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Ed
 Post subject: Texas Jigsaw Killer 41
PostPosted: Thu Apr 01, 2010 9:21 am 
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This is not a practical joke, just a really hard Texas Jigsaw Killer (TJK). :x Found a way to make big inroads early but there must be more conventional ways to do it.

Texas Jigsaw Killer 41

Many thanks to Børge for making the pics for me.
Image
Other pic options:
Ruud TJK#33 inspired:
Image


Image
Cages with cells in 3 jigsaw nonets:  pink
Cages with cells in 2 jigsaw nonets:  green and yellow
Cages with cells in 1 jigsaw nonet:   red, blue and grey



Image
Cages with cells in 3 jigsaw nonets:  lilac
Cages with cells in 2 jigsaw nonets:  green and yellow
Cages with cells in 1 jigsaw nonet:   red, blue and grey



Image


Ruud TJK#33 inspired:
Image


Image
Cages with cells in 3 jigsaw nonets:  pink
Cages with cells in 2 jigsaw nonets:  green and yellow
Cages with cells in 1 jigsaw nonet:   red, blue and grey



Image
Cages with cells in 3 jigsaw nonets:  lilac
Cages with cells in 2 jigsaw nonets:  green and yellow
Cages with cells in 1 jigsaw nonet:   red, blue and grey
code for SumoCue compatible solvers:
SumoCueV1=16J0+0J1=31J1+2J1+2J1+2J1=12J2=13J2+7J3+0J0=11J0=7J1+11J1+2J1+6J2+6J2=18J3+7J3+0J4+10J0=15J0=9J1=19J2=15J2+16J3+16J3=14J3=5J4=26J4+20J0+21J0+22J2+23J2=9J3+16J3+26J5+27J4+28J4+28J4+21J0+22J0+23J2+33J3=12J5=22J5=17J4+28J4=20J6+47J6=23J7=8J7+50J5+43J5+44J5+45J4+45J6+47J6+49J6+49J8+49J7+49J7+44J5+44J5=31J6+45J6+47J6+63J8=19J8+67J8=22J7+69J7=11J5+63J6+63J8+63J8+63J8+67J8+69J8+69J7+71J7+71J7
solution:
528749613
871632459
149583726

256397148
367125894
485916237

912874365
634258971
793461582
Cheers
Ed
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mhparker
PostPosted: Fri Apr 16, 2010 11:54 am 
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Wow, that was a difficult one! :shock: You certainly got me working hard there, Ed! Thanks for the puzzle, which proved to be much more interesting than it looked at first sight (TJK18 feeling again... :pallid: ).

Ed wrote:
... but there must be more conventional ways to do it.

Maybe. But as you know, I'm not exactly the most conventional of solvers ;) , so we'll have to wait for someone else (or a software solver) to do it "by the book".

Here's the WT. Found a couple of really interesting "inroads" (as Ed referred to them). I wonder whether there the same ones that he used?

Texas Jigsaw Killer 41 Walkthrough:
Nonet Layout:

122222334
112223344
511233444
551133446
555113466
557788666
577798866
777999886
799999888

Prelims

a) 11(2) at R2C2 = {29/38/47/56} (no 1)
b) 7(2) at R2C3 = {16/25/34} (no 7..9)
c) 15(2) at R3C3 = {69/78} (no 1..5)
d) 9(3) at R3C4 = {126/135/234} (no 7..9)
e) 19(3) at R3C5 and R8C5 = {289/379/469/478/568} (no 1)
f) 14(2) at R3C9 = {59/68} (no 1..4,7)
g) 5(2) at R4C1 = {14/23} (no 5..9)
h) 26(4) at R4C2 = {2789/3689/4589/4679/5678} (no 1)
i) 9(2) at R4C7 = {18/27/36/45} (no 9)
j) 12(2) at R5C8 = {39/48/57} (no 1,2,6)
k) 8(2) at R6C6 = {17/26/35} (no 4,8,9)
l) 11(3) at R8C9 = {128/137/146/236/245} (no 9)


