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sudokuEd
Grandmaster

Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

 Posted: Mon May 14, 2007 11:51 am    Post subject: Texas Jigsaw Killer 29 Fwah Ruud: you're torturing me. That is a fantastic puzzle. Had to use a chain move to unlock it. But perhaps someone can find a better way. Found some really interesting ways to use LoL - hope they are valid. Couldn't find a way to use Jean-Christophe's really great use of LoL and cage sums from TJK28 though. Perhaps that's why I found this puzzle so hard. Won't put the walk-through into tiny text this time. Please let me know of any shortcuts missed, or improvements/corrections. [Thanks to Glyn for some improvements/corrections and naming ][And more improvements and corrections from Andrew. Thanks!] Enjoy! Ed Texas Jigsaw Killer 29 1. "45" r12: 3 outies r3c456 = 7 = {124} 1a. {124} locked for r3 and not elsewhere in 17(5) cage 2. "45" r12: 2 innies r2c46 = 10 = {37} 2a. {37} locked for r2 2b. Common Peer Elimination (CPE) -> no 3 or 7 r1c6 3. 13(2)r1c5 = {49/58}/[76](no 6 r1c5) 4. 24(3)r3c8 = {789} 4a. -> no 789 in r12c9 or r4c78 5. 14(4)r1c8: no 9 6. 8(3)r5c7 = 1{25/34} 6a. 1 locked for r5 6b. CPE ->no 1 r6c7 7. 15(3)r3c7. All combinations have 7/8/9 which are only in r3c7. The exception is {456} 7a. -> r3c7 = 5..9 8. 7 and 9 now only in r3 in n4(r1c9) 8a. 7 & 9 locked for r3 8b. 17(3)r3c1 - no 1,2,5,7 r4c1 8c. 17(3) = {359/368/458} 8d. deleted 8e. 18(3)r3c3: {279} combo blocked by r3c3 -> no 2 r4c23 9. 3 in r3 only in c123 9a. CPE: no 3 r1c1 or r4c2 10. 6(2)r8c5 = {15/24} 10a. -> 1 in c5 locked in 6(2) or r3c5 (6(2) = {24} -> r3c5 = 1) 11. "45" c123: r19c4 = 17 = {89}: locked for c4 12. 14(3)r1c3 must have 8/9 12a. = {149/158/239/248} 12b. cannot have both 8 and 9 -> r12c3 = {14/15/23/24} = 1..5 13. 16(3)r8c3 must have 8/9 13a. {367/457} blocked 13b. cannot have both 8 & 9 -> no 8,9 r89c3 14. "45" c123: 4 innies: r1289c3 = 13 = h13(4)c3 14a. must have 1: 1 locked for c3 14b. -> {259} combo blocked from 16(3)r8c3: (forces 14(3)r1c3 = {149}: 2 9's c4) 14c. -> 16(3)r8c3 = {169/178/268/349/358} 14d. -> r12-89c3 = {14-26/14-35/15-34/23-17/24-16} 15. deleted 16. "45" r1234: 3 innies = 9 = h9(3)r4 16a. = {126/135/234}(no 789) = [2/5..] 16b. ->{258} combo blocked from 15(3)r3c7 17. 15(3)r3c7: all combo's without 1 have 2/3/4 in r4 17a. -> 1 in r4 in h9(3) or r4c78 18. 