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PostPosted: Tue Oct 21, 2014 11:14 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 44 Practice by Ed (September 2010) here

Puzzle Diagrams:
Image
Image
Many thanks to Børge for the pics. Take your pick!

Image
More Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration:
Image


Image
Cages with cells in 3 jigsaw nonets:  pink and orange
Cages with cells in 2 jigsaw nonets: green and yellow
Cages with cells in 1 jigsaw nonet: red, blue and grey
Code: Select, Copy & Paste into solver:
SumoCueV1=24J0=38J0+1J1+1J1=15J1+4J1=15J2+6J2+6J2+0J0=13J0+10J0+1J1+4J1=22J3+14J2+14J2=12J2+0J0+10J0+1J1+1J1=35J1+14J3=16J4=9J2+17J2+0J0=12J0+1J5=10J5+22J3+22J3+24J4+24J4+25J2=13J5+28J5+1J5+30J5+22J3=7J4=43J4=15J4+25J4+36J6=14J5+46J5+22J3+22J3+41J4+42J4+43J7=21J7=6J6+36J6+46J5=25J3+22J8+42J8+42J8=13J7+53J7+54J6+57J6+57J6+57J3=14J8+42J8+61J7+61J7+53J7=13J6+72J6+72J6+67J8+67J8+42J8+42J8+42J7+53J7
Solution:
+-------+-------+-------+
| 2 3 9 | 4 7 5 | 8 1 6 |
| 6 1 4 | 8 3 7 | 9 2 5 |
| 9 8 1 | 2 6 4 | 5 3 7 |
+-------+-------+-------+
| 7 5 6 | 9 1 2 | 3 8 4 |
| 3 7 5 | 1 8 6 | 4 9 2 |
| 8 4 2 | 5 9 1 | 7 6 3 |
+-------+-------+-------+
| 5 2 8 | 3 4 9 | 6 7 1 |
| 1 9 7 | 6 5 3 | 2 4 8 |
| 4 6 3 | 7 2 8 | 1 5 9 |
+-------+-------+-------+

Quote:
Ed: This is a return to lots of big cages, really hard but with a short way to crack it. Perfect! A warning though, more conventional ways may be very tough. Put on your creative hat! A practice version with the same cage pattern is below. I didn't find it easy either. It helped me realize some of the fun tricks with this nonet and cage pattern. Really glad JSudoku finally spat out a really hard one that forces some of them to be used.

Andrew (in 2013): I tried the TJK 44 Practice version first.
It seemed harder than the SS(v3.6.1) score of 1.25, but SS scores for easier and moderately difficult TJKs often seem a bit low.

Andrew's walkthrough:
I tried the TJK 44 Practice version first.

It seemed harder than the SS(v3.6.1) score of 1.25, but SS scores for easier and moderately difficult TJKs often seem a bit low.

Prelims

a) R23C9 = {39/48/57}, no 1,2,6
b) R45C2 = {39/48/57}, no 1,2,6
c) R45C4 = {19/28/37/46}, no 5
d) R56C6 = {16/25/34}, no 7,8,9
d) R56C8 = {69/78}
e) R78C1 = {15/24}
f) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
g) 38(8) cage at R1C2 = {12345689}, no 7
h) 43(8) cage at R5C7 = {13456789}, no 2

1. 45 rule on NR1C1 2 innies R14C2 = 8 = [17/35/53], R5C2 = [579]
1a. 13(3) cage at R2C2 = {148/238/247/256/346} (cannot be {139/157} which clash with R14C2), no 9
1b. 9 in NR1C1 only in 24(4) cage at R1C1, locked for C1

2. 45 rule on NR6C8 2 innies R69C8 = 11 = [65/74/83], clean-up: no 6 in R5C8

[Just high enough SS score to use Law of Leftovers(LoL) very early, particularly as there are two obvious ones to use and also that this puzzle was set up to be a practice version for the main puzzle.]

3. LoL on C123 two outies R45C4 must exactly equal two innies R13C3
3a. No 5 in R45C4 -> no 5 in R13C3
3b. No 7 in R13C3 -> no 7 in R45C4, clean-up: no 3 in R45C4
3c. R45C4 = {19/28/46} -> R13C3 = {19/28/46}, no 3

4. LoL on C789 two outies R56C6 must exactly equal two innies R79C7
4a. No 2 in R79C7 -> no 2 in R56C6, clean-up: no 5 in R56C6
4b. R56C6 = {16/34} -> R79C7 = {16/34}

5. 45 rule on NR6C1 4 innies R6C1 + R7C2 + R8C23 = 26 = {2789/3689/4679/5678} (cannot be {4589} which clashes with R78C1), no 1

6. 45 rule on NR6C1 2 innies R8C23 = 1 outie R5C1 + 13
6a. Max R8C23 = 17 -> max R5C1 = 4
6b. Min R8C23 = 14, no 2,3,4 in R8C23
6c. R8C23 cannot be {59} (from combinations in R6C1 + R7C2 + R8C23, step 5), no 5 in R8C23
[Step 6c can be skipped, since these eliminations would be made in step 9c.]

