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 Post subject: Texas Jigsaw Killer 48
PostPosted: Sun Apr 26, 2015 4:36 am 
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Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
Here is a Jigsaw Killer for your enjoyment. Hopefully you will find it to be of interest, if it is too easy I can supply a V2.

ImageImage
SS Score: 1.30

Note the diagonally connected nonets at cells at R2C3-R3C2 and at R7C8-R8C7, as well as the nonet equivalent to D\.

Code: paste into solver:
SumoCueV1=18J0+0J1+0J1+0J2=23J2+4J2+4J2+4J3=22J3=26J4=0J0=0J1=0J2=19J2=10J2+14J5=0J6+8J3+9J4=19J1=0J0+13J2+13J2+13J5=0J5=10J6+8J3+9J4+19J1=0J7=0J0=0J5=0J5=0J5+25J6+8J3+9J4+19J1=0J7=0J7=0J0=0J5=0J5=8J6=14J3=18J4=12J1=0J7=0J7=0J7=0J0=0J5+43J6+44J3+45J4+46J1=0J7=25J7+57J8+57J8=0J0+43J6+44J3+45J4=0J1=13J7+65J8+57J8=0J8=0J6=0J0+44J3+45J4=16J4+73J8+73J8+73J8=26J8+77J6+77J6+77J0

Solution:
172865394
821974635
783129546
259483167
968257413
497316258
634598721
546731982
315642879


As this is the first Jigsaw Killer I've posted, feedback is greatly appreciated.


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PostPosted: Mon Apr 27, 2015 4:51 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for posting your first Texas Jigsaw Killer. :D An interesting puzzle and definitely hard enough to be a TJK. It's probably a bit harder than the SS score suggests; SS scores tend to be a bit low for most jigsaw killers. Also the early placements may reduce the SS score slightly.

I look forward to more TJKs from you, and possibly more from Ed.

The cage pattern is an interesting one:
However I hope you won't be using diagonal nonets very often in future puzzles, as they limit the possibilities of using Law of Leftovers for solving. In this puzzle LoL could still be used but only for columns because the nonets in C1289 were almost vertical. I couldn't find any useful LoLs based on rows.

Killer-Xs can be used for TJKs. Also, although I can't remember ever seeing one, I don't think there's any reason why a puzzle shouldn't have no repeated numbers only on one diagonal although maybe SudokuSolver and other software solvers wouldn't be able to cope with that.

Here is my walkthrough for Texas Jigsaw Killer 48:
I've made a few minor corrections and clarifications.
Nonets are diagonally connected between R2C3 and R3C2, and between R7C8 and R8C7; there is also a diagonal nonet between R1C1 and R9C9.

Prelims

a) R2C67 = {19/28/37/46}, no 5
b) R34C8 = {19/28/37/46}, no 5
c) R67C2 = {39/48/57}, no 1,2,6
d) R8C34 = {49/58/67}, no 1,2,3
e) 19(3) cage at R3C2 = {289/379/469/478/568}, no 1
f) 8(3) cage at R5C8 = {125/134}
g) 26(4) cage at R2C1 = {2789/3689/4589/4679/5678}, no 1
h) 14(4) cage at R5C9 = {1238/1247/1256/1346/2345}, no 9
i) 26(4) cage at R9C6 = {2789/3689/4589/4679/5678}, no 1

1. 8(3) cage at R5C8 = {125/134}, 1 locked for C8 and NR2C8, clean-up: no 9 in R34C8

2. 45 rule on R1 1 innie R1C9 = 4
2a. 14(4) cage at R5C9 = {1238/1256}, no 7, 1,2 locked for C9 and NR1C8

3. 45 rule on R9 1 innie R9C1 = 3

4. 45 rule on C1 1 innie R1C1 = 1, placed for diagonal nonet
4a. R9C2 = 1 (hidden single in NR2C1)
4b. R2C3 = 1 (hidden single in NR1C2) , clean-up: no 9 in R2C67

5. 45 rule on C9 1 innie R9C9 = 9, placed for diagonal nonet
5a. R1C8 = 9 (hidden single in NR1C8)
5b. R8C7 = 9 (hidden single in NR2C8) , clean-up: no 4 in R8C34

