SudokuSolver Forum

Assassin 189 X

Obvious start and then it gets harder. I avoided fishes and found a move in the middle which I think is within limits, that then makes it flow.

I hope you enjoy it.



SS Code(as originally posted - I thought that this was the standard for the forum):
3x3:d:k:2305:2305:3842:5635:5635:5635:3844:2309:2309:2305:3842:3334:0000:4103:0000:4104:3844:2309:3842:0000:3334:0000:4103:0000:4104:0000:3844:0000:0000:3334:0000:4103:0000:4104:4617:4617:4618:4618:4875:4875:4875:4875:4875:4617:0000:0000:4618:3596:0000:0000:0000:5389:0000:0000:4110:0000:3596:0000:0000:0000:5389:0000:3855:2320:4110:3596:0000:4881:4881:5389:3855:2322:2320:2320:4110:0000:0000:4881:3855:2322:2322:

JS Code:
3x3:d:k:2304:2304:3842:5635:5635:5635:3846:2311:2311:2304:3842:3339:72:4109:73:4111:3846:2311:3842:74:3339:75:4109:76:4111:77:3846:78:79:3339:80:4109:81:4111:4642:4642:4644:4644:4902:4902:4902:4902:4902:4642:82:83:4644:3631:84:85:86:5427:87:88:4150:89:3631:90:91:92:5427:93:3902:2367:4150:3631:94:4931:4931:5427:3902:2375:2367:2367:4150:95:96:4931:3902:2375:2375:

Sumocue PS code:
3x3:d:k:2304:2304:3842:5635:5635:5635:3846:2311:2311:2304:3842:3339:12:4109:14:4111:3846:2311:3842:19:3339:21:4109:23:4111:25:3846:27:28:3339:30:4109:32:4111:4642:4642:4644:4644:4902:4902:4902:4902:4902:4642:44:45:4644:3631:48:49:50:5427:52:53:4150:55:3631:57:58:59:5427:61:3902:2367:4150:3631:66:4931:4931:5427:3902:2375:2367:2367:4150:75:76:4931:3902:2375:2375:
To get this I downloaded sumocue and found that it accepted the JS code but not the SS code. I note that all three codes differ.

Solution:

317958426
524763981
698421573
731684259
956217348
842395617
489132765
173546892
265879134

Here is the PS code that even works for SumoCue:

3x3:d:k:2304:2304:3842:5635:5635:5635:3846:2311:2311:2304:3842:3339:12:4109:14:4111:3846:2311:3842:19:3339:21:4109:23:4111:25:3846:27:28:3339:30:4109:32:4111:4642:4642:4644:4644:4902:4902:4902:4902:4902:4642:44:45:4644:3631:48:49:50:5427:52:53:4150:55:3631:57:58:59:5427:61:3902:2367:4150:3631:66:4931:4931:5427:3902:2375:2367:2367:4150:75:76:4931:3902:2375:2375:

SS-Score: 1.58.

I would appreciate it, if you test your PS code since a lot of your (probably JSudokus) zero Killer PS codes didn't work for SumoCue.

Thanks HATMAN for a challenging Zero Killer-X. While it had some characteristics of your Human Solvables, it felt more like an Assassin than any HS which I've managed to solve so I'm glad that you posted it as an Assassin. I didn't feel that I had to adopt a different approach, which I've had to do when working on HS.

I wonder whether my step 22 is anything like the move you referred to in your introduction; the basic step was easy to find but it took me a long time to see how to use it.


Here is my walkthrough for A189X. I've re-worked from step 32b, when I first overlooked eliminations from placements on diagonals (those who use software solvers in editor mode won't have that problem ), plus a few earlier minor corrections. Then Mike has pointed out that my original step 32 was flawed because I overlooked a permutation; I've now re-worked that step and also simplified the early part of it. Thanks also to Afmob and Ed for their feedback about my walkthrough.

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

10. 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

11. 45 rule on N9 1 outie R6C7 = 1 innie R7C8, no 8 in R6C7, no 1,2 in R7C8
11a. 45 rule on N9 3 innies R7C78 + R8C7 = 21 = {489/579/678}

12. 21(3) cage at R6C7 = {489/579/678}
12a. 8 of {489/678} must be in R8C7 -> no 4,6 in R8C7

13. 45 rule on N3 3 innies R2C7 + R3C78 = 21 = {489/579/678}
13a. 9 of {489/579} must be in R2C7 -> no 4,5 in R2C7

14. 18(3) cage in N4 = {378/459}
14a. 8,9 only in R5C1 -> R5C1 = {89}
14b. 3 of {378} must be in R6C2 -> no 7 in R6C2

15. 45 rule on R5 4 innies R5C1289 = 26 = {2789/4589}
15a. 7 of {2789} must be in R5C2 -> no 7 in R5C89

16. 16(3) cage at R2C5 = {169/178/259/268/349/358/367/457}
16a. 9 of {259} must be in R4C5, 2 of {268} must be in R23C5 (R23C5 cannot be {68} which clashes with 22(3) cage), no 2 in R4C5
16b. 9 of {349} must be in R4C5, 4 of {457} must be in R23C5 (R23C5 cannot be {57} which clashes with 22(3) cage), no 4 in R4C5