7. 45 rule on C1234 2 innies R69C4 = 12 = {39/48/57}, no 1,2,6
7a. 2 in NR7C5 only in R789C5, locked for C5

8. 45 rule on C6789 2 innies R14C6 = 7 = {16/25/34}, no 7,8,9
8a. 7 in NR1C3 only in R123C5, locked for C5

9. 45 rule on C1 1 innie R9C1 = 1 outie R7C2 + 2, no 7,8,9 in R7C2, no 1,2,3 in R9C1
9a. 13(3) cage at R9C1 = {157/238/247/346} (cannot be {139} because no 1,3,9 in R9C1, cannot be {148/256} which clash with R78C1), no 9
9b. 9 in NR6C1 only in R8C23, locked for R8 and 25(4) cage at R7C4, no 9 in R7C4
9c. R6C1 + R7C2 + R8C23 (step 5) contains 9 = {2789/3689/4679}, no 5, clean-up: no 7 in R9C1
9d. 2 of {2789} must be in R7C2 -> no 2 in R6C1
9e. 13(3) cage at R5C1 = {238/247/346} (cannot be {148} which clashes with R78C1), no 1

10. 45 rule on C9 1 innie R1C9 = 1 outie R3C8 + 3, no 1,2,3 in R1C9

11. 45 rule on C1 3 innies R569C1 = 15 = {267/348} (cannot be {258/456} which clashes with R78C1, cannot be {357} because 13(3) cage at R5C1 cannot be [373]), no 5, clean-up: no 3 in R7C2 (step 9)
11a. 6 of {267} must be in R9C1 -> no 6 in R6C1

12. R78C1 = {15} (cannot be {24} which clashes with R569C1), locked for C1 and NR6C1

13. 13(3) cage at R9C1 (step 9a) = {238/346} (cannot be {247} = 4{27} which clashes with R7C2 + R9C1 = [24], innie-outie difference clash), no 7, 3 locked for R9 and N7, clean-up: no 9 in R6C4 (step 7), no 8 in R6C8 (step 2), no 7 in R5C8, no 4 in R7C7 (step 4b)
13a. 8 of {238} must be in R9C1 -> no 8 in R9C23
13b. R569C1 (step 11) = {267/348}
13c. 2,3 only in R5C1 -> R5C1 = {23}

14. 9 in C1 only in 24(4) cage at R1C1 = {2679/3489}
14a. Killer pair 3,7 in 24(4) cage and R14C2, locked for NR1C1

15. 45 rule on NR1C1 + NR1C3 + NR4C3 2 innies R3C5 + R5C1 = 9, R5C1 = {23} -> R3C5 = {67}

16. 45 rule on NR3C7 + NR6C8 + NR7C5 2(1+1) innies R5C9 + R7C5 = 6 = {15/24}/[33], no 6,8,9

17. 14(3) cage at R8C5 = {158/167/239/248/257/347} (cannot be {149/356} which clash with R79C7)
17a. Hidden killer triple 7,8,9 in 14(3) cage and R789C6 for NR7C5, 14(3) cage contains one of 7,8,9 -> R789C6 must contain two of 7,8,9
17b. Hidden killer triple 7,8,9 in R23C6 and R789C6 for C6, R789C6 contains two of 7,8,9 -> R23C6 must contain one of 7,8,9
17c. 45 rule on NR1C7 3(2+1) outies R23C6 + R5C9 = 13
17d. R23C6 contain one of 7,8,9 -> max (other cell in R23C6 + R5C9) = 6, no 6 in R23C6

18. Consider combinations for 13(3) cage at R9C1 (step 13) = {238/346}
13(3) cage = {238}, R9C1 = 8
or 13(3) cage = {346}, locked for NR6C1, R7C2 = 2, R5C1 = 3, R6C1 = 8 (cage sum)
-> 8 in R69C1, locked for C1 and NR6C1
18a. 24(4) cage at R1C1 (step 14) = {2679} (only remaining combination), locked for C1 and NR1C1 -> R5C1 = 3, placed for NR4C3, R69C1 = {48}, locked for NR6C1, R3C5 = 6 (step 15), placed for NR1C3, clean-up: no 1 in R1C2 (step 1), no 4 in R13C3 (step 3c), no 1 in R14C6 (step 8), no 9 in R1C9 (step 10), no 5 in R5C2, no 4 in R6C6, no 3 in R7C5 (step 16)
18b. Naked pair {35} in R14C2, locked for C2 and NR1C1
18c. Naked pair {26} in R79C2, locked for C2 and NR6C1 -> R9C3 = 3
[Cracked. The rest is fairly straightforward.]

19. Naked pair {79} in R8C23, 7 locked for R8 and 25(4) cage at R7C4, no 7 in R7C4
19a. R8C23 = {79} = 16 -> R78C4 = 9 = {18/36/45}, no 2

20. 6 in 38(8) cage at R1C2 only in R45C3, locked for C3 and NR4C3, clean-up: no 4 in R45C4

21. 7 in C5 only in 15(3) cage at R1C5 = {357} (only remaining combination), locked for NR1C3
21a. Naked pair {35} in R1C26, locked for R1 -> R1C5 = 7, clean-up: no 2,4 in R3C8 (step 10)

22. 38(8) cage at R1C2 = {12345689} -> R1C2 = 3, R4C2 = 5, R5C2 = 7, placed for NR4C3, R8C23 = [97], R1C6 = 5, R2C5 = 3, clean-up: no 9 in R3C9
22a. 38(8) cage = {12345689} -> R5C3 = 5, R4C3 = 6, clean-up: no 1 in R7C5 (step 16)
22b. 38(8) cage = {12345689}, 4 locked for C4, clean-up: no 8 in R69C4 (step 7), no 5 in R78C4 (step 19a)

23. R69C4 = {57} (hidden pair in C4)
23a. R78C4 = {36} (hidden pair in C4), 3 locked for NR2C6

24. 35(7) cage at R3C5 = {1245689} (only remaining combination), no 7 -> R6C4 = 5, R9C4 = 7, placed for NR7C5, clean-up: no 1 in R5C9 (step 16)

