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Ed
 Post subject: Texas Jigsaw Killer 47
PostPosted: Thu Nov 13, 2014 9:09 pm 
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Joined: Wed Apr 16, 2008 1:16 am
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Found a way to get lots of placements near the start but didn't help! Kept finding "simple" things I missed. Bit rusty with this jigsaw stuff. Warped!! Really enjoy them, will have to keep making these. It gets a SudokuSolver score of 'just' 1.25. Made mistakes on my first two solves so hope I have a valid way this time.

Texas Jigsaw Killer 47

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code: paste into solver:
SumoCueV1=17J0+0J0=34J0+2J1+2J1=3J1=41J2+6J2+6J2+0J0=24J0+2J0=27J3+2J3+5J1+12J1=13J2+6J2+10J0+10J0+2J0+12J3+12J3+12J4+12J1+16J1+6J2+10J5=21J3=10J3+29J3=19J4=22J4+32J1+32J1+6J2=10J5+28J3+31J3+31J4+31J4+32J4=15J6+6J6+6J2+36J5+28J5+28J4=25J4+48J4=25J6+42J6+42J6+42J2=36J7+54J5+48J5+48J5+48J6+50J6+50J8=20J8+61J8=8J7+54J7+54J5+54J5=9J6+50J6=26J8+69J8+61J8+63J7+63J7+54J7+54J7+67J7+69J7+69J8+69J8+61J8
solution: 
3 9 4 5 7 1 6 8 2 
5 6 8 1 9 2 3 4 7 
7 2 1 6 5 4 8 9 3 
9 3 2 8 1 7 4 6 5 
6 4 7 3 8 5 2 1 9 
4 8 6 9 2 3 7 5 1 
8 1 3 7 4 9 5 2 6 
1 7 5 2 6 8 9 3 4 
2 5 9 4 3 6 1 7 8
Cheers
Ed
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Andrew
PostPosted: Wed Dec 03, 2014 9:06 pm 
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Many thanks Ed for posting another TJK, the first for more than a year and the first specifically posted as a TJK since 2010. Maybe the TJK Archive and my walkthroughs in it encouraged you to post this new one. I hope so!

Ed wrote:
Found a way to get lots of placements near the start but didn't help!
I wouldn't go as far as that, but after those placements one has to start working again. The first pair of placements come immediately, the remaining early ones take a bit of work; I'll be interested to see whether you found a better way to get them.

I enjoyed this puzzle; I was able to find some interesting steps. :D

The way I got those early placements:
used a series of hidden cages before I used one of them in a 45. I assume that SudokuSolver must remember each of those hidden cages; if it had chained them together it would have come up with a higher score than 1.25.

Here is my walkthrough for TJK 47:
Prelims

a) R12C6 = {12}
b) R23C8 = {49/58/67}, no 1,2,3
c) R4C34 = {19/28/37/46}, no 5
d) R56C1 = {19/28/37/46}, no 5
e) R89C5 = {18/27/36/45}, no 9
f) 8(3) cage at R8C1 = {125/134}
g) 41(8) cage at R1C7 = {12356789}, no 4

Steps resulting from Prelims
1a. Naked pair {12} in R12C6, locked for C6 and NR1C4
1b. 8(3) cage at R8C1 = {125/134}, 1 locked for NR7C1, clean-up: no 8 in R8C5

[Since the SS score is 1.25 and Ed has commented that he got a lot of early placements, the puzzle is probably a bit harder than that, so I’ll start using Law of Leftovers (LoL) as soon as possible. A SS score of 1.25 is about the level where I decide whether to use LoL early or avoid using it as long as possible.]

