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mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

 Posted: Sat Mar 10, 2007 10:13 pm    Post subject: Texas Jigsaw Killer 22 Better late than never - thought I'd give one of the Texas Jigsaws from the back catalog a spin. Made a bit of a meal of it the first time through, but was able to tighten up the solving path considerably whilst working on this walkthrough. By the way, preparing the walkthrough took ages this time, mainly because of the extremely high symmetry of the puzzle, requiring an equally meticulous solution. This puzzle was very heavy on naked/hidden subsets and involved some powerful applications of the Law of Leftovers. Anyway - here's the walkthrough: Walkthrough - Texas Jigsaw Killer 022 Nonet layout: 112222233 111222333 411123335 441666355 444666555 447666855 477798885 777999888 779999988 1. Preliminaries: a) 11/3 cage at R1C3 - no 9 b) 24/3 cage at R3C6 = {789} -> no 7,8,9 anywhere else in N3 c) 8/3 cage at R2C7 = {1(25|34)} -> no 1 in 13/3 cage at R1C8 d) 6 in N3 now locked in 13/3 cage at R1C8 = {6(25|34)} e) 19/3 cage at R3C1 - no 1 f) 10/3 cage at R4C5 - no 8,9 g) 21/3 cage at R4C6 - no 1,2,3 h) 24/3 cage at R6C8 = {789} -> no 7,8,9 anywhere else in N5 i) 8/3 cage at R5C7 = {1(25|34)} -> no 1 elsewhere in N5 and R5 j) 1 in N4 now locked in 9/3 cage at R6C1 = {1(26|35)}, no 4,7,8,9 k) 6 in N5 now locked in 13/3 cage at R3C9 = {6(25|34)} l) 10/3 cage at R6C7 - no 8,9 m) 8/3 cage at R7C2 = {1(25|34)} -> no 1 elsewhere in N7 n) 21/3 cage at R7C8 - no 1,2,3 o) 20/3 cage at R8C1 - no 1,2 p) 6/3 cage at R8C6 = {123} -> no 1,2,3 anywhere else in N9 2. Innies/outies: a) Innies R5: R5C456 = 20/3 -> no 2,3 in R5C4, no 2 in R5C5 -> no 7 in R46C5 b) Innies R1234: R4C456 = 13/3 -> no 9 in R4C4 c) Innies R6789: R6C456 = 12/3 -> no 8,9 in R6C4 d) Outies R12: R3C258 = 6/3 = {123} -> no 1,2,3 elsewhere in R3 and R12C5 -> no 7,8,9 in R4C3 e) Outies C89: R258C7 = 11/3 -> no 9 in R8C7 f) Outies R89: R7C258 = 18/3 g) Outies C12: R258C2 = 13/3 3. LoL C789: R7C6 = R9C7 = {123}, R1C7 = R3C6 = {789} 4. Naked triple on {789} in C7 at R134C7 -> no 7,8,9 elsewhere in C7 5. Naked triple on {123} in C6 at R789C6 -> no 1,2,3 in R12C6 6. Hidden killer triple on {456} in C6 at R12C6 and 21/3 cage at R4C6 -> no 7,8,9 in R12C6 Clarification: i) 21/3 cage at R4C6 can only contain one of {456} ii) Only other 2 candidate positions for {456} in C6 are R12C6, which therefore cannot contain any other value Note: We could have also arrived at the same result by analysing the possible permutations for the 18/3 cage at R1C6. 7. LoL R123: R4C3 = R3C9 = {456}, R3C1 = R4C7 = {789} 8. Naked triple on {789} in R3 at R3C167 -> no 7,8,9 in R3C34 -> cage 15/3 at R3C3 = {456} -> no 4,5,6 elsewhere in N1 9. LoL C12: a) R89C12+R7C2 must contain {456} -> no 4,5,6 elsewhere in N7 b) Cage 8/3 at R7C2 can only contain 1 of {456} -> cage 20/3 at R8C1 must contain 2 of {456} -> cage 20/3 at R8C1 = {569} -> cage 8/3 at R7C2 = {134} -> cage 17/3 at R6C3 = {278} c) 4 in N7 locked in R78C2 -> no 4 elsewhere in C2 d) (other direction now) R25C3 = {(1|3)9} -> R2C3 = {139}, R5C3 = {39} e) 9 is thus locked in R25C3 -> no 9 in R9C3 f) {1|3} in R25C3 forms hidden naked pair with R8C3 -> no 1,3 in R1C3 10a. LoL R789: R6C3 = R7C9 = {78} -> R6C7 = R7C1 -> no 4 in R6C7 10b. 9 in 24/3 cage at R6C8 locked in R6C89 -> no 9 in R6C6 11. LoL R89: a) Innie R89C89+R8C7 = {278..