6. 45 rule on C8 3 remaining innies R289C8 = 18 = {378/468/567}, no 2

7. Law of Leftovers (LoL) for C12 2 outies R12C3 must exactly equal two innies R1C1 + R2C2, R1C1 = R2C3 -> R1C3 = R2C2, no 4 in R2C2

8. LoL for C89 2 outies R89C7 must exactly equal two innies R8C8 + R9C9, R8C7 = R9C9 -> R8C8 = R9C7, no 3 in R8C8, no 2 in R9C7

9. 45 rule on NR1C2 1 outie R1C4 = 1 remaining innie R8C2 + 4 -> R1C4 = {678}, R8C2 = {234}

10. 45 rule on NR2C8 1 remaining innie R2C8 = 1 outie R9C6 + 1, no 4 in R2C8, no 8 in R9C6

11. 1 in C7 only in R3456C7, locked for NR2C7
11a. 1 in C6 only in R78C6, locked for NR7C5
11b. 9 in C3 only in R4567C3, locked for NR4C3
11c. 9 in C4 only in R23C4, locked for NR1C4
11d. 2 in R9 only in R9C3456, locked for NR7C5
11e. 9 in NR7C5 only in R7C56, locked for R7, clean-up: no 3 in R6C2
11f. R4C7 = 1 (hidden single in R4)

12. 45 rule on NR7C5 2 remaining outies R7C4 + R8C3 = 2 innies R89C6 + 8
12a. Min R89C6 = 3 -> min R7C4 + R8C3 = 11, no 1,2 in R7C4
12b. Max R7C4 + R8C3 = 15 -> max R89C6 = 7, no 6,7,8 in R8C6, no 7 in R9C6, clean-up: no 8 in R2C8 (step 10)

13. Hidden killer pair 1,3 in 25(4) cage at R7C4 and R8C4 for NR7C5, 25(4) cage cannot contain both of 1,3 -> 25(4) cage must contain one of 1,3 in NR7C5 and R8C6 = {13}
13a. 25(4) cage contains one of 1,3 in NR7C5 -> no 3 in R7C4

14. 45 rule on NR2C8 3 innies R2C8 + R9C78 = 18 = {378/468/567}
14a. 3 of {378} must be in R2C8, 5 of {567} must be in R2C8 (R9C78 cannot be {56/57} because 26(4) cage at R9C6 cannot be 6{56}9/5{57}9) -> no 7 in R2C8, no 5 in R9C78, clean-up: no 5 in R8C8 (step 8), no 6 in R9C6 (step 10)
14b. 5 in R9 only in R9C3456, locked for NR7C5, clean-up: no 8 in R8C3

15. 45 rule on NR1C2 3 innies R1C23 + R8C2 = 13 = {238/247/346} (cannot be {256} because 18(4) cage at R1C1 cannot be 1{56}6), no 5 in R1C23, clean-up: no 5 in R2C2 (step 7)
15a. 5 in R1 only in R1C567, locked for NR1C3
15b. 23(4) cage at R1C6 = {2579/3569}, no 8

16. 45 rule on C2 3 innies R128C2 = 13 = {238/247/346}
16a. 19(3) cage at R3C2 = {289/469/568} (cannot be {379/478} which clash with R128C2), no 3,7
16b. R67C2 = {57}/[93] (cannot be {48} which clashes with R128C2), no 4,8

17. 25(4) cage at R7C4 must contain one of 1,3 (step 13) = {1789/3589/3679}, no 4
17a. 4 in NR7C5 only in R9C3456, locked for R9, clean-up: no 4 in R8C8 (step 8)
17b. R2C8 + R9C78 (step 14) = {378/567}
17c. 5 of {567} must be in R2C8 (step 14a) -> no 6 in R2C8, clean-up: no 5 in R9C6 (step 10)
[I overlooked 7 locked for R9 in step 17b; it comes in step 19.]