1. 1 in N5 locked in R34567 for C1

2. 1 in N1 locked in R45C4 for C4
2a. 9(3) at R3C4 (prelim d) = {1..} = {126/135} (no 4)
2b. cleanup: no 6 in R2C3

3. Innies N2: R1C2+R3C4 = 7(2) = [16/25/43/52] (no 3,6..9 in R1C2)

4. Outies N1234: R3C1+R4C9 = 9(2) = [18/36/45] (no 2,7,9; no 5,6,8 in R3C1)
4a. cleanup: no 5 in R3C9

5. Innie/outie difference (IOD) N123: R3C1 = R1C8
5a. -> R1C8 = {134}

6. IOD N3: R5C5 = R1C8 + 1
6a. -> R5C5 = {245}
6b. 19(3) at R3C5 (prelim e) = {(2/4/5)..} = {289/469/478/568} (no 3)
6c. can only contain 1 of {245}, which must go in R5C5
6d. -> no 2,4,5 in R34C5

7. Innies N6: R4C9+R6C7+R8C9 = 11(3) = {128/146/236/245} (no 7)
(note: {137} blocked because none of these digits in R4C9)
7a. only 1 of 5,6,8, which must go in R4C9
7b. -> no 5,6,8 in R6C7+R8C9
7c. cleanup: no 1,2,3 in R6C6

Now for what's probably the most complicated move I've ever made in a walkthrough...

8a. Law of Leftovers (LoL) C89: R3456C7 (outies) = R189C8+R9C9 (innies)
8b. R3456C7 (being all peers of each other) cannot contain any repeats
8c. -> R189C8+R9C9 cannot contain any repeats either
8d. IOD C89: R3C7 = R8C8
8e. -> R3C7 maps to R8C8
8f. The remaining three outies R456C7 must map to R19C8+R9C9
8g. if R6C7 = R1C8, the same digit would be forced into R9C9**, which is impossible (see step 8c)
(**Reason: R12C9 could not contain the digit because they are peers of R1C8 (same cage),
R45678C9 could not contain the digit because they are peers of R6C7, and
R3C9 could not contain the digit because it has no candidates in common with R6C7)
8h. -> R6C7 must map to one of R9C89
8i. -> 11(3) at R8C9 and 11(3) at R4C9+R6C7+R8C9 (step 7) (which both share the cell R8C9)
must contain the same combination!
8j. -> R4C9 = R9C8 (the only non-peer of R4C9 in 11(3) at R8C9)
8k. -> R9C8 = {568}
8l. -> R6C7 = R9C9
8m. -> R9C9 = {123}
8n. -> the remaining two outies from step 8a, R45C7 (= 9(2)), must map to R19C8
8o. -> R19C8 must also sum to 9
8p. Outies C9: R179C8 = 15(3)
8q. -> R7C8 = 6 :dance: (from outie cage split using R19C8 = 9(2) from step 8o)
8r. -> R45C7 must contain 1 of {58} (step 8n)
8s. -> 9(2) at R45C7 = {18/45} (no 2,3,6,7)
8t. cleanup: no 8 in R3C9, no 6 in R3C7 (step 8e), no 3 in R3C1 (step 4), no 3 in R1C8 (step 5), no 4 in R5C5 (step 6)

