cannot be 8 -> no 5 in R1C5

40. 45 rule on R123 5 innies R3C14569 = 19 = 1{2349/2358/2367/2457/3456}
40a. {12349} must have 9 in R3C9 -> no 9 in R3C56

41. R1C4 = {79} -> 24(4) cage cannot contain both 7 and 9
41a. 24(4) cage = {1689/2589/3489/3678/4569/4578} (cannot be {2679/3579}

42. 45 rule on C1234 4 innies R258C4 + R5C3 = 23 with R5C3 = {4568}
If R5C3 = 4, R258C4 = [496] (cannot be {379} which clashes with R1C4)
If R5C3 = 5, R258C4 = {369/459/567} (cannot be {279} which clashes with R1C4)
If R5C3 = 6, R258C4 = {359/467} (cannot be {179} which clashes with R1C4, cannot be {269} which clashes with R7C4)
If R5C3 = 8, R258C4 = {159/249/357/456} (cannot be {267} which clashes with R7C4)
42a. Only combination with 2 is {249}8, 4,9 only in R25C4 -> no 2 in R25C4

At this stage I was stuck although I hadn’t looked seriously for contradiction moves. Then I happened to see Mike’s step on the forum which works at this stage. If I’d looked seriously for contradiction moves I might have found it since there are only two positions for 1 in R1, the sort of thing that points toward contradiction moves. Alternatively I might have found Para's contradiction move based on the two positions for 4 in R1.

43. (Mike’s step) R1C6=1 -> R3C456<>1 -> R3C1=1 -> R1C3=6 -> R1C4=7 -> R1C67<>{17} -> R1C6<>1 (contradiction) -> R1C6<>1 Nice one Mike!
43a. R1C8 = 1 (hidden single in R1), clean-up: no 7 in R1C7
43b. R12C9 = 13 = [94], R1C4 = 7, R1C3 = 6, clean-up: no 3 in R4C9

44. Naked pair {35} in R1C67, locked for R1 -> R1C12 = [24], R1C5 = 8, R2C1 = 7 (cage sum), R5C1 = 6, R9C12 = [56]

45. R5C1 = 6 -> R456C2 = 10 = {127}, locked for C2 and N4 -> R7C2 = 3, R8C2 = 9, R78C3 = [17], R4C1 = 3, R3C1 = 1

46. R7C456 (step 34) = {279} -> R7C4 = 2
46a. Naked pair {79} locked in R7C56, locked for N8

47. Naked pair {57} in R34C9, locked for C9 -> R5C9 = 2

48. Naked pair {13} in R89C9, locked for N9 -> R9C8 = 7

49. Naked pair {56} in R7C78, locked for N9

50. 24(4) cage in N2 = {1689} (only remaining combination), locked for N2
50a. Naked triple {169} locked in R2C456, locked for R2 -> R23C3 = [39]

51. 19(4) cage in N3 = {2368} (only remaining combination), locked for N3 -> R1C67 = [35], R34C9 = [75], R7C78 = [65]

52. Naked pair {28} in R2C78, locked for R2 and N3 -> R23C2 = [58], R3C78 = [36]

53. 22(4) cage in N6 = {2389} (only remaining combination) -> R456C8 = {389}, locked for C8 and N6 -> R2C78 = [82], R8C78 = [24]

54. 13(3) cage in N254 = {148} (only remaining combination) -> R3C4 = 4, R4C34 = [81], R6C34 = [45], R5C3 = 5, R3C5 = 2, R3C6 = 5, R4C8 = 9

55. R8C5 = 5 (hidden single in R8)

56. R3C6 = 5 -> R4C67 = 11 = [74]

and the rest is naked singles

Mike’s step was clearly the breakthrough that I needed, the rest was routine. If I’d realised how close I was to finishing this puzzle, I would have looked harder for that move instead of going off to work on other puzzles including Assassin 50V0.2