2. LoL for C789 four outies R1C45 + R12C6 must exactly equal four innies R56C78, R12C6 = {12} -> R56C78 must contain both of 1,2, locked for NR5C7, clean-up: no 7,8 in R9C5

3. 45 rule on NR1C7 2 innies R2C8 + R6C9 = 1 outie R5C8 + 4, IOU no 4 in R6C9
[I’d missed 41(8) cage at R1C7 = {12356789}, CPE no 5,6,7,8,9 in R2C8 -> R2C8 = 4.]
3a. R2C8 = 4 (hidden single in NR1C7) -> R3C8 = 9, placed for NR1C4
3b. 41(8) cage at R1C7 = {12356789}, 9 locked for NR1C7, no 9 in R6C9
3c. 4 in C9 only in R789C9, locked for NR7C7
3d. LoL for C789 four outies R1C45 + R12C6 must exactly equal four innies R56C78, no 9 in four outies -> no 9 in R56C7
3e. 34(6) cage at R1C3 must contain 9, CPE no 9 in R2C12 + R45C3, clean-up: no 1 in R4C4

4. 45 rule on NR7C7 1 outie R9C6 = 1 innie R7C7 + 1, no 1,9 in R7C7, no 5 in R9C6

5. LoL for R789 four outies R456C1 + R6C2 must exactly equal four innies R78C56, no 1,2 in R78C56 -> no 1,2 in R456C1 + R6C2, clean-up: no 8,9 in R56C1
5a. 2 in NR4C1 only in R7C234 + R8C34, CPE no 2 in R7C1

6. 45 rule on NR1C1 4(3+1) outies R1C45 + R2C5 + R4C1 = 30
6a. Max R1C45 + R2C5 = 24 -> min R4C1 = 6
6b. Min R1C45 + R2C5 = 21, no 1,2,3 in R1C45 + R2C5
6c. Min R1C45 + R2C5 = 21, max R1C45 = 15 -> min R2C5 = 6
6d. LoL for C789 four outies R1C45 + R12C6 must exactly equal four innies R56C78, no 3 in R1C45 + R12C6 -> no 3 in R56C78
6e. 41(8) cage at R1C7 = {12356789}, 3 locked for NR1C7, no 3 in R6C9

7. 45 rule on NR7C7 4 outies R6789C6 = 26
7a. 45 rule on C6 using R6789C6 = 26, 3 remaining innies R345C6 = 16
7b. 45 rule on C6789 3 innies R2C7 + R3C67 = 15
7c. R2C7 + R3C67 + 22(4) cage at R4C6 = 37, R345C6 = 16 -> R234C7 + R4C8 = 21
[Alternatively can use 45 rule on C789 combined with innies-outies for NR7C7 to get R234C7 + R4C8 = 21; however R345C6 is still useful later.]
7d. 45 rule on NR1C1 + NR1C4 4 innies R234C7 + R4C8 = 2(1+1) outies R2C5 + R4C1 + 3
7e. R234C7 + R4C8 = 21 -> R2C5 + R4C1 = 18 -> R2C5 = 9, placed for NR2C4, R4C1 = 9, placed for NR4C1, clean-up: no 1 in R4C3
7f. R1C2 = 9 (hidden single in NR1C1) -> R12C1 = 8 = {17/26/35}, no 4,8
7g. R5C9 = 9 (hidden single in NR1C7)
7h. R7C6 = 9 (hidden single in R7) , clean-up: no 8 in R7C7 (step 4)
7i. R8C7 = 9 (hidden single in R8)

8. R1C45 + R2C5 + R4C1 = 30 (step 6), R2C5 = 9, R4C1 = 9 -> R1C45 = 12 = {48/57}, no 6
8a. 4 in R1 only in R1C345, locked for 34(6) cage at R1C3, no 4 in R3C3
8b. 34(6) cage at R1C3 = {145789/245689/345679}, CPE no 5 in R1C1, clean-up: no 3 in R2C1 (step 7f)
8c. LoL for C789 four outies R1C45 + R12C6 must exactly equal four innies R56C78, R1C45 + R12C6 = {1248/1257} -> R56C78 = {1248/1257}, no 6
8d. 41(8) cage at R1C7 = {12356789}, 6 locked for NR1C7, no 6 in R6C9