25. 5 in C5 only in 14(3) cage at R8C5 = {257} -> R89C5 = {25}, locked for C5 -> R7C5 = 4, placed for NR7C5, R5C9 = 2 (step 16), placed for NR3C7, clean-up: no 8 in R4C4, no 3 in R7C7 (step 4b)
25a. Naked pair {16} in R79C7, locked for C7 and NR7C5
25b. Naked triple {389} in R789C6, locked for C6 and 43(8) cage at R5C7 -> R56C7 = [47], both placed for NR3C7, R69C8 = [65], both placed for NR6C8, R5C8 = 9, placed for NR3C7, R89C5 = [52], R9C2 = 6, R9C1 = 4 (cage sum), R6C1 = 8, R7C2 = 2, R78C1 = [51], R79C7 = [61], R78C4 = [36], clean-up: no 1 in R4C4
25c. R56C6 = [61] -> R4C6 = 2, R4C4 = 9, R5C4 = 1, R456C5 = [189], R6C23 = [42], R7C3 = 8 (cage sum), R789C6 = [938]

26. R5C9 = 2 -> R3C8 + R4C9 = 7 = [34], R1C9 = 6 (step 10), clean-up: no 8,9 in R23C9

27. R23C6 = {47} = 11 -> R2C78 = 11 = [92], placed for NR1C7 -> R1C7 = 8, R1C8 = 1 (cage sum)

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


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PostPosted: Tue Oct 21, 2014 11:26 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 44 Main by Ed (September 2010) here

Puzzle Diagram:
Image
Many thanks to Børge for the pic!

Image
More Børge's images with udosuk Style Killer Cages and Ruud TJK#33 inspiration:
Image


Image
Cages with cells in 3 jigsaw nonets:  lilac and orange
Cages with cells in 2 jigsaw nonets: green and yellow
Cages with cells in 1 jigsaw nonet: red, blue and grey
Code: Select, Copy & Paste into solver:
SumoCueV1=19J0=37J0+1J1+1J1=13J1+4J1=14J2+6J2+6J2+0J0=13J0+10J0+1J1+4J1=20J3+14J2+14J2=13J2+0J0+10J0+1J1+1J1=40J1+14J3=19J4=9J2+17J2+0J0=17J0+1J5=8J5+22J3+22J3+24J4+24J4+25J2=13J5+28J5+1J5+30J5+22J3=10J4=41J4=7J4+25J4+36J6=15J5+46J5+22J3+22J3+41J4+42J4+43J7=22J7=12J6+36J6+46J5=17J3+22J8+42J8+42J8=15J7+53J7+54J6+57J6+57J6+57J3=15J8+42J8+61J7+61J7+53J7=16J6+72J6+72J6+67J8+67J8+42J8+42J8+42J7+53J7
Solution:
+-------+-------+-------+
| 1 5 6 | 7 8 4 | 3 9 2 |
| 9 2 7 | 3 1 5 | 4 8 6 |
| 6 4 2 | 9 5 3 | 8 1 7 |
+-------+-------+-------+
| 3 8 1 | 2 9 6 | 7 4 5 |
| 8 9 4 | 6 7 1 | 5 2 3 |
| 4 7 3 | 8 2 9 | 6 5 1 |
+-------+-------+-------+
| 7 1 5 | 4 3 2 | 9 6 8 |
| 5 3 9 | 1 6 8 | 2 7 4 |
| 2 6 8 | 5 4 7 | 1 3 9 |
+-------+-------+-------+

Quote:
Ed: This is a return to lots of big cages, really hard but with a short way to crack it. Perfect! A warning though, more conventional ways may be very tough. Put on your creative hat! A practice version with the same cage pattern is below. I didn't find it easy either. It helped me realize some of the fun tricks with this nonet and cage pattern. Really glad JSudoku finally spat out a really hard one that forces some of them to be used.

Andrew (in 2013): I'll give a few comments from PM exchanges with Ed, before I post my walkthrough for the main version of TJK 44.

Andrew wrote:
If that's the practice version, the main one is going to be really hard.
Ed wrote:
A practice version with the same cage pattern is below. I didn't find it easy either.
Andrew wrote:
At least that's some consolation for me. ;)


Ed wrote:
Put on your creative hat!
Andrew wrote:
Maybe I wasn't creative enough.


And later, when I managed to make some progress with the main version
Andrew wrote:
I've managed to see further into that LoL for C1234. It looks interesting and useful. I'd be surprised if SS managed to find what I think I've just found. Almost a "one trick pony", but I had to use the breakthrough step several ways to fully crack the puzzle.
Ed wrote:
:applause: Looks like you had the same creative hat on as I did. Great that you found it. I sure enjoyed it. I saw it slightly differently by the looks. Please post your way on the forum not the archive - deserves lots of attention.


Ed wrote:
Put on your creative hat!
I certainly needed to do that!

This puzzle turned out to be almost a “one trick pony”, but it took me a long time to spot the key step; then it needed to be used in several different ways. Nice puzzle, Ed!

The practice version certainly helped in getting used to the cage patterns, both jigsaw and killer, but I'm not sure whether the key step for the main version can be used for the practice version; I found it was definitely an extra for the main version.

Andrew's walkthrough:
Ed wrote:
Put on your creative hat!
I certainly needed to do that!

This puzzle turned out to be almost a “one trick pony”, but it took me a long time to spot the key step; then it needed to be used in several different ways. Nice puzzle, Ed!

Prelims

a) R23C9 = {49/58/67}, no 1,2,3
b) R45C2 = {89}
c) R45C4 = {17/26/35}, no 4,8,9
d) R56C6 = {19/28/37/46}, no 5
d) R56C8 = {16/25/34}, no 7,8,9
e) R78C1 = {39/48/57}, no 1,2,6
f) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
g) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
h) 37(8) cage at R1C2 = {12345679}, no 8
i) 41(8) cage at R5C7 = {12356789}, no 4

1. Naked pair {89} in R45C2, locked for C2
1a. 45 rule on NR1C1 2 innies R14C2 = 13 = [49/58]

2. 45 rule on NR6C8 2 innies R69C8 = 8 = [17]/{26/35}, no 4,8,9, no 1 in R9C8, clean-up: no 3 in R5C8