1 in n5(r3c1) only in r67c1 or r6c2 18a. CPE: no 1 r7c2 19. LoL r6789: 3 innies r67c1+r6c2 = 3 outies r4c9+r5c89 19a.innies must have 1 (step 18) -> outies must have 1 19b. 1 in r5c89 19c. 1 locked for r5 (no 1 r5c7) & 1 locked for n6(r4c9) 19d. deleted, faulty [Thanks Andrew] 20. 9(3)r6c7 = {126/135/234} -> r7c7 = 1..4 21. 16(3)r5c1 = {259/268/349/367} ({358/457} blocked by 8(3)r5c7) 21a. 16(3) = [2/3..], 8(3)r5c7 = [2/3]: Killer pair 2/3: 2 & 3 locked for r5 [Andrew noticed that “45” on r5 3 innies r5c456 = 21 is a simpler way to do the above and I use that "45" in the next step. Thanks] 21b. 2 in n5(r2c1) is either in the innies of LoLr6789 (step 19) -> must be in r5c89 for outies OR 2 in n5 is in 16(3)r5c1. 21c. Either way, no 2 r5c7. Is there a name for this move? ( LoLR - "Law of Left(&Right)-overs") 21d. -> no 5 r5c89 ({125} combo must have 5 in r5c7) 21e. -> no 5 in innies of LoL r6789 (step 19) in r6c12+r7c1 (rest of this step deleted) 21f. no 6 in the outies -> no 6 in innies-> no {156} combo in 12(3)r7c1 22. "45" r5: r5c456 = 21 = h21(3)r5 22a. = {489/579/678} 23. "45" r6789: 3 innies r6c456 = 15 = h15(3)r6 23a. = {159/168/249/267/348/357} ({258/456} blocked by h9(3)r4 in 45(9) see step 16a.) 24. "45" r89: 2 innies r8c46 = 8 = h8(2): 24a. = {17/26/35}(no 4,8,9) 24b.-> 2 locked for n9(r7c5) in h8(2) or 6(2) ({15} in 6(2) -> {26} in h8(2)) 25. "45" r89: 3 outies r7c456 = 20 = h20(3) 25a. = {389/479/569/578}(no 1,2, no 3 in r7c56) 25b. 28(5)r7c4: all combinations must work for both the h8(2) and h30(3) 25c. {14689/24589/34678} all blocked 26. "45" c89: 1 outie r5c7 + 5 = 2 innies r46c8 26a. min r5c7 = 3 -> min r46c8 = 8 -> no 1 r4c8 27. "45" c89: 5 outies = 19 27a. -> must have 1:1 locked for c7 28. "45" c789: 2 outies r19c6 = 9. 28a. no 9, no 6 r9c6 29. "45" n4(r1c9): r1c8 + 16 = 3 innies 29a. Max. 3 innies = {589} = 22 29b. max, r1c8 = 6 29c. CPE: no 8 r1c6 since it sees all 8's in n3(r1c7) 29d. no 1 r9c6 (h9(2)c7) 30. 17(3)r1c7 must have 8/9 for n3(r1c6): r5c6 only other place with 8/9 30a. 17(3) = {179/269/278/359/368/458} = [8/9..] not both 30b. only other place for 8 or 9 is in r5c6 = {89} 31. [18] blocked from h9(2)c6. 