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Texas Jigsaw Killer 26

 
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mhparker
Grandmaster
Grandmaster


Joined: 20 Jan 2007
Posts: 345
Location: Germany

PostPosted: Sun Feb 25, 2007 6:38 pm    Post subject: Texas Jigsaw Killer 26 Reply with quote

Fascinating creatures, these jigsaw killers, requiring all the skills for solving a regular killer, plus the ability to "think round corners". Thought they may be becoming extinct after waiting 4 weeks since puzzle #25. To show that they are very much appreciated (despite the relative inactivity on this forum), I've decided to post this walkthrough:


Walkthrough - Texas Jigsaw Killer 026

Nonets (N1 through N9 are numbered in order of their top-left cells, reading from left to right, top to bottom, as shown below:

111222223
411222323
441155333
441155333
444555566
774775666
777788866
999788866
999999888

1. Preliminaries:

a) 11/3 at R1C8: no 9
b) 6/3 at R234C1 = {123} -> no 1,2,3 elsewhere in C1 or N4
c) 9 locked in 22/3 at R2C5 -> no 9 in R1C6
d) 16/2 at R45C4 = {79} -> no 7 or 9 in R1236789C4 and R4C56
e) 11/2 at R45C8: no 1
f) 6/3 at R456C9 = {123} -> no 1,2,3 elsewhere in C9
g) 21/3 at R5C7: no 1,2,3
h) 8/2 at R67C6: no 4,8,9
i) 15/3 at R789C1 = {456} -> no 4,5,6 elsewhere in C1
j) 8/2 at R7C78: no 4,8,9
k) 20/3 at R8C567: no 1,2
l) 7/2 at R9C67: no 7,8,9
m) 11/2 at R9C89: no 1

2. Outie N4: R47C3 = 5 -> R47C3 = {1234}

3. Outie R89: R7C19 = 14 = [59|68] -> R8C8 = {12}, R8C9 = {45}

4. Innie N8: R7C567+R9C7 = 14 -> no 9 in R7C5

5. Innie/outie difference N9: R7C1+R8C4-R9C6 = 7 -> R8C4-R9C6 = 1|2 -> no 1 in R8C4

6. Naked triple {123} at R56C9+R8C8 in N6 -> no 1,2,3 elsewhere in N6

7. Innie N1: R34C4+R4C3 = 17 -> no 1 in R4C3 (would require 7|9 in R3C4 -> clash with R45C4)

8. R4C3 is peer of all candidate positions for digit 4 in N4 -> no 4 in R4C3 -> R47C3 = {23} (see step 2)

9. Naked triple {123} at R4C139 in R4 -> no 1,2,3 elsewhere in R4

10. Innie N789: R7C367 = 9 = {1(26|35)} (no 4 available) -> R7C67 = {156}

11. From step 10: Innie N789 (R7C367) forms killer pair on {56} with R7C1 -> no 5,6 elsewhere in R7

12. Naked single R7C8 = 7 -> R7C7 = 1, R7C6 = {56}, R7C5 = {23}

13. Innie N8: Split cage 13/3 at R7C56+R9C7 -> no 8 in R7C5, no 2 in R9C7

14. R45C8 = {56} -> no 5,6 elsewhere in C8

15. LoL R89: Outie R7C567 = {1..} -> innie R8C489 = {1..} -> R8C8 = 1 -> R4C9 = 1

16. 11/3 at R1C8 = {2..} (1 no longer available) -> 2 in N2 locked in R12C8 -> no 2 elsewhere in C8 or N2

17. Hidden single N8: R7C5 = 2 -> R7C3 = 3, R4C3 = 2 (see step 8), R4C1 = 3

18. Innie N789: R7C6 = 5 (see step 10) -> R6C6 = 3 -> R6C9 = 2, R5C9 = 3

19. R7C19 = [68] -> R7C24 = [94], R89C1 = [45], R8C9 = 5 -> R45C8 = [56]

20. LoL R89: Outie R7C567 = [251] -> R8C4 = 2

...
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Cheers,
Mike


Last edited by mhparker on Fri May 04, 2007 5:08 pm; edited 3 times in total
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Ruud
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Joined: 30 Dec 2005
Posts: 601

PostPosted: Mon Feb 26, 2007 5:50 pm    Post subject: Reply with quote

Thanks for the encouragement, Mike. I'll try to create and post a new Jigsaw Killer every 2 weeks, but missed the last one because I've been busy with too many other things.

These Jigsaw Killers are not only fun to solve, but also fun to make. It usually takes me 1 to 2 hours to create one with the right difficulty and mix of techniques. This is one of the few puzzle types that I create manually. I also seem to be the only one (intending) to create them on a regular basis.

cheers,
Ruud
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“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
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PsyMar
Hooked
Hooked


Joined: 17 Nov 2006
Posts: 32
Location: The Triad, North Carolina, US

PostPosted: Tue Mar 06, 2007 7:14 pm    Post subject: Reply with quote

I just finished this one -- couldn't do it in one sitting but finished it in the next (which is a rarity, usually if I can't finish it at once I give up altogether).

