SudokuSolver Forum

Once again, a late puzzle.

Ever since udosuk posted A175 I've been thinking about making a puzzle with the same kind of symmetry: diagonal reflection. That just means that if you fold the puzzle in half along the diagonal (in this case /), the cage pattern in the two resulting triangles match. As udosuk pointed out, this symmetry was first popularized by the KSO site, and still is frequently encountered there. I also think that Borge is currently working on a puzzle generator for this type of symmetry. We'll have to wait and see!

I was going to save this one for a V1.5, but since tarek gave us a fairly easy Assassin last week, I decided to make this the official A184. I've included a "lite" version for you newbies (we still have some newbies don't we?? )

Assassin 184


3x3::k:1536:1536:3586:3586:4868:9477:9477:9477:9477:1289:1289:3083:3586:4868:4868:5135:5135:9477:5906:5906:3083:3586:6166:4119:4119:5135:9477:5906:4124:4381:4381:6166:4119:4119:4130:9477:5906:4124:4124:4381:6166:6166:6166:4130:4130:3117:6958:6958:1328:3633:3633:5939:5939:5939:3117:7735:1328:6958:4410:3633:1084:1084:5939:7735:7735:7735:6958:4410:4410:3141:3654:2375:7735:7735:3402:3402:3141:3141:3141:3654:2375:




Assassin 184 "lite"



3x3::k:2304:2304:3330:3330:5892:9989:9989:9989:9989:1289:1289:3339:3330:5892:5892:4111:4111:9989:4882:4882:3339:3330:4886:3863:3863:4111:9989:4882:4636:4381:4381:4886:3863:3863:4898:9989:4882:4636:4636:4381:4886:4886:4886:4898:4898:3373:6702:6702:1328:4145:4145:4915:4915:4915:3373:6455:1328:6702:4410:4145:828:828:4915:6455:6455:6455:6702:4410:4410:4165:3910:2119:6455:6455:4426:4426:4165:4165:4165:3910:2119:



Enjoy!

This time I have also made images with row and column numbers.
Ed needed row and column numbers on some images for an upcoming puzzle, so I had to whip up a frame including row and column numbers.
Future images for regular Assassins I can do with or without row and column numbers, but NOT both.
You, "the scribblers" just have to decide what you want and let me know.

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Thanks for your efforts Børge.

Personally I do not need or use row and column numbers. The images from you that I really value are the coloured images when a puzzle contains diagonally linked cages.

Thanks Ronnie for this challenging puzzle : I don't remember having solved something that seems to me as difficult as this one without using any chain or contradiction steps. So, it's really interesting. Hope there is no important mistake in my WT.


ASSASSIN 184 Walkthrough



.

Elaine,
Again thanks for your kind and much appreciated feedback.
If there is anything regarding the images you would like to see done differently, at least until I get my software released, so you can do them yourself (hopefully you have a copy of Excel) please do not hesitate to let me know.

in case of interest this is a clickable link to my main SkyDrive folder for Killer images.
Here you can find coloured and BW images for some 66 Killer Sudokus, including some older ones, which have either not been published or Ed has used as additional images in his magnificent Killer archives.


When Ed asked for images with row column numbers I replied:I also assume that the people who do read the WTs use some software for processing the puzzle while stepping through the WT. And since most software can display row and column numbers, they should also not need this on the images.

As Ed was planning to publish his puzzle this weekend, I have a teenie-weenie suspicion that Ed requested row and column numbers, so that he would have an excuse for using his own image(s) instead of mine. But since I was fast adding row and column numbers, I have a hunch that he is now be sitting with clenched teeth trying to outdo mine.

_________________
Quis custodiet ipsos custodes?

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Most of them probably do. I only use an Excel worksheet and do all my own eliminations. I've never downloaded a software solver; maybe I'll do that sometime but I'm not in a hurry to do it.

I hope we do. A184-Lite is a good puzzle for newbies; I've also listed some other good starter ones in my Advice for Newbies and Regulars "sticky".

I decided to do the Lite version first. I hope that newbies don't get stuck on this puzzle but, just in case they do, I've posted my walkthrough below; I'll leave it in hidden text since Ronnie has posted it as a good puzzle for newbies.

Thanks Ronnie for a very challenging Assassin!