Grid state after step 8:
Code:
.-----------------------.-----------------------------------------------.-----------.-----------------------.
| 23456789    1245      | 123456789   23456789    123456789   123456789 | 123456789 | 14          123456789 |
|           .-----------+-----------------------.           .-----------'           :-----------.           |
| 23456789  | 23456789  | 12345       23456     | 123456789 | 123456789   123456789 | 12345789  | 123456789 |
|           |           :-----------.-----------+-----------+-----------.-----------'           :-----------:
| 14        | 23456789  | 6789      | 2356      | 6789      | 123456789 | 12345789    12345789  | 69        |
:-----------+-----------:           |           |           |           :-----------.           |           |
| 1234      | 23456789  | 6789      | 12356     | 6789      | 123456789 | 1458      | 12345789  | 58        |
|           |           '-----------:           |           |           |           :-----------+-----------:
| 1234      | 23456789    23456789  | 12356     | 25        | 123456789 | 1458      | 345789    | 12345789  |
:-----------:           .-----------'-----------+-----------+-----------'-----------:           |           |
| 123456789 | 23456789  | 123456789   23456789  | 123456789 | 567         123       | 345789    | 12345789  |
|           '-----------:           .-----------'           '-----------------------+-----------'           |
| 12345789    12345789  | 12345789  | 2345789     12345789    12345789    12345789  | 6           12345789  |
:-----------.           |           :-----------.-----------------------.-----------'-----------.-----------:
| 23456789  | 123456789 | 123456789 | 23456789  | 23456789    23456789  | 123456789   12345789  | 1234      |
|           '-----------'-----------'           |           .-----------'           .-----------'           |
| 23456789    123456789   123456789   23456789  | 23456789  | 123456789   123456789 | 58          123       |
'-----------------------------------------------'-----------'-----------------------'-----------------------'

9. R45C1 (prelim g) = {23}, locked for C1 and N5
(Note: {14} blocked by R3C1)

10. R4C9+R6C7+R8C9 (step 7) and 11(3) at R8C9 (step 8i) = {128/245} (no 3)
10a. 2 locked in R89C9 for C9
10b. cleanup: no 5 in R6C6

11. 19(3) at R3C5 (step 6b) = {289/568} (no 7)
11a. 8 locked in R34C5 for C5 and N3

12. 8 in N2 locked in R1C346 for R1

13. Innies R89: R8C23 = 7(2) = {16/25/34} (no 7..9)
13a. -> R78C2 cannot sum to 7 (combo crossover clash (CCC))
13b. -> R67C1 (remaining two cells of 17(4) at R6C1) cannot sum to 10
13c. -> R3C1 (remaining innie cell in N5) cannot sum to 4 (= 45 - 10 - 5 - 26)
13d. -> no 4 in R3C1

14. Naked single (NS) at R3C1 = 1
14a. -> R4C9 = 8 (step 4), R1C8 = 1 (step 5), R5C5 = 2 (step 6)
14b. -> R3C9 = 6, R45C1 = [23], R9C8 = 8 (step 8j), R34C5 = [89] (step 11)
14c. -> R34C3 = [96] (prelim c, last permutation), R45C7 = [18] (step 8n)
14d. -> R6C67 = [62]
14e. -> R9C9 = 2 (step 8l)
14f. -> R8C9 = 1 (cage sum)
14g. cleanup: no 5 in R23C2, no 3 in R2C2, no 4 in R56C8, no 9 in R6C8, no 9 in R8C8 (step 8e)

15. Hidden single (HS) in C4 at R5C4 = 1
15a. -> split 8(2) at R34C4 = {35} (last combo), locked for C4
15b. cleanup: no 2,4 in R2C3, no 5 in R1C2 (step 3)

16. 4 in N1 locked in R12C1+R23C2
16a. -> no 4 in R1C2 (CPE)

17. NS at R1C2 = 2
17a. -> R3C4 = 5 (step 3)
17b. -> R4C4 = 3
17c. cleanup: no 8 in R2C2, no 5 in R8C8 (step 8e)

18. 15(3) at R3C6 = {357} (last combo)
18a. -> R3C6 = 3, R45C6 = {57}, locked for C6 and N3
18b. cleanup: no 3 in R8C8 (step 8e)

19. Naked pair (NP) at R2C47 = {46}, locked for R2

All singles and cage sums to end.

_________________
Cheers,
Mike
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Ed
PostPosted: Mon Apr 19, 2010 10:56 am 
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mhparker wrote:
as you know, I'm not exactly the most conventional of solvers ;) ... Found a couple of really interesting "inroads" (as Ed referred to them). I wonder whether there the same ones that he used?
Wow Mike! Step 8!! We both picked on exactly the same area to get into this one. I couldn't believe how many of the same elements we both used (I only missed :lol: ;) ).