3. 45 rule on C1234 2 innies R69C4 = 13 = {49/58/67}, no 1,2,3

4. 45 rule on C6789 2 innies R14C6 = 10 = {19/28/37/46}, no 5

5. Law of Leftovers (LoL) for C123 two outies R45C4 must exactly equal two innies R13C3
5a. R45C4 = {17/26/35} -> R13C3 = {17/26/35}, no 4,9

6. LoL for C789 two outies R56C6 must exactly equal two innies R79C7
6a. No 4 in R79C7 -> no 4 in R56C6, clean-up: no 6 in R56C6
6b. R56C6 = {19/28/37} -> R79C7 = {19/28/37}, no 5,6

7. 45 rule on NR1C1 + NR1C3 + NR4C3 2 innies R3C5 + R5C1 = 13 = {49/58/67}, no 1,2,3

8. 45 rule on NR3C7 + NR6C8 + NR7C5 2(1+1) innies R5C9 + R7C5 = 6 = {15/24}/[33], no 6,7,8,9

9. 45 rule on C1 1 innie R9C1 = 1 outie R7C2 + 1, no 1,9 in R9C1

10. 45 rule on C9 1 innie R1C9 = 1 outie R3C8 + 1, no 1,8,9 in R1C9

11. 45 rule on C9 3 innies R145C9 = 10 = {127/136/145/235}
11a. 4 of {145} must be in R1C9 (R45C9 cannot be {14} because 9(3) cage at R3C8 cannot be 4{14}), no 4 in R45C9, clean-up: no 2 in R7C5 (step 8)

12. 45 rule on NR1C1 + NR1C3 + NR4C3 + NR6C1 2 outies R78C4 = 1 innie R3C5
12a. Max R78C4 = 9, no 9 in R78C4
[45 rule on NR6C1 3(1+2) outies R5C1 + R78C4 = 13, min R5C1 = 4 -> max R78C4 = 9, no 9 in R78C4 is simpler.]

[However my original version of step 12 helps with this step …]
13. 40(7) cage at R3C5 = {1456789/2356789}
13a. 5 in 40(7) cage only in R3C5 => R78C4 = {14/23} (step 12) or R456C5 + R6C4, locked for NR2C6 or in R7C5 -> no 5 in R7C4 (a sort of killer locking-out cages)

14. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4 -> there must be a hidden 13(3) cage in R6789C4 but R69C4 = 13 (step 3) -> R78C4 + one of R69C4 must form a hidden 13(3) cage
14a. Looking at this LoL the other way round, R69C4 = 13, two cells of the 13(3) cage cannot total 13 -> R3C5 + one cell of the 13(3) cage must total 13
14b. 8 in NR1C3 only in 13(3) cage = {148/238} => R3C5 = {59} (step 14a) or 8 in R3C5 -> R3C5 = {589}, R5C1 = {458} (step 7)

15. 40(7) cage at R3C5 = {1456789/2356789}, 6,7 locked for NR2C6, no 6,7 in R23C6 + R78C4
15a. 8,9 in 40(7) cage only in R3C5 or R4C56 + R5C5 + R6C45, locked for NR3C7 -> no 8,9 in R3C6 (CPE using NR2C6)

16. R69C4 = 13 (step 3)
16a. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4, 13(3) cage cannot contain both of 6,7 -> no 6,7 in 13(3) cage, no 6,7 in R69C4, clean-up: no 3,4 in R4C6 (step 4)
16b. 6,7 in NR1C3 only in R13C3 + R123C4, locked for 37(8) cage at R1C1, no 6,7 in R45C3

17. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4
17a. R78C4 = R3C5 (step 12)
17b. R78C4 cannot total 8 (because 13(3) cage cannot contain both of 3,5 and 8 would be in R3C5 if R78C4 totalled 8) -> R3C5 = {59}, clean-up: no 5 in R5C1 (step 7)
17c. 8 in 40(7) cage only in R4C56 + R5C5 + R6C45, locked for NR2C6, no 8 in R2C6 + R78C4

18. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4
18a. 8 in NR1C3 only in 13(3) cage at R1C5 = {148/238}, no 5,9
18b. R6789C4 contains one of 8,9, 13(3) cage contains 8 -> no 9 in R3C5 -> R3C5 = 5, placed for NR1C3, R5C1 = 8 (step 7), R5C2 = 9, both placed for NR4C3, R4C2 = 8, R1C2 = 5 (step 1a), both placed for NR1C1, clean-up: no 3 in R13C3 (step 5a), no 2 in R1C6 (step 4), no 6 in R1C9 (step 10), no 8 in R2C9, no 4 in R3C8 (step 10), no 1 in R4C6 (step 4), no 1 in R5C9 (step 8), no 1,2 in R6C6, no 4 in R78C1, no 7 in R7C2 (step 9), no 6 in R9C1 (step 9), no 8 in R9C4 (step 3)
18c. LoL for C123 (step 5a) R13C3 = {17/26} -> R45C4 = {17/26}
18d. R78C4 = R3C5 (step 12), R3C5 = 5 -> R78C4 = {14/23}
[Cracked. The rest is fairly straightforward.]