17. 15(3) cage in N3 = {159/168/249/267/348/357} (cannot be {258/456} which clash with R2C7 + R3C78)
17a. 9 of {159/249} must be in R2C8, 1,2 of {168/267} must be in R1C7 -> no 1,2 in R2C8

18. R9C456 = {789} (hidden triple in R9), locked for N8
18a. 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
18b. 3 in R9 only in R9C89, locked for N9
18c. Deleted

19. 9(3) cage in N3 = {126/135/234}
[The combination in this cage must be different from the combinations in the 9(3) cages in N1 and N9 but at this stage I don’t know whether those cages have the same combination or different ones.]
19a. 6 of {126} must be in R1C89 (R1C89 cannot be {12} which clashes with R1C2), no 6 in R2C9

20. 15(3) cage in N9 = {159/168/249/267} (cannot be {258/456} which clash with R7C78 + R8C7)
20a. 6 of {267} must be in R7C9 -> no 7 in R7C9

21. 45 rule on R5 2 innies R5C89 = 1 outie R6C2 + 8
21a. R6C2 = {345} -> R5C89 = 11,12,13 = {29/48/58} ( cannot be {49} because R5C12 = [85] (step 15) clashes with the combinations for the 18(3) cage in N4)
21b. 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
21c. 8 of {468} must be in R5C8 (cannot be {68}4 which clashes with R5C89, CCC), no 8 in R4C89
21d. 2 of {29} (for R5C89) must be in R5C9 -> no 9 in R5C9

22. 45 rule on R1 2 innies R1C37 = 2 outies R2C19 + 5
22a. Min R2C19 = [31] = 4 -> min R1C37 = 9 = [72] (cannot be [81] which clashes with R2C19 = [31]) -> no 1 in R1C7
22b. Max R2C19 = 8 (because min R1C1289 = 10)
22c. Max R1C37 = [85] = 13 -> max R2C19 = 8 = [53] (cannot be [35] which clashes with R1C37 = [85]) -> no 5 in R2C9
22d. R1C3 = 8 is not possible at the same time as R2C1 = 5 (because they would clash with R23C3) -> max R2C19 = 7 -> min R1C1289 = 11
[Step 22b was unnecessary, because step 22c gave max R2C19 = 8, but I’ve left it in as an interesting observation.]

23. Min R1C1289 = 11 -> R1C1289 must contain one of 5,6
23a. Killer pair 5,6 in R12C89 and 22(3) cage at R1C4, locked for R1

24. 15(3) cage in N3 (step 17) = {249/267/348/357} (cannot be {159/168} because R1C7 only contains 2,3,4), no 1

25. 1 in N3 only in 9(3) cage = {126/135}, no 4
25a. 4 in R1 only in R1C17, CPE using D\ no 4 in R7C7

26. R159C7 (step 4) = {125/134}
26a. 2 of {125} must be in R1C7 -> no 2 in R59C7

27. 45 rule on R9 2 remaining innies R9C37 = 2 outies R8C19 + 3
27a. Min R8C19 = 3 -> min R9C37 = 6 -> R9C37 = {15/45}, 5 locked for R9
27b. 9(3) cage in N9 (step 10) = {135/234}
27c. 5 of {135} must be in R8C9 -> no 1 in R8C9

28. 15(3) cage in N9 (step 20) = {159/168/249} (cannot be {267} because R9C7 only contains 1,4,5), no 7
28a. 4 of {249} must be in R9C7 -> no 4 in R7C9 + R8C8

29. 7 in N9 only in R7C78 + R8C7 (step 11a) = {579/678}, no 4, clean-up: no 4 in R6C7 (step 11)
29a. 21(3) cage at R6C7 = {579/678}, 7 locked for C7

30. R8C2 cannot be 5, here’s how
30a. R8C9 = 2 => R9C89 = {34} => R9C3 = 5 => no 5 in R8C2
R8C9 = {45} => naked triple {456} in R8C569, locked for R8 => R8C2 = 7
30b. -> no 5 in R8C2

31. 5 in C2 only in R456C2, locked for N4
31a. Killer pair 4,7 in 18(3) cage at R5C1 (in R56C2) and R8C2, locked for C2

[Mike pointed out that my original step 32 was flawed, because I’d overlooked a permutation for R8C19, so I’ve re-worked it and simplified the early part of it.]
32. Only one remaining combination for R5C1289, here’s how
32a. R8C9 = 2 => no 2 in R5C9
R8C9 = {45} => naked triple {456} in R8C569, locked for R8 => R8C2 => 7 => no 7 in R5C2
-> R5C1289 (step 15) = {4589} (only remaining combination, cannot be {2789} because no 2 in R5C9 or no 7 in R5C2), no 2,7
32b. R8C2 = 7 (hidden single in C2), placed for D/
[I’d earlier re-worked from step 32b, where I first overlooked a placement on a diagonal.]