So, here's my alternate step 8. Could only stretch it out to 8k. ;) [edit: went a bit too far with original ALT step]

Alt. step 8 & alt ending

8. "45" on c89: 1 outie r3c7 = 1 innie r8c8
8a. -> r1c8 "sees" all of n4 directly through c8, the 13(3) cage and it sees r3c7 indirectly since r8c8 = r3c7 EXCEPT r3c9, r45c7
8b. since r1c8 cannot equal r3c9 (no common candidates) -> r1c8 must be cloned in one cell of 9(2) at r45c7
8c. -> 9(2) must have 1,3,4 = {18/36/45}(no 2,7)

8d. "45" on n4: 2 outies r1c8 + r4c9 = 9
8e. since this outie cage and the clone celled cage (step 8b) have the same total -> r4c9 equals the other cell of 9(2) at r45c7
8f. since r4c9 sees r4c7 -> r4c9 = r5c7 = (568) (Clone CCC), r4c7 = (134)

8g. "45" on n34: 2 outies r4c9 + r5c5 = 10
8h. since r4c9 = r5c7 -> r5c57 = 10 = [28/46](no 5)
8i. -> no 5 in r4c9 -> no 4 in r1c8 (outies n4 = 9)
8j. no 4 in r4c7

8k. 14(2) at r34c9 = {68}: both locked for c9
Added from here
8l. no 3 in R3C1 (step 4)

9. 5(2)r4c1 = {23}, locked for c1 and n5 ({14} blocked by r3c1)

10. 19(3)r3c5 must have 2,4 = {289/469/478} ie, must have 6 or 8 in r34c5

11. 6 & 8 in r34: 14(2)r3c9 has 2 of; r34c5 has 1 of (step 10); 15(2)r3c3 has 1 of: -> both 6 & 8 locked for r34
11a. no 3,5 in r2c2

12. 9(3)r3c4, {126} must be [216] but this clashes with [1/6] in 9(2) at r4c7
12a. 9(3) = {135}: all locked for c4 and no 3 or 5 in r3c2
12b. no 2,4 in r2c3
12c. no 6,8 in r2c2

13. 3 in n1 only in r45c4 -> no 3 in r3c4
13a. r3c4 = 5
13b. no 2 in r2c4

14. 1 innie n2: r1c2 = 2
Cracked now.


Conventional walkthrough welcome!

Cheers
Ed
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Andrew
PostPosted: Mon Dec 23, 2013 10:59 pm 
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An interesting puzzle, once one found a way in. Loved Ed’s step 8. I found another way in, without needing that step. Must admit I didn't work through Mike's step 8, which looked extremely complicated.

Ed wrote:
Conventional walkthrough welcome!
Maybe this is it? I think the main difference from Mike's and Ed's solving paths is that they used LoL for C89; I used LoL for C789.

The SSv3.6.1 score of 1.80 looks far too high. Maybe SS couldn't find my step 10. Mike's step 4?

Here is my walkthrough for TJK 41:
My walkthrough has been simplified while checking it, before posting the archive entry for TJK 41.

Prelims

a) R23C2 = {29/38/47/56}, no 1
b) R2C34 = {16/25/34}, no 7,8,9
c) R34C3 = {69/78}
d) R34C9 = {59/68}
e) R45C1 = {14/23}
f) R45C7 = {18/27/36/45}, no 9
g) R56C8 = {39/48/57}, no 1,2,6
h) R6C67 = {17/26/35}, no 4,8,9
i) 9(3) cage at R3C4 = {126/135/234}, no 7,8,9
j) 19(3) cage at R3C5 = {289/379/469/478/568}, no 1
k) 19(3) cage at R8C5 = {289/379/469/478/568}, no 1
l) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9
m) 26(4) cage at R4C2 = {2789/3689/4589/4679/5678}, no 1