19. R6C4 = 8 (hidden single in C4), R9C4 = 5 (step 3), placed for NR7C5, clean-up: no 2 in R5C6, no 3 in R6C8 (step 2), no 4 in R5C8, no 4 in R7C2 (step 9)

20. Killer pair 1,2 in R45C4 and R78C4, locked for C4
20a. 1,2 in 37(8) cage at R1C3 only in R1345C3, locked for C3

21. 45 rule on C1 2 remaining innies R69C1 = 6 = {24} (cannot be {15} because 1,5 only in R6C1), locked for C1 and NR6C1, R7C2 = {13} (step 9)
21a. 19(4) cage at R1C1 = {1369} (only remaining combination), locked for C1 and NR1C1
21b. Naked pair {57} in R78C1, locked for NR6C1
21c. Naked triple {136} in R789C2, locked for C2 and NR6C1

22. 5 in NR4C3 only in 15(3) cage at R6C2 = {357/456}, no 2
22a. R6C2 = {47} -> no 4,7 in R67C3

23. R78C4 (step 18d) = {14/23} = 5 -> R8C23 = 12 = [39], R7C2 = 1, R9C23 = [68], R9C1 = 2 (cage sum), R6C1 = 4, R6C2 = 7, placed for NR4C3, clean-up: no 1 in R45C4, no 3 in R5C6, no 2,6 in R6C8 (step 2), no 1,5 in R5C8
23a. Naked pair {26} in R45C4, locked for NR4C3 and C4 -> R78C4 = [41], both placed for NR2C6, R7C5 = 3, placed for NR7C5, R67C3 = [35], R78C1 = [75], R5C9 = 3 (step 8), placed for NR3C7, clean-up: no 7 in R56C6
23b. R56C6 = [19], placed for NR3C7, R9C6 = 7, placed for NR7C5, R9C8 = 3, R6C8 = 5 (step 8), R5C8 = 2, placed for NR3C7

24. R2C3 = 7 (hidden single in NR1C1), clean-up: no 6 in R3C9
24a. R13C3 = {26} (hidden pair in C3), locked for NR1C3
24b. Naked triple {379} in R123C4, locked for NR1C3

25. R45C4 = [26], R4C6 = 6, placed for NR2C6, R6C5 = 2, placed for NR2C6
25a. R23C6 = [53] = 8 -> R2C78 = 12 = {48}, locked for R2 and NR1C7, clean-up: no 9 in R23C9
25b. R23C9 = [67], placed for NR1C7

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

The practice version certainly helped in getting used to the cage patterns, both jigsaw and killer, but I'm not sure whether the key step for the main version can be used for the practice version; I found it was definitely an extra for the main version.


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PostPosted: Wed Oct 22, 2014 1:42 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Pinata Killer Sudoku 20 (aka Texas Jigsaw Killer 45) by Pinata (December 2012) here

Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=18J0=27J0+1J0+1J1=31J1+4J1+4J2+4J2+4J2+0J0+0J0+0J1+1J1+1J3=17J1+14J1=18J2+16J2=18J4+18J0+18J1=7J3=14J3+14J3+14J1+16J2=7J5=29J4+27J0+27J0+21J0+22J3+22J2=15J2+33J2+26J5=17J4+36J4+27J4=13J3+39J3+39J3=21J5+33J5+33J5=7J4+36J6+36J6=21J7+48J3=9J7+42J8+42J8+42J5+45J4=14J6=14J6+56J7+48J7+50J7=18J8+60J8+60J5+55J4+55J4+56J6+56J6=24J7+67J8=18J8+69J5+69J5=28J6+72J6+72J6+72J7+72J7+67J7+67J8+67J8+69J8
Solution:
+-------+-------+-------+
| 2 3 5 | 4 1 9 | 7 8 6 |
| 1 9 6 | 7 8 2 | 3 4 5 |
| 6 4 8 | 1 2 7 | 5 9 3 |
+-------+-------+-------+
| 5 8 7 | 6 9 3 | 1 2 4 |
| 8 1 9 | 3 6 4 | 2 5 7 |
| 3 6 2 | 9 5 1 | 4 7 8 |
+-------+-------+-------+
| 4 5 1 | 2 7 8 | 6 3 9 |
| 7 2 3 | 8 4 5 | 9 6 1 |
| 9 7 4 | 5 3 6 | 8 1 2 |
+-------+-------+-------+

Quote:
Pinata: Sudoku Solver Score: 1.45

Andrew: Since this is a jigsaw killer with an appropriate SS score, I've taken the liberty of re-naming it Pinata Killer Sudoku 20 (aka Texas Jigsaw Killer 45) and have added it to the Texas Jigsaw Killer Archive, which I started last month. The archive was started both to preserve Ruud's TJKs and to encourage the posting of new ones if there's sufficient interest. This renaming follows the example of a few other jigsaw killers which were renamed as TJKs.

When I started the Texas Jigsaw Killer Archive I hoped that I'd start with the earlier, easier ones because I'd only ever solved one jigsaw killer. Then Pinata Sudoku Killer 20 appeared.

I expect that more experienced jigsaw killer solvers, including Ed:
will be able to solve this puzzle more directly, probably using Law of Leftovers (LoL) earlier than I have. I regularly use LoL when solving "newspaper" jigsaw sudokus at Tough, Diabolical and Extreme level, but deliberately avoid using LoL for Gentle and Moderate even though it might help to solve these puzzles more quickly.

Andrew's walkthrough:
I’m not experienced at solving jigsaw killers, only having done one before; a simpler one which didn’t require a walkthrough. While starting to compile the Texas Jigsaw Killer archive I noticed that some solvers draw diagrams to label the Jigsaw Houses. In this walkthrough I’ve described them by their left-hand cell in their upper row, for example the first house is HR1C1, the next three HR1C4, HR1C7 and HR2C5. I hope this is clear enough; it saves cross-referencing between two diagrams.

