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PostPosted: Mon Apr 01, 2019 12:11 pm 
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Joined: Sat Jan 05, 2019 1:02 pm
Posts: 40
Location: Canberra, Australia
My new solver/generator can now generate TJK's, and to introduce it I have produced this sample puzzle.

The Jigsaw and Cage layout is the same as TJK #31 (v2). That puzzle had an SS score of 2.2, but this one is not so hard, it has SS score = 0.95. (Andrew has suggested 0.75 - 1.25 as a suitable range for P&P solving, so this is pretty much dead-center in that range).

The puzzle definition (paste into SS):
Puzzle:
SumoCueV1=17J0+0J0=19J0+2J1=14J1+4J1=27J1+6J1=20J2=16J0+0J0+0J0+2J1+4J1=14J1+6J1+8J2+8J2+9J0+9J0=8J0+20J3+20J3+14J3+6J2+6J2+8J2=25J4+27J4=20J4+29J4=21J3=10J2+32J2+32J2=24J5+27J4+29J4+29J4+29J4+31J3=21J5+41J5+41J5+35J5+27J4=14J6+46J6+46J6+31J3+41J5+41J5+35J5+35J5=19J6=31J6+55J6=11J3=18J3+58J3+58J7=7J7+61J7+54J6+54J6+55J8+57J8=10J8=14J8=25J7+69J7+61J7+54J6+55J8+55J8+67J8+67J8+68J8+68J7+69J7+69J7

Attachment:
TJK-031-B.png
TJK-031-B.png [ 11.99 KiB | Viewed 4616 times ]


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PostPosted: Thu Apr 04, 2019 6:41 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Mathimagics for starting to post Texas Jigsaw Killers. :) I'd been a bit frustrated that they'd only reached number 49, although Ruud's About the number 4 was really a TJK and ought to have been numbered as such, at least in parentheses. So when MM started posting a variety of other variants I suggested making some TJKs.

I hope that I won't be the only person solving MM's TJKs and that others will also solve them and occasionally post comments, even if they don't post walkthroughs.

This sample one is fairly easy. I always use Law of Leftovers for Jigsaw Killers. If anyone doesn't understand LoL, I hope that my LoL steps make it clear what it is, or please feel free to ask me by PM for more details.

Here is my walkthrough for Texas Jigsaw Killer Sample:
Prelims

a) R23C6 = {59/68}
b) R78C4 = {29/38/47/56}, no 1
c) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
d) 8(3) cage at R3C3 = {125/134}
e) 21(3) cage at R4C5 = {489/579/678}, no 1,2,3
f) 10(3) cage at R4C6 = {127/136/145/235}, no 8,9
g) 7(3) cage at R7C8 = {124}
h) 10(3) cage at R8C5 = {127/136/145/235}, no 8,9

1a. 45 rule on NR1C1 2 innies R13C3 = 12 = [75/84/93]
1b. 8(3) cage at R3C3 = {125/134}, 1 locked for R3 and NR3C4
1c. Law of Leftovers (LoL) for R123 10(3) cage at R4C6 must contain the same digits as R3C456 -> R3C6 = {56}, 10(3) cage at R4C6 must contain 1 and one of 5,6 = {136/145}, no 2,7, 1 locked for R4 and NR1C9
1d. No 2 in 10(3) cage -> no 2 in R3C45 -> 8(3) cage at R3C3 = {134}, locked for R3
1e. R3C3 = {34} -> R1C3 = {89}
1f. R3C6 = {56} -> R2C6 = {89}

2a. 2 in NR3C4 only in R7C456, locked for R7
2b. Naked pair {14} in R7C89, locked for R7 and NR7C7 -> R8C9 = 2
2c. 45 rule on NR7C7 2 innies R79C7 = 13 = {58/67}, no 3,9
2d. Min R9C7 = 5 -> max R89C6 = 9, no 9 in R89C6
2e. LoL for R789, 14(3) cage at R6C2 must contain the same digits as R7C456 -> R7C456 = 14(3)
2f. R7C456 contains 2 = {239/257}, no 6,8
2g. R7C456 = {239/257} -> 14(3) cage at R6C2 = {239/257}, no 1,4,6,8, 2 locked for R6 and NR6C2
2h. 2 in R4 only in R4C1234, locked for NR4C1
2i. R7C456 = 14(3), 18(3) cage at R7C5 -> R7C7 4 more than R7C4 -> R7C4 = {23}, R7C7 = {67} -> R8C4 = {89}, R9C7 = {67}
2j. Naked pair {67} in R79C7, locked for C7 and NR7C7
2k. Min R9C7 = 6 -> max R89C6 = 8, no 8 in R89C6
2l. 8 in NR3C4 only in 21(3) cage at R4C5, locked for C5
2m. 21(3) cage = {489/678}, no 5