1. 1 in NR3C1 only in R34567C1, locked for C1
1a. 1 in NR1C1 only in R45C4, locked for C4, clean-up: no 6 in R2C3
1b. 9(3) cage at R3C4 contains 1 = {126/135}, no 4

2. 45 rule on R12 2 outies R3C12 = 1 innie R2C8
2a. Min R3C12 = 3 -> min R2C8 = 3
2b. Max R3C12 = 9, no 8,9 in R3C1, no 9 in R3C2, clean-up: no 2 in R2C2

3. 45 rule on R89 2 innies R8C23 = 7 = {16/25/34}, no 7,8,9

4. 45 rule on C1234 3(2+1) innies R1C34 + R7C4 = 23
4a. Max R1C34 = 17 -> min R7C4 = 6
4b. Max R17C4 = 17 -> min R1C3 = 6
4c. Max R1C3 + R7C4 = 18 -> min R1C4 = 5

5. 45 rule on NR1C2 2 innies R1C2 + R3C4 = 7 = [16/25/43/52], R1C2 = {1245}

6. 45 rule on NR1C9 1 innie R3C9 = 1 outie R1C8 + 5 -> R3C9 = {689}, R1C8 = {134}, clean-up: no 9 in R4C9

7. 45 rule on NR1C7 1 outie R5C5 = 1 innie R1C8 + 1 -> R5C5 = {245}

8. 45 rule on NR4C9 3 innies R4C9 + R6C7 + R8C9 = 11 = {128/146/236/245} (cannot be {137} because R4C9 only contains 5,6,8), no 7, clean-up: no 1 in R6C6
8a. R4C9 = {568} -> no 5,6,8 in R6C7 + R8C9, clean-up: no 2,3 in R6C6

9. Law of Leftovers (LoL) for C789 three outies R6C56 + R7C6 must exactly equal three innies R1C78 + R2C7
9a. R6C6 = {567} -> R12C7 must contain at least one of 5,6,7
9b. 12(3) cage at R1C7 = {147/156/237/246/345} (cannot be {129/138} which don’t contain any of 5,6,7), no 8,9
9c. LoL for C789 no 8,9 in R1C78 + R2C7 -> no 8,9 in R6C5 + R7C6

10. 45 rule on NR1C1 + NR1C2 + NR1C7 + NR1C9 1 innie R3C9 = 1 outie R3C1 + 5 -> R3C1 = {134}

11. 45 rule on NR3C1 2 outies R78C2 = 1 innie R3C1 + 3
11a. Max R3C1 = 4 -> max R78C2 = 7, no 7,8,9 in R7C2
11b. R8C23 = 7 (step 3) -> max R78C2 = 6 (cannot be 7 which clashes with R8C23, CCC), no 6 in R78C2, clean-up: no 1 in R8C3 (step 3)
11c. Max R78C2 = 6 -> max R3C1 = 3, clean-up: no 9 in R3C9 (step 10), no 4 in R1C8 (step 6), no 5 in R4C9, no 5 in R5C5 (step 7)
11d. Killer pair 1,3 in R3C1 and R45C1, locked for C1 and NR3C1
11e. Naked pair {68} in R34C9, locked for C9
11f. Naked pair {68} in R34C9, CPE no 6,8 in R4C78 using NR1C9, clean-up: no 1,3 in R5C7

12. 19(3) cage at R3C5 = {289/469/478} (cannot be {379/568} because R5C5 only contains 2,4), no 3,5
12a. R5C5 = {24} -> no 2,4 in R34C5

13. 13(3) cage at R1C8 = {139/157} (cannot be {247} because R1C8 only contains 1,3), no 2,4
13a. 13(3) cage = {139/157}, CPE no 1 in R34C8 using NR1C9