Prelims

a) R34C4 = {16/25/34}, no 7,8,9
b) R34C9 = {16/25/34}, no 7,8,9
c) R67C1 = {16/25/34}, no 7,8,9
d) R67C6 = {18/27/36/45}, no 9
e) 21(3) cage at R6C4 = {489/579/678}, no 1,2,3
f) 29(4) cage at R4C1 = {5789}
g) 14(4) cage at R7C3 = {1238/1247/1256/1346/2345}, no 9

1. 31(5) cage at R1C5 contains 9, locked for R1

2. 45 rule on R12 3 outies R3C678 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on R12 1 outie R3C8 = 2 innies R2C67 + 4
2b. Min R2C67 = 3 -> min R3C8 = 7
2c. Max R2C67 = 5, no 5,6,7,8,9 in R2C67

3. 45 rule on R89 3 outies R7C234 = 8 = {125/134}, 1 locked for R7, clean-up: no 6 in R6C1, no 8 in R6C6
3a. R7C234 = {125/134}, CPE no 1 in R8C4 using HR6C2

4. 45 rule on R123 3 innies R3C459 = 6 = {123}, locked for R3, clean-up: no 1,2,3 in R4C4, no 1,2,3 in R4C9
4a. Max R3C5 = 3 -> min R4C56 = 11, no 1 in R4C56

5. 45 rule on R1234 1 outie R5C3 = 2 innies R4C78 + 6 -> R5C3 = 9, R4C78 = 3 = {12}, locked for R4, HR1C7 and 15(4) cage at R4C8, no 1,2 in R45C89
5a. R4C78 = 3 -> R5C89 = 12 = {48/57}, no 3,6

6. Naked triple {578} in R4C123, locked for R4, clean-up: no 2 in R3C4, no 2 in R3C9
6a. Naked triple {578} in R4C123, CPE no 5,7,8 in R12C1 using HR1C1

7. R3C5 = 2 (hidden single in R3), R4C56 = {39} (hidden pair in R4)
7a. 13(3) cage at R5C4 = {148/157/346}
7b. Killer pair 4,5 in 13(3) cage and R5C89, locked for R5
7c. Killer pair 4,7 in 13(3) cage and R5C89, locked for R5
7d. Killer pair 1,3 in R3C4 and 13(3) cage, locked for HR2C5 -> R4C56 = [93], clean-up: no 6 in R67C6

8. 9 in R7 only in 18(3) cage at R7C7 = {279/369} (cannot be {459} which clashes with R7C234), no 4,5,8
8a. Killer pair 2,3 in R7C234 and 18(3) cage, locked for R7, clean-up: no 4,5 in R6C1, no 7 in R6C6
8b. 8 in R7 only in R7C56, locked for HR6C4, no 8 in R6C4 + R8C5 + R9C456

9. 45 rule on R789 3 innies R7C156 = 19 = {478/568}
9a. 4 of {478} must be in R7C1 -> no 4 in R7C56, clean-up: no 5 in R6C6

10. 21(3) cage at R6C4 = {489/579/678}
10a. 9 of {489/579} must be in R6C4 -> no 4,5 in R6C4

11. 18(3) cage at R2C8 = {459/468/567}
11a. R3C8 = {789} -> no 7,8,9 in R2C89

12. 45 rule on R12 4 innies R2C6789 = 14 = {1256/1346/2345}
12a. 1,2,3 of {1346/2345} must be in R2C67 -> no 4 in R2C67

13. 45 rule on HR1C7 2 outies R1C56 = 10 = [19/37/46/64/82], no 5,7 in R1C5, no 1,5,8 in R1C6

14. 45 rule on R1 2 outies R2C45 = 1 innie R1C1 + 13
14a. Max R2C45 = 17 -> max R1C1 = 4
14b. Min R2C45 = 14, no 1,2,3,4, no 5 in R2C4

15. Law of Leftovers (LoL) using HR1C7 + HR3C9 + HR6C7, R23C7 and R48C6 must contain the same numbers, R4C6 = 3 -> R2C7 = 3, R3C7 = {456789} -> R8C6 = {456789}, no 1,2, clean-up: no 7 in R1C6 (step 13)

16. LoL using HR1C1 + HR3C1 + HR6C2, R23C3 and R48C4 must contain the same numbers, no 3 in R23C3 -> no 3 in R8C4
16a. Same LoL, R4C4 = {46} -> one of R23C3 must be {46}
16b. R1C56 (step 13) = [19/82] (cannot be {46} which clashes with one of R23C3), no 4,6
16c. Killer pair 1,2 in R1C56 and R2C6, locked for HR1C4
16d. Same LoL, no 2 in R23C3 -> no 2 in R8C4
16e. 2 in C4 only in R79C4, locked for HR6C4, no 2 in R69C6, clean-up: no 7 in R7C6

17. R1C56 (step 16b) = [19/82] -> 31(5) cage at R1C5 = {16789/25789} (other combinations don’t contain 1 or 2), no 4, 7,8 locked for R1, 7 also locked for HR1C7, no 7 in R3C8
17a. 4 in HR1C7 only in R2C89, locked for R2

18. 21(3) cage at R6C4 = {579/678} (cannot be {489} which clashes with R67C6), no 4

19. R2C45 = R1C1 + 13 (step 14)
19a. Max R2C45 = 16 (cannot be [98] which clashes with R1C56) -> max R1C1 = 3
19b. R1C1 = {123} -> R2C45 = 14,15,16 = {59/68/69/78/79}

20. 4 in R1 only in 27(5) cage at R1C2 = {14679/34569/34578} (cannot be {14589/24678} which clash with 31(5) cage at R1C5, cannot be {24579} which clashes with R1C6), no 2
20a. 9 of {14679/34569} must be in R2C4 -> no 6 in R2C4

21. Hidden killer pair 8,9 in R2C123 and R2C45 for R2, R2C45 contains one of 8,9 -> R2C123 must contain one of 8,9
21a. 2 in HR1C1 only in 18(4) cage at R1C1 = {1269/1278/2358} (cannot be {2367} which doesn’t contain 8 or 9)
21b. 6 of {1269} must be in R2C3 -> no 6 in R2C12

22. 2 in C3 only in R6789C3, locked for HR6C2, no 2 in R67C2 + R9C12

23. 2 in C9 only in R6789C9, CPE no 2 in R8C8

24. 3,9 in HR3C9 only in R367C9 + R8C89, CPE no 3,9 in R9C9

25. 3 in HR6C7 only in R679C8, locked for C8

26. LoL for HR1C1 + HR1C4 + HR1C7 + HR2C5 R34C19 must contain the same numbers as 13(3) cage at R5C4 + R6C5
26a. R34C9 = [16/34], 13(3) cage at R5C4 (step 7a) = {148/157/346}
26b. 13(3) cage = {148/157} => R34C9 = [16] (LoL) => R6C5 = 6 (LoL) or 13(3) cage = {346}
-> 6 in 13(3) cage + R6C5, locked for HR2C5, no 6 in R2C5 + R3C6
26c. When 13(3) cage = {148} => R34C9 = [16], R34C1 = [48] -> no 8 in R3C1