I found it a bit harder than manu, who found a useful hidden killer pair in C4.


Here is my walkthrough for A184.

Prelims

a) R1C12 = {15/24}
b) R2C12 = {14/23}
c) R23C3 = {39/48/57}, no 1,2,6
d) R67C1 = {39/48/57}, no 1,2,6
e) 5(2) cage at R6C4 = {14/23}
f) R7C78 = {13}
g) R89C8 = {59/68}
h) R89C9 = {18/27/36/45}, no 9
i) R9C34 = {49/58/67}, no 1,2,3
j) 19(3) cage in N2 = {289/379/469/478/568}, no 1
k) 20(3) cage in N3 = {389/479/569/578}, no 1,2
l) 14(4) cage at R1C3 = {1238/1247/1256/1346/2345}, no 9
m) 27(4) cage at R6C2 = {3789/4689/5679}, no 1,2
n) 12(4) cage at R8C7 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1a. R2C12 = {23} (cannot be {14} which clashes with R1C12), locked for R2 and N1, clean-up: no 4 in R1C12, no 9 in R23C3
1b. Naked pair {15} in R1C12, locked for R1 and N1, clean-up: no 7 in R23C3
1c. Naked pair {48} in R23C3, locked for C3 and N1, clean-up: no 1 in R6C4, no 5,9 in R9C4
1d. Naked pair {13} in R7C78, locked for R7 and N9 -> R7C3 = 2, R6C4 = 3, clean-up: no 9 in R67C1, no 6,8 in R89C9
1e. 12(4) cage at R8C7 = {1236/1245}, 1 only in R9C56, locked for R9 and N8, CPE no 2 in R9C9, clean-up: no 7 in R8C9

2. 9 in N1 only in R3C12, locked for R3 and 23(4) cage at R3C1, no 9 in R45C1
2a. Min R3C12 = 15 -> max R45C1 = 8, no 8 in R45C1

3. 45 rule on N7 1 outie R9C4 = 1 innie R7C1, no 5 in R7C1, no 6 in R9C4, clean-up: no 7 in R6C1, no 7 in R9C3

4. 14(4) cage at R1C3 = {1247/1256}, no 8, 1,2 only in R123C4, locked for C4 and N2
4a. R1C3 = {67} -> no 6,7 in R123C4

5. Hidden killer pair 8,9 in R7C9 and R89C8 for N9, R89C8 contains one of {89} -> R7C9 = {89}

6. R9C9 = 7 (hidden single in N9), R8C9 = 2, clean-up: no 7 in R7C1 (step 3), no 5 in R6C1, no 6 in R9C3
6a. Naked pair {48} in R67C1, locked for C1

7. 12(4) cage at R8C7 = {1245} (only remaining combination, cannot be {1236} because 1,2,3 only in R9C56) -> R9C56 = {12}, R89C7 = {45}, locked for C7 and N9, clean-up: no 9 in R89C8
7a. Naked pair {68} in R89C8, locked for C8 and N9 -> R7C9 = 9
7b. Killer pair 4,5 in R9C34 and R9C7, locked for R9
7c. 3,9 in R9 only in R9C123, locked for N7
7d. 3 in C3 only in R45C3, locked for N4

8. 23(4) cage at R6C7 = {1589/1679/2579} (cannot be {2489} which clashes with R6C1), no 4

9. 3 in N8 only in R8C56 -> 17(3) cage in N8 = {359/368}, no 4,7
9a. 5 of {359} must be in R7C5 -> no 5 in R8C56

10. 45 rule on N8 4 remaining innies R7C46 + R89C4 = 25 = {4579/4678}
10a. 4 of {4579} must be in R9C4 with 5 in R7C6 (R789C4 cannot be {57/59}4 which clash with R123C4), no 5 in R78C4
10b. 6 of {4678} must be in R78C4 (R78C4 cannot be {48} which clashes with R9C4, cannot be {47/78} which clash with combinations for 27(4) cage at R6C2), no 6 in R7C6

11. 27(4) cage at R6C2 = {4689/5679}
11a. 7 of {5679} must be in R78C4 (because no 5 in R78C4 and R78C4 = {69} clashes with 17(3) cage), no 7 in R6C23