14. 19(3) cage at R3C5 (step 12) = {289/469/478}
14a. 19(3) cage at R8C5 = {289/379/469/478/568}
14b. 2,3,5 of {289/379/568} must be in R89C5 (R89C5 cannot be {89/79/68} which clash with 19(3) cage at R3C5), no 2,3,5 in R8C6

15. R34C3 contains one of 6,8, 19(3) cage at R3C5 contains one of 6,8 in R34, naked pair {68} in R34C9 -> double caged X-Wing for 6,8 in R34C3, 19(3) cage and R34C9, no other 6,8 in R34, clean-up: no 1 in R1C2 (step 5), no 3,5 in R2C2

16. 9(3) cage at R3C4 (step 1b) = {126/135}
16a. 2 of {126} must be in R3C4 -> no 2 in R45C4

17. 45 rule on C89 1 outie R3C7 = 1 innie R8C8, no 6,8 in R8C8

18. Deleted. Unnecessary after I found steps 19 and 20. This was analysis of 22(4) cage at R5C9 looking at interactions with R4C9 + R6C7 + R8C9 and with 13(3) cage at R1C8.

[I should have spotted this a lot earlier, and the next step after step 15. However they are much more powerful now …]
19. 16(4) cage at R1C1 must contain one of 6,7,8,9 in R12C1 -> killer quad 6,7,8,9 in 16(4) cage, R23C2 and R34C3, locked for NR1
19a. 9(3) cage at R3C4 (step 1b) = {135} (only remaining combination), locked for C4, clean-up: no 5 in R1C2 (step 5), no 2,4 in R2C3

20. 3 in NR1C1 only in R3C2 + R45C4, CPE no 3 in R3C4 -> R3C4 = 5, R1C2 = 2 (step 5), both placed for NR1C2, naked pair {13} in R45C4, locked for NR1C1, clean-up: no 6,8,9 in R2C2, no 5 in R8C3 (step 3)
[Cracked. The rest is fairly straightforward.]

21. Naked pair {47} in R23C2, locked for C2 and NR1C1 -> R5C5 = 2, R1C8 = 1 (step 7), placed for NR1C7, R3C9 = 6 (step 6), placed for NR1C9, R4C9 = 8, placed for NR4C9, R3C1 = 1 (step 10)
21a. R4C7 = 1 (hidden single in NR1C9), R5C7 = 8, placed for NR1C9, R45C4 = [31]
21b. R1C2 = 2, R3C1 = 1 -> R12C1 = 13 = {58}, locked for C1 and NR1C1 -> R34C3 = [96]
21c. R5C5 = 2 -> R34C5 = 17 = [89], 9 placed for NR1C7, R4C2 = 5
21d. Clean-ups: no 4 in R45C1, no 4 in R56C8, no 7 in R6C6, no 1 in R8C2, no 2,3 in R8C3 (both step 3)

22. R78C2 = [13], R8C3 = 4, all placed for NR6C3

23. 26(4) cage at R4C2 = {5678} (only remaining combination) -> R5C3 = 7, R56C2 = [68], 6,7 placed for NR3C1, R1C3 = 8, R12C1 = [58], R9C2 = 9, placed for NR7C5, clean-up: no 5 in R6C8

24. R45C1 = [23], R89C1 = {67}, locked for NR7C3 and 31(6) cage at R8C1, no 6,7 in R89C4
24a. Naked pair {25} in R67C3, locked for C3 and 20(4) cage at R6C3 -> R6C4 = 9, R7C4 = 8, R89C4 = [24], both placed for NR7C5, R2C4 = 6, placed for NR1C2, R2C3 = 1, R9C3 = 3, placed for NR7C5, R1C4 = 7
24b. Naked pair {34} in R12C5, locked for C5 and 31(5) cage at R1C3 -> R1C6 = 9, R1C9 = 3, placed for NR1C9, R2C9 = 9 (cage sum), R12C5 = [43]
24c. R1C7 = 6, R2C67 = 6 = {24}, locked for R2 and NR1C7
24d. 15(3) cage at R3C6 = [375], R5C8 = 9, R6C8 = 3

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