27. R1C1 = {123} -> R2C45 = 14,15,16 = {59/78/79} (step 19b) -> R1C1 + R2C45 = 1[95]/2{78}/3[97]
27a. 18(4) cage at R1C1 (step 22a) = {1269/1278/2358} = 2{19}6/[12]{78}/[32]{58} (cannot be 1{29}6 which clashes with R1C1 + R2C45 = 1[95], cannot be [21]{78} which clashes with R1C1 + R2C45 = 2{78}) -> no 2 in R2C2
27b. 2 in 18(4) cage only in R12C1, locked for C1, clean-up: no 5 in R7C1

28. R7C156 (step 9) = {478/568}
28a. R7C1 = {46} -> no 6 in R7C5

29. Consider combinations for 21(3) cage at R6C4 (step 18) = {579/678}
21(3) cage = {579} => R6C4 = 9 => no 9 in R9C6
or 21(3) cage = {678}, 8 locked for C5 => R1C5 = 1, R1C6 = 9 (step 16b) => no 9 in R9C6
-> no 9 in R9C6
29a. 9 in HR6C4 only in R69C4, locked for C4

30. 9 in R2 only in R2C12 -> 18(4) cage at R1C1 (step 21a) = {1269} (only remaining combination) -> R2C3 = 6, R2C89 = {45}, locked for R2 and HR1C7, no 5 in R1C789, R3C8 = 9 (cage sum), R2C45 = {78}, locked for R2
30a. R2C45 = {78} -> R1C1 = 2 (step 27), R1C6 = 9, R1C5 = 1 (step 16b), R2C6 = 2
30b. Naked triple {678} in R1C789, locked for R1

31. 21(3) cage at R6C4 (step 18) = {579/678} = 9{57}/7[68] (cannot be 6{78} which clashes with R2C5), no 6 in R6C4, no 8 in R6C5
31a. Killer pair 7,8 in R2C5 and R67C5, locked for C5

32. 13(3) cage at R5C4 (step 7a) = {148/157/346}
32a. 5 in {157} must be in R5C5 -> no 5 in R5C46

33. 6 in R3 only in R3C12, CPE no 6 in R5C2 and R8C2 using HR3C1

34. 45 rule on R6789 3 outies R5C127 = 11 = {128/236}
34a. {236} must be [326] (only remaining permutation, cannot be [632] which clashes with R78C1) -> no 6 in R5C1, no 3 in R5C2

35. R5C127 (step 34) = {128/236}
35a. Consider permutations for R34C9 = [16/34]
R34C9 = [16] => no 6 in R5C7 => R5C127 = {128}
or R34C9 = [34] => 13(3) cage at R5C4 = {346} (LoL, step 26b), locked for R5 => R5C127 = {128}
-> R5C127 = {128}, locked for R5
35b. 13(3) cage at R5C4 (step 7a) = {346} (only remaining combination), locked for R5 and HR2C5 -> R3C4 = 1, R4C4 = 6, R34C9 = [34]
35c. Naked pair {57} in R5C89, locked for HR3C9, no 5,7 in R67C9 + R8C89

36. 21(3) cage at R6C4 (step 18) = {579} (only remaining combination) -> R6C4 = 9, R67C5 = {57}, locked for C5 -> R2C45 = [78]

37. R2C67 = [23] = 5 -> R3C67 = 12 = [75], R6C5 = 5, R7C5 = 7, R1C4 = 4, R3C3 = 8, R5C4 = 3

38. 18(3) cage at R7C7 (step 8) = {369} (only remaining combination), locked for R7 -> R7C1 = 4, R6C1 = 3, R3C1 = 6, R3C2 = 4
38a. R7C6 = 8 (hidden single in R7), R6C6 = 1

39. R8C4 = 8 (hidden single in C4)
39a. 14(4) cage at R7C3 = {1238} (only remaining combination) -> R7C34 = [12], R8C3 = 3, R7C2 = 5, R9C4 = 5

40. R7C2 = 5 -> R8C12 = 9 = [72]

41. R1C23 = [35], R4C3 = 7, R4C2 = 8, R4C1 = 5

42. R5C12 = [81] = 9 -> R6C23 = 8 = [62]

and the rest is naked singles.


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PostPosted: Wed Oct 22, 2014 1:58 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Jigsaw Killer Sudoku (aka Texas Jigsaw Killer 46) by Para (August 2013) here

Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=0J019J1+1J2=15J2+3J2=28J2+5J3=22J3+7J3=0J0+1J1+1J1+3J1+3J1+5J2+5J2+7J3+7J3=20J0+18J0=20J0+20J1=23J4+22J4=22J2+24J3=0J3+18J0+18J1+20J1+20J1+22J4+22J2+24J2+24J3=0J3=25J0+36J0+36J0+36J4=0J4=15J4+41J5+41J5+41J5=0J6=25J6+46J7=23J7+48J4=17J8+50J8=15J8+52J5=0J6+46J6+46J7+48J4+48J4+50J8+50J5+52J5+52J5=14J6+63J6=16J7+65J7=22J8+67J8=22J8+69J8=0J5+63J6+63J6+65J6+65J7+67J7+67J7+69J7+69J8=0J5
Note. This code does not work for SudokuSolver.
Solution:
+-------+-------+-------+
| 2 9 5 | 3 1 7 | 4 6 8 |
| 4 3 2 | 5 6 8 | 9 7 1 |
| 8 5 1 | 4 7 3 | 6 9 2 |
+-------+-------+-------+
| 6 1 8 | 7 9 4 | 2 5 3 |
| 9 7 3 | 6 5 1 | 8 2 4 |
| 3 8 7 | 9 4 2 | 5 1 6 |
+-------+-------+-------+
| 7 4 6 | 8 2 9 | 1 3 5 |
| 5 2 4 | 1 3 6 | 7 8 9 |
| 1 6 9 | 2 8 5 | 3 4 7 |
+-------+-------+-------+