9. 45 rule on R123 2 remaining outies R4C9 + R5C8 = 6 = {15}, locked for 41(8) cage at R1C7
9a. Naked pair {15} in R4C9 + R5C8, CPE no 5 in R4C8
9b. R46C9 = {15} (hidden pair in NR1C7), locked for C9
9c. 5 in R1 only in R1C345, locked for 34(6) cage at R1C3, no 5 in R23C3
9d. Hidden killer pair 4,5 in R1C3 and R1C45 for R1, R1C45 contains one of 4,5 -> R1C3 = {45}

10. 3,6 in NR5C7 only in R68C6 + R78C5, R78C5 cannot contain both of 3,6 (which would clash with R89C5, CCC) -> R68C6 must contain at least one of 3,6
10a. 25(4) cage at R6C6 contains 9 = {2689/3589/3679} (cannot be {4579} which doesn’t contain 3 or 6), no 4
10b. 5 of {3589} must be in R7C7 (R68C6 cannot be {58} which clashes with R56C78), no 5 in R68C6

11. 5 in C6 only in R345C6, locked for NR3C6
11a. R345C6 (step 7a) = 16 = {358/457}, no 6

12. 45 rule on C6789 3 outies R2C4 + R3C45 = 12 cannot contain both of 1,2 (because no 9)
12a. 27(6) cage at R2C4 = {134568/234567} (cannot be {123678/124578} because R2C4 + R3C45 cannot contain both of 1,2), 4 locked for R3
12b. R1C3 = 4 (hidden single in NR1C1), clean-up: no 8 in R1C45 (step 8), no 6 in R4C4
12c. Naked pair {57} in R1C45, locked for R1, 34(6) cage at R1C3 and NR1C4, clean-up: no 1 in R2C1 (step 7f)
12d. 8 in R1 only in R1C789, locked for NR1C7
12e. And, for the last time, LoL for C789 four outies R1C45 + R12C6 must exactly equal four innies R56C78, R1C45 + R12C6 = {1257} -> R56C78 = {1257}, locked for NR5C7, clean-up: no 2,4 in R9C5
12f. 41(8) cage at R1C7 = {12356789}, 7 locked for C9
12g. R1C3 = 4, R1C45 = {57} = 12, R2C5 = 9 -> R23C3 = 9 = {18/36}, no 2

13. 25(4) cage at R6C6 (step 10a) = {2689/3589/3679}
13a. R68C6 = {368} -> no 3,6 in R7C7, clean-up: no 4,7 in R9C6 (step 4)
13b. R345C6 = {457} (hidden triple in C6), locked for NR3C6

14. 22(4) cage at R4C6 = {3478/4567} (cannot be {3568} because R45C6 only contain 4,5,7), 7 locked for C6
14a. 6 of {4567} must be in R4C8 -> no 6 in R4C7
14b. 4 of {4567} must be in R4C7, 4 of {3478} must be in R5C6 (R4C678 cannot be {478} which clashes with R4C34) -> no 4 in R4C6
14c. R2C7 + R3C67 = 15 (step 7b) = {348/456}, 4 locked for R3
14d. 6 of {456} must be in R2C7 -> no 6 in R3C7

15. 4 in R6 only in R6C12, locked for NR4C1, clean-up: no 6 in R6C1

16. 19(4) cage at R4C5 = {1378/2368} (cannot be {1567} because 5,7 only in R5C3), no 5
16a. 7 of {1378} must be in R5C3 -> no 1 in R5C3
16b. 5 in C3 only in C789C3, CPE no 5 in R7C12

17. 20(4) cage at R7C8 contains 4 = {2468/3458/3467} (cannot be {1478} because 1,7 only in R7C8), no 1
17a. 5,7 of {3458/3467} must be in R7C8 -> no 3 in R7C8
17b. 1 in R7 only in R7C234, locked for NR4C1

18. 24(4) cage at R2C2 contains 9 = {2589/2679/3579} (cannot be {1689} which clashes with R23C3), no 1

19. 1 in R123 only in NR1C1 + NR1C4 + NR2C4 -> NR2C4 must contain 1 in 27(6) cage at R2C4 (step 12a) = {134568}, no 2,7, 1 locked for NR2C4
[Step 12 would have been a bit simpler if I’d spotted this back then.]