33. 18(3) cage in N4 (step 14) = {459} (only remaining combination) -> R5C1 = 9, R56C2 = {45}, locked for N4 -> R4C2 = 3, R4C7 = 2, R3C8 = 7 (step 3), clean-up: no 5 in R59C7, (step 4)
33a. Naked triple {458} in R5C289, locked for R5, 8 locked for N6

34. Naked triple {134} in R159C7, locked for C7

35. R9C3 = 5 (hidden single in R9), R7C1 = 4
35a. 45 rule on C3 1 remaining innie R1C3 = 7, clean-up: no 6 in 22(3) cage at R1C4

36. Naked triple {589} in 22(3) cage at R1C4, locked for R1 and N2 -> R1C1 = 3, placed for D\, R2C1 = 5, R1C2 = 1 (step 9), R1C7 = 4, R9C7 = 1, R5C7 = 3

37. Naked pair {26} in R9C12, locked for R9 and N7 -> R8C1 = 1, R9C9 = 4, placed for D\, R9C8 = 3, R8C9 = 2 (step 10), R1C9 = 6, placed for D/, R1C8 = 2, R2C9 = 1 (step 19), R9C1 = 2, placed for D/

38. 15(3) cage in N9 (step 28) = {159} (only remaining combination), locked for N9 -> R7C8 = 6, R7C7 = 7, placed for D\, R8C7 = 8, R2C7 = 9, R3C7 = 5, placed for D/, R6C7 = 6, R2C8 = 8, placed for D/, R9C1 = 2, placed for D/

39. R5C5 = 1, naked pair {27} in R5C46, locked for N5

40. 18(3) cage in N6 (step 21b) = {459} (only remaining combination), locked for N6, 9 also locked for R4 -> R4C6 = 4, R5C9 = 8, R6C89 = [17], R3C9 = 3, R2C8 = 8, R9C89 = [34], R46C1 = [78], R2C3 = 4, R3C3 = 8, placed for D\, R3C1 = 6, R2C2 = 2

41. Naked pair {59} in R4C89, locked for R4 and N6 -> R4C45 = [68], R5C8 = 4

42. 16(3) cage at R2C5 (step 16) = {268} (only remaining combination) -> R23C5 = [62]

43. R8C5 = 4 (hidden single in C5), R89C6 (step 18a) = [69], R6C6 = 5, placed for D\, R8C8 = 9, R8C3 = 3, R7C3 = 9, placed for D/
[Could alternatively have got R8C6 from naked pair {59} in R6C6 + R8C8 for D\, CPE no 5 in R8C6 but would still need to use hidden single in C5.]

and the rest is naked singles, without using the diagonals.

Andrew
Your WT is an improved version of my original one (I found 22 very hard to sort) . As you say an assassin in its style. I then picked up the second half of something you got, which put it slightly more in the HS spectrum.

I'll give it a few days before I post this, but I'll PM it to you.

_________________
Quis custodiet ipsos custodes?

Normal: [D  Y-m-d,  G:i]     PM->email: [D, d M Y H:i:s]

Many thanks to HATMAN for providing this puzzle.

At first I had reservations about it being a zero killer and thus not fitting the traditional Assassin mould, but it turned out to be a high quality puzzle that indeed deserves the name "Assassin". In particular, it had one very interesting move that allowed me to break the puzzle relatively early on, and which - who knows - may be the one that HATMAN was intending us to find?


Note: Walkthrough edited to correct optimization error and typos. Thanks Andrew + Afmob!
Edit2: Further minor revisions applied (e.g., to do less in prelims, split/combine moves in more logical fashion, etc.

_________________
Cheers,
Mike

Hi HATMAN,


Interesting observation! I did some research on this (comparing with Perfect Sudoku itself), and can proudly pronounce that the winner is ... Sumocue!

Sumocue is the only one that seems to always get the PS code right. JSudoku PS code is correct for regular killers, but not for zero killers (indeed, trying to import the JSudoku PS code for this puzzle crashed Perfect Sudoku with an "index out of range" error!). SudokuSolver gets it wrong for both regular and zero killers, but at least the PS code in the former case can be understood by JSudoku and Sumocue correctly.

I'll PM Richard on this, so that he can get it fixed for an upcoming SS version.

_________________
Cheers,
Mike

Mike

I liked 6b - is there a name for it?

13 is excellent - not my move but did a similar job in a much tighter fashion (but isn't it a fish?).

Maurice

Afmob had suggested to me that the Sumocue code was the most robust.

Mike used a clone move and CPE in his step 6. Quite clever!

My move in terms of Andrew's WT was:
15b. if r5c2=7 r5c1=8 r6c2=3 r4c2=4/5 and r5c89={29} r4c7=3
15b1. if [29] fail as 18(3)=279
15b2. if[92] fail as 18(3)={45}9 clash r4c2

I had the first part as Andrew did. Then on going through it again thought what if I can disprove [92].

It then falls out easily with Andrew's 22 greatly simplified and 27 becoming obvious.

It is not as neat as Mike's move but it is definitely not fishy. I believe it is easier to see so perhaps a lower rating?