31a. 1 in r1c6 -> r23c7 = [79] -> r5c6 = 8: clash with r9c6 31b. no 1 r1c6, no 8 r9c6 32. LoL c1234: 4 outies r1c56+r25c5 = 4 innies r8c4+r9c234 32a. no 1,3 in 4 outies -> no 1 or 3 in 4 innies 32b. 16(3)r8c3 = [1/2/3] only in r8c3 = {123} 33. LoL c6789: 3 outies r346c5 = 3 innies r189c6 33a. no 8 or 9 in innies -> no 8 or 9 in r6c5 Now - a contradiction chain. Is there another way? 34. no 2 r1c6 because of LoL c6789 (step 33) 34a. 2 in r1c6 -> r9c6 = 7 (h9(2)c6) -> {27} in innies 34b. -> {27} in outies r346c5 -> 6(2)r8c5 = {15} -> 13(2)r1c5 = {49} 34c. but {249} in n2 forces 1 into both r3c4 and {158} in 14(3)r1c3 34d. no 2 r1c6 34e. no 7 r9c6 (h9(2)c6) 34e. no 2 r8c4 (LoL c1234 step 32) 34f. oops should have done this earlier too: h8(2)r8 = [53/62/71] 35. 17(3)r1c6 must have 4,5,6 35a. = {269/359/368/458} 36. LoL c1234: Outies r125c5+r1c6 must have 4/5. Here's how. 36a. since 13(2)r1c5 = [4/5] or {67} 36b. if {67} -> r1c6 = 4/5 36c. -> LoLc1234: innies r8c4 + r9c234 must have 4/5 36d. -> Killer pair 4/5 with 6(2)r8c5: 4 and 5 locked for n9(r7c5) 37. r9c6 = 3 finally! 37a. r89c7 = {69/78} = [8/9..] 37b. no 5 r8c4 (h8(2)r8) 38. r2c46 = [37] 39. r1c6 = 6 (h9(2)c6) 39a. r12c7 = {29}/[38]=[8/9..] 40. Killer Pair 8/9 in r1289c7:8 and 9 locked for c7 41. 9 in r3 only in 24(3)r3c7 -> no 9 r4c9 41a. -> no 9 in r7c12 + r7c1 (innies LoL r6789) 42. 13(2)r1c5 = {49/58}(no 7) = [4/5..] 43. Killer Pair 4/5 in 13(2) & 6(2)c5: 4 and 5 locked c5 44. r1c2 = 7 (hsingle n2) 45. 15(3)r3c7 = {267/357/456}(no 1) 46. r7c7 = 1 (hsingle c7) 46a. r6c78 = {26/35}(no 4) 47. 1 in r4 in h9(3) = 1{26/35}(no 4) 47a. 1 locked for 45(9) 48. h15(3)r6 = {249/267/348/357} ({258/456}blocked by r6c78) 49. h13(4)c3: r12-89c3 49a. from step 14d ={14-35/14-26/15-34/24-16}(no 7 r9c3) 49b. = 14{35/26} 49c. 4 locked c3 49b. CPE for 7's n9(r7c5): no 7 r7c4 50. Killer pair 1/2 in c5 in r3c5 and 6(2) 50a. 2 locked c5 50b. [edit:this step added]. LoLc6789: no 7 in 3 innies -> no 7 r6c5. (or 3 and 6 placed in innies -> outies r347c5 must have {36} for c5) 50c.{36} pair r46c5: 3 and 6 locked c5 and 45(9) 51. 28(5)r7c4 = 67{159/249/258} 51a. deleted 52. r4c5 = 6 (hsingle n3) How long has that been there? 52a. r6c5 = 3 52b. h9(3)r4: r4c46 = {12}: 52c. 1 and 2 locked r4 & 45(9) 53. naked pair {12}:locked for n3 53a. r3c6 = 4 53b. r12c7 = [38] the rest is cage sums, hidden/naked singles. [some more typos fixed: thanks Mike]Last edited by sudokuEd on Sat Dec 07, 2013 9:25 pm; edited 2 times in total
mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