I'm going to post my walkthrough as it's rather different -- it may be somewhat circuitous, I'm sure it isn't minimal, but it's the way I solved it. Despite what was said at the top (that the puzzle requires "lots of LoL") I only used one LoL move in the entire puzzle.

Nonet numbering:
111222223
411222323
441155333
441155333
444555566
774775666
777799966
888799966
888888999


0a. 7/2 in R9 does not contain 789 (sums)
0b. 8/2 in C6 does not contain 489 (sums)
0c. 8/2 in R7 does not contain 489 (sums)
0d. 11/2 in C8 does not contain 1 (sums)
0e. 11/2 in R9 does not contain 1 (sums)
0f. 16/2 in C4 = {79} naked pair (sums), elim 79 from rest of C4
0g. 6/3 in C1 = {123} naked triple (sums), elim 123 from rest of C1 & N4
0h. 6/3 in C9 = {123} naked triple (sums), elim 123 from rest of C9
0i. 11/3 in R12 does not contain 9 (sums)
0j. 20/3 in R8 does not contain 12 (sums)
0k. 21/3 in R78 does not contain 123 (sums)
0l. 22/3 in R23 does not contain 1234, must contain 9 (sums), elim 9 from R1C6
1. 15/3 in C1 without 123 must be {456} naked triple (sums), elim 456 from rest of C1
2. outies of R89 = 14/2 = [59|68]
3. 4 of c1 locked in N8 -> elim from rest of N8
4. outies of N4 = R47C3 = 5/2 = {14|23}
5. combinations for 14/3 in N6 = [914|815|824]
6. R56C9+R8C8 = {123} naked triple, elim 123 from rest of N6
7. combinations for 8/2 in R7 = [17|26|35]
8. 24/4 in N8 must have 5 or 6, forms killer triple {456} with R89C1, elim 456 from rest of N8
9. Outies-innies of N14 = R7C3-R34C4 = -12 -> R34C4 >= 13 -> R3C4 >= 4; additionally, since R34C4 cannot be 16 (sums) R7C3 is not 4
10. R5C569 = hidden triple {123}
11. 8/2 in C6 must have 1, 2 or 3; forms killer triple {123} with R59C6; elim 123 from rest of C6
12. Outies-innies of N8 = R7C1+R8C4-R9C6 = 7 -> 8<=R7C1+R8C4<=10 -> 2<=R8C4<=5
13. sums for 7/2 in R9 = [16|25|34]
14. 1 of N9 locked in R7 -> elim from rest of R7
15. 1 of R9 locked in N8 -> elim from rest of N8
16. R8C8 = hidden single 1 in R8
17. R4C9 = hidden single 1 in R9
18. 1 of R5 locked in N5 -> elim from rest of N5
19. combinations for 11/3 in R12 = {236|245} (elim 78 from 11/3), 2 locked in R12C8 -> elim 2 from rest of N2 and C8
20. combinations for 11/2 in R9 = [38|47|56|65|74]
21. 9 of R9 locked in N8 -> elim from rest of N8
22. 9 of R8 locked in N9 -> elim from rest of N9
23. Repeat step 4, hidden cage 5/2 in R47C3 = {23} pair (sums) -> elim 23 from rest of C3
24. R4C13 = {23} naked pair -> elim 23 from rest of R4
25. combinations for 11/2 in C8 = {47|56}
26. R36C8 = hidden pair {89}
27. Outies-innies of C89 = R37C7-R6C8 = -5 -> 3<=R37C7<=4 -> R7C7 = 1 && R3C7 = {23} -> R7C8 = 7 (last digit in cage)
28. combinations for 11/2 in C8 = {56} pair -> elim 56 from rest of C8
29. Combinations for 11/2 in R9 = [38|47]
30. Combinations for 11/3 in R12 = [263|254|362|452] -> elim 4 from R1C9
31. LOL on R6789 -> R6C3 = {56}, R6C6 = {23}
32. Combinations for 14/3 in C3 = [563|653|752], elim 5 from rest of C3 and N4
33. only possibility for 13/3 in C3 is {148} -> elim 148 from rest of N1 and C3
34. R1C1+R4C4 = naked pair {79} in N1, elim 79 from rest of N1
35. R6C69 = naked pair {23} in R6, elim 23 from rest of R6
36. combinations for 8/2 in C6 = [26|35]
37. R7C16 = naked pair {56} in R7, elim 56 from rest of R7
38. R9C3 = hidden single 9 in C3
39. 4 of N4 locked in C2 -> elim 4 from rest of C2
40. 4 of R7 locked in 18/4 in C45, elim 4 from R6C45
41. rest is naked singles, hidden singles, and last-digit-in-cage moves
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