12. 45 rule on N3 2 outies R1C6 + R4C9 = 1 innie R3C7 + 12
12a. Min R1C6 + R4C9 = 13, no 3,4 in R1C6, no 1,3 in R4C9
12b. Max R1C6 + R4C9 = 17, no 6,7,8 in R3C7

13. 37(7) cage at R1C6 = {1246789/1345789/2345689}
13a. 9 only in R1C678, locked for R1
13b. Killer triple 1,2,3 in 37(7) cage (within N3) and R3C7, locked for N3

14. 17(3) cage at R4C3 = {179/359/368/467} (cannot be {458} which clashes with R9C4)
14a. 1,3 of {179/359} must be in R4C3 -> no 5,9 in R4C3

15. 45 rule on N6 3 remaining innies R4C79 + R5C7 = 15 = {168/249/258/267/348} (cannot be {159/357/456} which clash with R6C789)
15a. Killer triple 1,2,3 in R3C7, R45C7 and R7C7, locked for C7
15b. 23(4) cage at R6C7 (step 8) = {1589/1679/2579}
15c. 8 on {1589} must be in R6C7 -> no 8 in R6C9

16. 16(3) cage in N6 = {169/259/349/358/367} (cannot be {178/268/457} which clash with R6C789)
16a. 6 of {169} must be in R5C9 -> no 1 in R5C9

17. 45 rule on N2356 3(2+1) remaining outies R14C3 + R7C6 = 14
17a. Min R14C3 = 7 -> max R7C6 = 7
17b. Min R1C3 + R7C6 = 10 -> no 6,7 in R4C3

18. 17(3) cage at R4C3 (step 14) = {179/359/368} (cannot be {467} because R4C3 only contains 1,3), no 4

19. 37(7) cage at R1C6 = {1246789/1345789/2345689}
19a. 8 of {1246789} must be in R1C9 (R1C89 cannot be [24] which clashes with R1C4, R1C679 cannot contain both of 6,7 which would clash with R1C3), {1345789/2345689} can only have one of 4,5 in N3 (both of 4,5 in N3 would clash with 20(3) cage) so must have one of 4,5 in R4C9 -> no 8 in R4C9
19b. Min R1C6 + R4C9 = 13 (step 12a), no 6 in R1C6
[I could have reduced R1C6 to {89} here, see comment after step 29.]

20. R4C79 + R5C7 (step 15) = {168/249/258/267/348}
20a. 6 of {168/267} must be in R4C9 -> no 6 in R45C7

21. 45 rule on C12 2 outies R58C3 = 1 innie R6C2 + 2
21a. R58C3 cannot total 11 (R58C3 cannot be {56} which clashes with R69C3, ALS block) -> no 9 in R6C2

22. 27(4) cage at R6C2 (step 11) = {4689/5679}
22a. 5 of {5679} must be in R6C2 (R6C23 cannot be {56} which clashes with R6C789) -> no 5 in R6C3
22b. 6 of {4689} must be in R6C3 + R78C4 (R6C23 cannot be [69] because R78C4 = {48} clashes with R9C4), 5 of {5679} must be in R6C2 -> no 6 in R6C2

23. 23(4) cage at R3C1 = {1679/2579}
23a. Hidden killer triple 1,2,3 in 23(4) cage at R3C1, R4C3 and 16(3) cage for N4, 23(4) cage contains one of 1,2 in R45C1, R4C3 = {13} -> 16(3) cage contains one of 1,2,3
23b. 16(3) in N4 = {169/178/259/268/349/358/367} (cannot be {457} which doesn’t contain any of 1,2,3)

24. 27(4) cage at R6C2 = {4689/5679} can only be [49]{68}/[86][49]/[89]{46}/[59]{67} (I think I’ve given reasons why other permutations aren’t possible in the earlier steps) -> R6C23 = [49]/[59]/[86]/[89]
24a. 16(3) cage in N4 (step 23b) = {178/259/268/367} (cannot be {169} which clashes with R6C23, cannot be {349/358} which clash with R6C1 + R6C23, ALS block), no 4
24b. 4 in N4 only in R6C12, locked for R6