Posted: Mon May 21, 2007 9:24 am    Post subject:

Thanks for the great walkthrough, Ed!

 sudokuEd wrote: Now - a contradiction chain. Is there another way?

Yes, there is. See steps 35d, 36, 38 and 40 in the modified walkthrough below.

Also, for another way of progressing, see steps 22 and 23, which build nicely on your fascinating "LoLR" move to lead to an early placement.

Here is my modified walkthrough, taking as much as possible from Ed's excellent opening and early mid-game:

Edit: Simplified step 46 in response to Ed's post below - thanks, Ed

Texas Jigsaw Killer 29

1 - 21f. As for Ed's walkthrough

22. "45" n6(r4c9): 2 outies (r57c7) + 11 = 2 innies (r48c9)
22a. Min. 2 outies = {13} = 4
22b. -> Min. r48c9 = 15
22c. -> Min. r8c9 = 6 = {6789}

23. r48c9 contain 2 of {56789}
23a. 17(3)r6c9 must contain exactly 2 of {56789}
(if only 1 of {56789}, highest possible sum = 16 {349} - too low;
if 3 of {56789}, lowest possible sum = 18 {567} - too high)
23b. -> one of {56789} in n6(r4c9) unaccounted for -> must go in r6c78
23c. -> 9(3)r6c7 = {1(26|35)} (no 4)
23d. 1 in n6(r4c9) already locked in r5c89 (step 19b) -> r7c7 = 1

24. 1 in n5(r3c1) now locked in r6 -> no 1 elsewhere in r6 (r6c4)

25. 1 in 45(9)r4c4 now locked in r4 -> no 1 elsewhere in r4 (r4c8)
25a. h9(3)r4 (step 16) = {1(26|35)} (no 4)

26. 1 in n4(r1c9) locked in 14(4)r1c8 = {1..}
26a. no 1 in r1c8

27. no 1,5,6 in r7c1 -> 12(3)r6c1 <> {156}
27a. only other combo with 5 ({345}) already blocked (step 19d)
27b. -> no 5 in r7c2

28. "45" r789: 4 outies (r6c1239) = h22(4)r6
28a. 1 in r6 locked in h22(4)r6 = {1(489|579|678)} -> no 2,3 in r6c1239

29. "45" r5: r5c456 = 21 = h21(3)r5
29a. = {489/579/678}
29b. {89} only in r5c56 -> no 4 in r5c56

30. "45" r6789: 3 innies r6c456 = 15 = h15(3)r6
30a. = {159/168/249/267/348/357} ({258/456} blocked by h9(3)r4 in 45(9)split-cage see step 16a.)

31. "45" c789: 2 outies r19c7 = 9.
31a. no 9, no 2,6 r9c7

32. "45" n4(r1c9): r1c8 + 16 = 3 innies
32a. Max. 3 innies = {589} = 22
32b. max, r1c8 = 6
32c. CPE: no 8 r1c6 since it sees all 8's in n3(r1c7)
32d. no 1 r9c6 (h9(2)c7)

33. 17(3)r1c6 must have 8/9 for n3(r1c6): r5c6 only other place with 8/9
33a. 17(3) = {179/269/278/359/368/458} = [8/9..] not both
33b. only other place for 8 or 9 is in r5c6 = {89}

34. "45" r89: 2 innies r8c46 = 8 = h8(2):
34a. = {17/26/35}(no 4,8,9)
34b.-> 2 locked for n9(r7c5) in h8(2) or 6(2) ({15} in 6(2) -> {26} in h8(2))

35. "45" r89: 3 outies r7c456 = 20 = h20(3)
35a. = {389/479/569/578}(no 1,2)
35b. 28(5)r7c4: all combinations must work for both the h8(2) and h30(3)
35c. {14689/24589/34678} all blocked
35d. {89} only in r7c56 -> no 3 in r7c56

36. 3 in c5 locked in 45(9)r4c4 -> not elsewhere in 45(9)r4c4 (r46c46)

37. CPE: no 9 r6c5 since it sees all 9's in c6

38. LoL c1234: 4 outies r1c56+r25c5 = 4 innies r8c4+r9c234
38a. no 3 in 4 outies -> no 3 in 4 innies

39. 3 in n9(r7c5) locked in c6 -> not elsewhere in c6 (r2c6)
39a. CPE: no 3 r8c7 since it sees all 3's in c6

40. r2c6 = 7 (naked single)
40a. -> r2c4 = 3
40b. no 2 in r1c6 (step 31)
40c. 7 no longer available in 17(3)r1c6 -> no 1 in r1c6
40d. no 8 in r9c6 (step 31)

41. CPE: no 8 r6c5 since it sees all 8's in c6

42. 7 in n2(r1c2) locked in r1 -> not elsewhere in r1 (r1c1)