20. 7 in NR2C4 only in R4C234 + R5C23, 7 in NR3C6 only in R45C6
20a. Grouped X-Wing for 7 in R4C234 + R5C23 and R45C6, no other 7 in R4C45, clean-up: no 3 in R6C1
20b. 7 in NR5C7 only in R6C78, locked for C7, clean-up: no 3 in R5C1
[Alternatively Grouped Swordfish for 7 in R4C234 + R5C23, R45C6 and R5C7 + R6C78, no other 7 in R456, then 7 in R6C78, locked for NR5C7 …]
20c. R56C1 = [64], placed for NR4C1, clean-up: no 2 in R12C1 (step 7f)
20d. Killer pair 1,3 in R12C1 and R23C3, locked for NR1C1
20e. 6 in R1 only in R1C789, locked for NR1C7

21. R4C34 = {28/37}/[64], 22(4) cage at R4C6 (step 14) = {3478/4567} -> R4C78 = {38}/[46]
21a. Combined cage R4C3478 = {28}[46]/{37}[46]/[64]{38}, 4,6 locked for R4
21b. 19(4) cage at R4C5 (step 16) = {1378} (only remaining cage) -> R5C3 = 7, R4C5 + R5C45 = {138}, locked for NR4C5
21c. R4C6 = 7 (hidden single in C6), clean-up: no 3 in R4C34
21d. Combined cage R4C3478 = {28}[46]//[64]{38}, 8 locked for R4
21e. 19(4) cage = {1378}, 8 locked for R5
21f. Naked triple {269} in R6C345, locked for R6
21g. R6C26 = {38} (hidden pair in R6)
21h. R5C7 = 2 (hidden single in NR5C7), clean-up: no 3 in R9C6 (step 4)

22. 8(3) cage at R8C1 = {125} (only remaining combination, cannot be {134} = {13}4 which clashes with R1C1), locked for NR8C1, clean-up: no 4 in R8C5
22a. 3 in C6 only in R68C6, locked for NR5C7 -> R89C5 = [63], 3 placed for NR7C1
22b. R456C5 = [182], R5C4 = 3, R4C9 = 5, R5C8 = 1, R6C9 = 1, R3C5 = 5, R35C6 = [45], R5C2 = 4, placed for NR2C4, clean-up: no 6 in R4C3
22c. Naked pair {28} in R4C34, locked for R4 and NR2C4 -> R4C2 = 3, R6C2 = 8, placed for NR4C1, R6C3 = 6 (cage sum)
22d. R1C1 = 3 (hidden single in C1), R2C1 = 5 (cage sum)
22e. R68C6 = [38], R9C6 = 6, R7C7 = 5 (step 4), placed for NR7C7

23. 36(7) cage at R7C1 = {1245789} (only remaining combination), no 3

24. R9C7 = 1 (hidden single in NR7C7)

and the rest is naked singles, without using the nonets.
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Ed
PostPosted: Wed Dec 10, 2014 10:10 am 
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Andrew wrote:
Maybe the TJK Archive and my walkthroughs in it encouraged you to post this new one. I hope so!
Yes!! Loved reading through those again. Reminded me how good they are.
The way I got those early placements:
Quote:
if SS had chained them together it would have come up with a higher score than 1.25.
Maybe not! SS uses just a weighted step count so an extra step or two wouldn't make much of a difference. It's pretty dumb like that! Anyway, it does remember the hidden cages in the one step (though doesn't specifically mention one of them!!
Loved Andrew's WT! Simpler than my original way and lots of interesting steps. Missed Andrew's 12. & 12a which make a big difference. Have pinched that to make this a decent WT but still quite different to Andrew's solution. I started the same as Andrew but have used his nice alternative just to give it more prominence. Here goes. [Thanks Andrew for corrections!]