25. 27(4) cage at R6C2 (step 24) can only be [49]{68}/[89]{46}/[59]{67} (cannot be [86][49] because R789C4 cannot be [498] which clashes with 17(3) cage at R4C3) -> R6C3 = 9, R9C3 = 5, R89C7 = [54], R9C4 = 8, R7C1 = 8 (step 3), R6C1 = 4, R89C8 = [86], clean-up: no 6 in 17(3) cage in N8 (step 9)

26. R7C5 = 5
26a. 6 in N8 only in R78C4, locked for C4
26b. 9 in C4 only in R45C4, locked for N5

27. 23(4) cage at R6C7 (step 8) = {1679/2579} (cannot be {1589} which clashes with R6C2), no 8, 7 locked for R6 and N6
27a. 2 of {2579} must be in R6C8 -> no 5 in R6C8

28. R58C3 = R6C2 + 2 (step 21)
28a. R6C2 = {58} -> R58C3 = 7,10 = [16/61/37], no 7 in R5C3
28b. 16(3) cage in N4 (step 24a) = {178/268/367}, no 5
28c. 1 of {178} must be in R5C3 -> no 1 in R45C2

29. R14C3 + R7C6 = 14 (step 17) = [617/734], CPE no 7 in R1C6
[Then I spotted that I could have got R1C6 = {89} from combinations for the 37(7) cage because 8,9 both in 37(7) inside N3 would clash with the 20(3) cage.]

30. 19(3) cage in N2 = {379/469/478/568}
30a. 7 of {478} must be in R2C56 (R2C56 cannot be {48} which clashes with R2C3), no 7 in R1C5

31. Killer pair 8,9 in R1C6 and 19(3) cage, locked for N2
31a. Hidden killer pair 6,7 in 19(3) cage and R3C56 for N2, 19(3) cage has one of 6,7 -> R3C56 must have one of 6,7
31b. Killer pair 6,7 in R3C12 and R3C56, locked for R3

32. 20(3) cage in N3 = {479/569/578}
32a. R3C8 = {45} -> no 4,5 in R2C8

33. 19(3) cage in N2 (step 30) = {469/478/568} (cannot be {379} which clashes with R2C8), no 3
33a. 6 of {469} must be in R2C56 (R2C56 cannot be {49} because R2C3 + R2C56 clash with 20(3) cage in N3, ALS block)
[No eliminations for step 33a but I’ve included it for possible future use.]

34. 3 in N2 only in R3C56, locked for R3
34a. R3C56 contains 3 and contains one of 6,7 (step 31a) -> R3C56 = {367}, no 4,5

35. 3 in N3 only in R1C89 -> 37(7) cage at R1C6 (step 19) = {1345789/2345689}
35a. 37(7) cage can only have one of 4,5 in N3 (both of 4,5 in N3 would clash with R3C8) -> R4C9 = {45}, no 6
35b. 5 in 37(7) cage only in R234C9, locked for C9

36. 23(4) cage at R6C7 (step 27) = {1679} (only remaining combination), no 2, 1,6 locked for R6 and N6
36a. 2 in R6 only in R6C56, locked for N5

37. 16(3) cage in N6 = {349/358} (cannot be {259} because R5C9 only contains 3,4,8), no 2, 3 locked for N6

38. 2 in N6 only in R45C7, locked for C7 -> R3C7 = 1, R7C78 = [31], R6C789 = [671], R2C8 = 9
38a. Naked pair {78} in R12C7, locked for C7 and N3
38b. R2C4 = 1 (hidden single in C4), R1C8 = 2 (hidden single in C8), R5C9 = 8, then R1C9 = 3 and then R2C9 = 6 (hidden singles in C9), R1C4 = 4

39. 19(3) cage in N2 (step 33) = {568} (only remaining combination) -> R1C5 = 6, R2C56 = [85], R1C3 = 7, R2C7 = 7, R3C8 = 4 (step 32)
39a. R6C56 =[28], R6C2 = 5
39b. Naked pair {67} in R78C4, locked for C4 and N8 -> R7C6 = 4

40. R4C2 = 8 (hidden single in N4), R5C23 = 8 = [26/71], no 6 in R5C2, no 3 in R5C3
40a. R4C3 = 3 (hidden single in N4)

41. R1C6 = 9, R8C56 = [93], R3C56 = [37], R45C6 = [61], R5C3 = 6, R5C2 = 2 (step 40)

and the rest is naked singles.