43. CPE: no 7 r5c3 since it sees all 7's in n1(r1c1)

44. LoL c789: 3 outies r6c56+r7c6 = 3 innies r1c78+r2c7
44a. no 7 in 3 innies -> no 7 in 3 outies

45. LoL c1234 (revisited): 4 outies r1c56+r25c5 = 4 innies r8c4+r9c234
45a. no 1,2 in 4 outies -> no 1,2 in 4 innies
45b. 16(3)r8c3 = [1/2/63] only in r8c3 = {123}
45c. h8(2)r8 (step 34): no 5,6 in r8c6

46. Hidden killer pair on {12} in n9(r7c5), as follows:
46a. 6(2)r8c5 must contain exactly one of {12}
46b. only other place for {12} in n9 is r8c6 -> r8c6 = {12}
46c. r9c6 = 3 (hsingle n9)

46d. r1c6 = 6 (step 31)
46e. no 7 in 13(2) r12c5 = {49|58} = {4/5..}
46f. split 11(2)r12c7 = {29}|[38]
46g. split 15(2)r89c7: no 2,4,5

47. r1c2 = 7 (hsingle r1)

48. r4c5 = 6 (hsingle n3)
48a. split h3(2) r1234 innie cage at r4c46 = {12}, locked for r4 and 45(9)r4c4

49. r6c5 = 3 (hsingle c5)
49a. split h12(2) r6789 innie cage at r6c46 = [48|75]
49b. split 8(2) cage at r6c78 = {26}, locked for r6 and n6

50. r1c8 = 5 (hsingle n3)

51. r1c7 = 3 (hsingle n3) -> r2c7 = 8

52. r5c6 = 9 (naked single)

53. r6c7 = 2 (hsingle c7) -> r6c8 = 6

54. r4c8 = 3 (hsingle n4)
54a. r34c7 = [75] (only permutation possible)

55. r5c7 = 4 (naked single) -> r5c89 = [13]

The rest is now all naked and hidden singles.
_________________
Cheers,
Mike

Last edited by mhparker on Tue May 22, 2007 4:11 pm; edited 2 times in total
sudokuEd
Grandmaster

Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

Posted: Tue May 22, 2007 8:32 am    Post subject:

Excellent solution Mike. Have become totally hooked on these puzzles. Will try to make a X-KJ sometime.
 Ed wrote: Now - a contradiction chain. Is there another way?
 Mike wrote: Yes, there is. See steps 35d, 36,
Spot on. Tiny step 35d makes all the difference - your beautiful hidden quint moves in steps 22 and 23 are not essential (wish I'd found them though....sooo ).

BTW: we both missed a hidden Killer pair in n9 to get r8c6 = {12) -> r9c6 = 3. A slightly easier way than we both used.

Wow: what a puzzle. Bring on TJK30 please Ruud!

Cheers
Ed

Last edited by sudokuEd on Sat Dec 07, 2013 9:29 pm; edited 1 time in total
mhparker
Grandmaster

Joined: 20 Jan 2007
Posts: 345
Location: Germany

Posted: Tue May 22, 2007 4:20 pm    Post subject:

 sudokuEd wrote: BTW: we both missed a hidden Killer pair in n9 ... A slightly easier way than we both used.

Thanks for pointing that out. Seems so obvious once one knows it's there (as does everything, I suppose!). I've corrected the modified walkthrough above to make use of it.

Roll on TJK30...
_________________
Cheers,
Mike
Ruud
Site Owner

Joined: 30 Dec 2005
Posts: 601

 Posted: Tue May 22, 2007 9:02 pm    Post subject: Did anyone say TJK30? _________________“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
Jean-Christophe

Joined: 23 Apr 2007
Posts: 92
Location: Belgium

Posted: Thu May 24, 2007 7:06 am    Post subject:

 Ruud wrote: Did anyone say TJK30?

I noticed you published TJK30. Although JSudoku could solve it with many weird moves, I'm afraid it's too hard for me, poor mortal. So I stoped trying for find my own way into it.
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