18. Killer pair 3,5 in R2C8 and 8(3) cage at R5C8, locked for C8, clean-up: no 7 in R34C8

19. 26(4) cage at R9C6 = {2789/4679}, 7 locked for R9

[There may be a way to continue without using a chain, but if so I can’t see it at this stage.]
20. 16(4) cage at R9C2 = {1258/1456}
20a. Consider combinations for R8C34 = [58]/{67}
R8C34 = [58] => 16(4) cage = {1456}
or R8C34 = {67}, locked for R8 => R8C8 = 8 => R9C7 = 8 (step 8) => 16(4) cage = {1456}
-> 16(4) cage = {1456}, 4,5,6 locked for R9 and NR7C5 -> R9C6 = 2, clean-up: no 8 in R2C7, no 7 in R8C3
20b. Naked pair {78} in R9C78, locked for NR2C8, clean-up: no 2 in R34C8
20c. Naked pair {46} in R34C8, locked for C8, clean-up: no 3 in 8(3) cage at R5C8
20d. Naked triple {125} in 8(3) cage at R5C8, locked for C8 -> R2C8 = 3, clean-up: no 3 in R1C3 (step 7), no 7 in R2C67
20e. Naked pair {78} in R8C48, locked for R8 -> R8C56 = [31], clean-up: no 7 in R1C4 (step 9)

21. 25(4) cage at R7C4 = {3589/3679}
21a. 5,6 only in R7C4 -> R7C4 = {56}
21b. Naked pair {56} in R7C4 + R8C3, locked for NR4C3

22. R128C2 (step 16) = {238/247/346}
22a. 3 of {238/346} must be in R1C2 -> no 6,8 in R1C2

23. R8C34 = [67] (cannot be [58] because R78C4 = [68] clashes with R1C4), 7 placed for NR7C5 -> R7C4 = 5, R8C8 = 8, placed for diagonal nonet, R9C78 = [87], clean-up: no 7 in R6C2
23a. Naked pair {89} in R7C56, locked for R7
23b. Deleted

24. LoL for C123 4 outies R567C4 + R6C5 must exactly equal 4 innies R1C1 + R2C2 + R3C39, no 6 in R567C4 + R6C5 -> no 6 in R2C2

25. Naked triple {237} in R127C2, locked for C2 -> R8C2 = 4, R1C3 = 8 (step 9), placed for NR1C4, clean-up: no 2 in R2C7, no 9 in 19(3) cage at R3C2
25a. Naked pair {46} in R2C67, locked for R2
25b. Naked pair {46} in R2C67, CPE no 6 in R1C7, no 4,6 in R3C6
25c. Deleted
25d. Naked pair {27} in R2C25, locked for R2 -> R2C4 = 9

26. 45 rule on NR1C4 2 innies R12C4 = 1 outies R2C7 + R3C6 + 2
26a. R12C4 = [89] = 17 -> R2C7 + R3C6 = 15 -> R2C7 = 6, R3C6 = 9, both placed for NR2C7, R2C6 = 4, placed for NR1C4, R7C56 = [98]

27. R6C2 = 9 (hidden single in C2) -> R7C2 = 3

28. R1C567 = {356} (hidden triple in R1), locked for NR1C4
28a. 19(4) cage at R2C5 = {1279}, 7 locked for C5

29. R4C5 = 8 (hidden single in NR2C7)
29a. 2,4 in NR2C7 only in R356C7, locked for C7 -> R7C7 = 7, placed for diagonal nonet, R2C2 = 2, placed for diagonal nonet, R1C23 = [72], R7C3 = 4, placed for NR4C3, R9C3 = 5, R3C3 = 3, placed for diagonal nonet

30. 18(4) cage at R6C1 contains 3 = {2367/3456} (cannot be {2358} which clashes with R2C1) -> R7C1 = 6, R6C1 = {47}

31. R2C5 = 7, naked pair {12} in R3C45, locked for R3

32. 22(4) cage at R1C9 = {3478/4567}
32a. R2C9 = {58} -> no 5,8 in R34C9

[Just spotted]
33. R4C1 = 2 (hidden single in R4), R8C1 = 5, R6C1 = 4 (cage sum)

34. Naked pair {46} in R4C48, locked for R4 -> R4C2 = 5
34a. R4C3 = 9 (hidden single in R4)

35. R2C1 = 8, R3C1 = 7, R23C9 = [56] -> R4C9 = 7 (cage sum), R34C8 = [46], R3C7 = 5, placed for NR2C7

36. R6C6 = 6 (hidden single in R6), placed for diagonal nonet

and the rest is naked singles, without using the nonets.


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