} -> 2 locked in 14/3 cage at R8C9 -> no 2 elsewhere in N8 b) 14/3 cage at R8C9 can only accommodate one of {78} -> other must go in R8C8 -> R8C8 = {78} c) 14/3 cage at R8C9 must contain one of {78} -> {2(57|48)} -> no 1,3,6,9 d) Hidden single in C9 at R5C9 = 1 e) Hidden single in N8 at R7C8 = 9 f) Split cage R8C78 = 12 -> no 6 in R8C7 g) {13} locked in 10/3 cage at R6C7 = {136} 12. Naked pair on {78} in cage 24/3 at R6C8 -> no 7,8 in R6C9 -> R6C9 = 9 13. LoL C789: R9C7 = R7C6 = {13} 14. LoL R789: R7C1 = R6C7 = {136} 15. Hidden single in R7 at R7C5 = 5 -> Split cage 14/2 ar R89C5 = {68} -> no 6,8 elsewhere in N9 16. 20/3 cage at R8C4 = {479}, 9 locked in R89C4 -> no 9 in R5C4 17. Hidden single in R7 at R7C2 = 4 18. Split 4/2 cage at R8C23 = {13} -> no 1,3 elsewhere in R8 -> R8C6 = 2 19. Cage 17/3 at R5C1 = {269|359|368} -> no 4,7 -> Hidden single in N4 at R4C1 = 4 20. 7 in N4 locked in split cage 15/2 at R3C1+R4C2 = {78} 21. 9/3 cage at R6C1 = {135} (4 no longer available) 22. Naked pair on {13} in R7 at R7C16 -> no 1,3 in R7C7 -> R7C7 = 6 23. Cage 17/3 at R5C1 = {269} -> R5C3 = 9, no 2,6,9 elsewhere in R5 24. Hidden single in N6 at R4C6 = 9 25. Split cage 7/2 at R5C78 = {34} -> no 3,4 elsewhere in N5 26. Innie 20/3 cage at R5C456 = {578} -> no 5,7,8 elsewhere in N6 27. Naked single at R5C5 = 7 28. Hidden single in C6 at R3C6 = 7 -> R34C7 = [98], R4C2 = 7, R3C1 = 8, R1C7 = 7 29. Hidden single in C1 at R2C1 = 7 30. Hidden single in C6 at R5C6 = 8 -> R5C4 = 5, R6C6 = 4 31. Hidden single in C7 at R2C7 = 2 32. Hidden single in C7 at R8C7 = 5 -> R8C8 = 7 -> R6C8 = 8, R7C9 = 7 33. Naked single at R6C3 = 7 34. Naked single at R9C3 = 4 35. Naked single at R8C4 = 9 -> R9C4 = 7 ...and so on... The rest is all singles._________________Cheers, MikeLast edited by mhparker on Fri May 04, 2007 5:07 pm; edited 1 time in total
Para
Yokozuna

Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

 Posted: Sat Mar 10, 2007 10:16 pm    Post subject: I was looking back too but then i ran into puzzle number 18 and still finding nothing to crack it. If you like a challenge. I looked at the lay out and thought very interesting but that was over soon. Para p.s. i see the term hidden killer subset is catching on
mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

 Posted: Mon Mar 12, 2007 1:14 pm    Post subject: Hi Para, I've been taking a look at the puzzle you mentioned (TJK18), but unfortunately (despite intensive efforts) can only come to the same conclusion that you did, namely that there appears to be no way to crack this one without resorting to at least some sort of T&E. Interestingly, this looks like the ONLY Texas Jigsaw in the entire series of 26 so far that falls into this category. I guess it will just have to remain as "the one that got away". _________________Cheers, Mike
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