3a. 45 rule on NR1C9 2 innies R3C78 = 15 = [87/96]
3b. R3C78 = 15 -> R1C78 + R2C7 = 12
3c. R2C8 = 2 (hidden single in NR1C9)
3d. 2 in R3 only in 16(3) cage at R2C1 = {259/268}, no 1,3,4,7
3e. 7 in R3 only in R3C89, locked for NR1C9

4a. 45 rule on NR6C2 2 innies R7C23 = 12 = {39/57}, no 6,8
4b. R7C23 = 12 -> R8C3 + R9C23 = 19 = {289/469/478/568} (cannot be {379} which clashes with R7C23), no 1,3
4c. LoL for C123 3 outies R456C4 must contain the same digits as 3 innies R8C3 + R9C23 -> no 1,3 in R456C4
4d. R7C1 = 8 (hidden single in R7)
4e. R8C12 + R9C1 = {146} (hidden triple in NR6C2)
4f. R7C7 = 6 (hidden single in R7) -> R7C56 = 12 = {39/57}, no 2
4g. R7C4 = 2 (hidden single in R7) -> R8C4 = 9
4h. R6C4 = {57} -> 14(3) cage at R6C2 (step 2g) = {257}, 5,7 locked for R6 and NR6C2
4i. Naked pair {39} in R7C23, locked for R7
4j. Naked pair {57} in R6C56, locked for NR3C4 -> R3C6 = 6, R2C6 = 8, R3C8 = 7 -> R3C7 = 8 (step 3a)
4k. 21(3) cage at R4C5 = {489}, 4,9 locked for C5 and NR3C3
4l. Naked pair {13} in R3C45, locked for R3 -> R3C3 = 4, R1C3 = 8 (step 1a)
4m. LoL for R123 (step 1c) R3C456 = {13}6 -> 10(3) cage at R4C6 = {136} -> R4C8 = 6, R4C67 = {13}, locked for R4 and NR1C9
4n. Naked triple {459} in R123C9, locked for C9

5a. 16(3) cage at R2C1 (step 3d) = {259} (only remaining combination), locked for NR1C1
5b. R1C3 = 8 -> R12C4 = 11 = {47/56}, no 3
5c. Killer pair 5,7 in R12C4 and R6C4, locked for C4
5d. 8 in C4 only in R45C4, locked for NR4C1
5e. R9C2 = 8 (hidden single in C2), R8C3 + R9C23 = 19 (step 4b) -> R89C3 = 11 = {56}, locked for C3 and NR8C3
5f. LoL for C123 (step 4c) R8C3 + R9C23 exactly equals R456C4 -> R456C4 = [865]
5g. R45C4 = [86] = 14 -> R4C3 + R5C23 = 6 = {123} -> R4C3 = 2, R5C23 = {13}, locked for R5 and NR4C1
5h. R6C23 = [27]
5i. R7C3 = 9 (hidden single in C3) -> R7C2 = 3, R5C23 = [13], R2C3 = 1
5j. Naked pair {47} in R12C4, locked for C4 and NR1C4
5k. R9C7 = 7 -> R89C6 = 7 = {34}, locked for C6 and NR8C3

and the rest is naked singles.

Solution:
3 7 8 4 6 5 2 1 9
5 6 1 7 3 8 9 2 4
2 9 4 3 1 6 8 7 5
9 5 2 8 4 1 3 6 7
7 1 3 6 9 2 4 5 8
4 2 7 5 8 9 1 3 6
8 3 9 2 5 7 6 4 1
1 4 6 9 7 3 5 8 2
6 8 5 1 2 4 7 9 3

As well as MM's TJKs, there are also more in the Texas Jigsaw Killer archive, of varying levels of difficulty.


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