TJK 47
20 steps:
Preliminaries
Cage 3(2) at r1c6 - cells ={12}
Cage 13(2) at r2c8 - cells do not use 123
Cage 9(2) at r8c5 - cells do not use 9
Cage 10(2) at r5c1 - cells do not use 5
Cage 10(2) at r4c3 - cells do not use 5
Cage 8(3) at r8c1 - cells do not use 6789
Cage 41(8) at r1c7 - cells ={12356789}

1. 41(8)r1c7= {12356789} is missing 4. R2c8 sees all the 41(8) through Nr1c7 and c8 -> no 5,6,7,8,9 in r2c8(Common Peer Elimination, CPE)
1a. ->r2c8 = 4
1b. r3c8=9

2. "45" on Nr7c7: 4 outies r6789c6 = 26 (no 1)

3. "45" on c6: remembering h26(4)r6789c6, 3 innies r345c6 = 16
3a. "45" on c6789: 3 outies r2c4+r3c45 = 12
3b. note: those 6 cells in 3. and 3a sum to 28
3c. "45" on Nr1c1+Nr1c4: r2c8=4 ->8 remaining outies (the 6 from step 3b) + r2c5+r4c1 = 46 -> r2c5+r4c1 = 18
3d. -> r2c5=9, r4c1 = 9!

4. Hidden single 9 in Nr1c1 -> r1c2 = 9
4a. -> r12c1 = 8: no 4,8
4b. Hidden single 9 in 41(8)r1c7 which must have a 9 -> r5c9 = 9

5. "45" on Nr7c7, 1 innie r7c7+1 = 1 outie r9c6
5a. no 9 in r7c7

6. Hidden single 9 in r7 -> r7c6 = 9

7. Hidden single 9 in r8 -> r8c7 = 9

8. 3(2)r1c6 = {12}: both locked for c6 and Nr1c4

Pinched this key step from Andrew's WT. It makes a big difference.
9. h12(3)r2c4+r3c45 can't have both 1&2 because no 9
9a. -> 27(6)r2c4: {123678} blocked
9b. = {124578/134568/234567}
9c. must have 4 which is only in r3: 4 locked for r3

10. Hidden single 4 in Nr1c1 -> r1c3 = 4

11. "45" on Nr1c1: 2 remaining outies r1c45 = 12 = {57} only: both locked for r1 and Nr1c4 and 34(6)r1c3
11a. -> no 5,7 in r23c3
11b. r1c345+r2c5 = 25 -> r23c3 = 9 (cage sum) = {18/36}(no 2)

12. Law of Leftovers (LOL) on c789: 4 outies r1c456+r2c6 must exactly match 4 innies r56c78
12a. 4 outies = {1257} -> 4 innies r56c78 = {1257} only: all locked for Nr5c7

13. 25(4)r6c6 must have two of {3468} for r68c6 = {2689/3589/3679}(no 1,4)
13a. must have exactly two of 3,4,6,8 which must go in r68c7 -> no 3,6,8 in r7c7

14. "45" on Nr7c7: 1 innie r7c7 + 1 = 1 outie r9c6 -> r9c6 = 3,6,8

15. 4 & 7 in c6 only in r345c6 in h16(3) = {457} only: all locked for Nr3c6 [Alternatively, have a naked triple {368} in r689c6]

16. "45" on r789: 3 outies r6c456 = 14 = {239} only -> r6c6 = 3, r6c45 = [92] only permutation

17. "45" on r123: 2 remaining outies r4c9+r5c8 = 6 = {15} only: both locked for 41(8)r1c7

18. "45" on Nr1c7: 1 remaining outie r5c8 = 1 remaining innie r6c9
18a. ->r6c9 = (15)
[Alternatively, Andrew noticed r46c9 = {15} (hidden pair in Nr1c7)]

19. Naked triple {157} in r6c789: all locked for r6 and 15(4) -> r5c7 = 2

20. 10(2)r5c1 = {46} only valid combo: both locked for c1 and Nr4c1
20a. -> r6c23 = [86], r56c1 = [64]

on from there
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