Quote:
Para: Here's a Jigsaw Killer Sudoku I wrote a while back. I thought you guys might enjoy it too. I can't currently get a code for it, so if anyone would want to post one, that is appreciated.

http://puzzleparasite.blogspot.com.au/2 ... iller.html

enxio27: I'm sure this one is over my head, but here's the code:

Andrew: I’d done Para’s Toroidal Killer 2 immediately before this puzzle. It felt a lot easier than this one.

An interesting jigsaw pattern, which I haven’t seen before, and an enjoyable puzzle.

Andrew's walkthrough:
I’d done Para’s Toroidal Killer 2 immediately before this puzzle. It felt a lot easier than this one.

An interesting jigsaw pattern, which I haven’t seen before, and an enjoyable puzzle.

Prelims

a) 28(4) cage at R1C6 = {4789/5689}, no 1,2,3
b) 14(4) cage at R8C1 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on R5 1 innie R5C5 = 5, placed for NR3C5

2. 45 rule on R12 2 innies R12C1 = 6 = {15/24}

3. 45 rule on R34 2 innies R34C9 = 5 = {14/23}

4. 45 rule on R67 2 innies R67C1 = 10 = {19/28/37/46}, no 5

5. 45 rule on R89 2 innies R89C9 = 16 = {79}, locked for C9 and NR5C7

6. 28(4) cage at R1C6 = {4789/5689}, CPE no 8,9 in R1C345 + R34C7

7. 45 rule on NR6C1 using R67C1 = 10 (step 4), 3 remaining innies R67C2 + R9C3 = 21 = {489/579/678}, no 1,2,3
7a. 14(4) cage at R8C1 = {1238/1256/1346/2345} (cannot be {1247} which clashes with R67C2 + R9C3), no 7

8. Law of Leftovers (LoL) for R6789 three outies R5C789 must exactly equal three innies R6C5 + R7C45, no 7,9 in R5C789 -> no 7,9 in R6C5 + R7C45
8a. R5C789 = R6C5 + R7C45 -> R6C4 = R5C6 + 8 (difference between 23(4) and 15(4) cages) -> R6C4 = 9, R5C6 = 1, 1 placed for NR3C5, 9 placed for NR6C3, clean-up: no 1 in R7C1 (step 4)
[Is there a technically simpler way to do this step?]
8b. 15(4) cage at R5C6 = {1248} (only remaining combination), 2,4,8 locked for R5 and NR5C7
8c. R5C789 = {248} -> R6C5 + R7C45 = {248} (LoL for R6789)
8d. Naked triple {248} in R6C5 + R7C45, locked for NR3C5

9. R5C9 + R6C89 = {1356} -> 15(4) cage at R6C8 = {1356} (only combination containing at least three of 1,3,5,6)
9a. 45 rule on NR5C7 using R5C789 = {248} = 14 and R89C9 = {79} = 16, 1 outie R7C7 = 1 innie R6C8 -> R7C7

10. LoL for R1234 three outies R5C123 must exactly equal three innies R3C56 + R4C5 -> R5C4 = R4C6 + 2 (difference between 25(4) and 23(4) cages) -> R5C4 = {67}, R4C6 = {45}

11. 25(5) cage at R5C1 = {3679}, 3,9 locked for NR1C1

12. 8,9 in NR1C3 only in R1C6 + R2C67, locked for 28(4) cage at R1C6, no 8,9 in R1C7
12a. 9 in NR1C7 only in R1234C8, locked for C8

13. 45 rule on NR1C7 using R34C9 = 5 (step 3), 3 remaining innies R1C7 + R34C8 = 18 = {279/369/378/459/468/567} (cannot be {189} because no 1,8,9 in R1C7), no 1

14. LoL for C89 three outies R157C7 must exactly equal three innies R689C8, R6C8 = R7C7 (step 9a) -> R15C7 must exactly equal R89C8, no 1,3 in R15C7 -> no 1,3 in R89C8

15. 28(4) cage at R1C6 = {4789/5689} contains one of 6,7
15a. Hidden killer pair 6,7 in R1C345 + R34C7 and R1C6 + R2C67 for NR1C3, R1C345 + R34C7 must contain one of 6,7 (cannot contain both because R1C345 + R34C7 “see” all cells of the 28(4) cage) -> R1C6 + R2C67 must contain one of 6,7 -> no 6,7 in R1C7
15b. R1C7 = {45} -> no 4,5 in R1C6 + R2C67

16. LoL for C89 (step 14), no 6,7 in R15C7 -> no 6,7 in R89C8

17. R1C7 + R34C8 (step 13) = {459/468/567} (cannot be {279/369/378} because R1C7 only contains 4,5), no 2,3 in R34C8

18. Hidden killer pair 2,3 in 22(4) cage at R1C8 and R34C9 for NR1C7, R34C9 must contain both or neither of 2,3 -> 22(4) cage must contain both or neither of 2,3
18a. 22(4) cage at R1C8 = {1489/1579/1678/2389} (cannot be {2479/2569/2578/3469/3478/3568} which only contain one of 2,3, cannot be {4567} which clashes with R1C7)
18b. 22(4) cage = {1489/1678/2389} (cannot be {1579} = {79}{15} which clashes with R34C9 + R67C9, killer ALS block), no 5, 8 locked for NR1C7
18c. 3 of {2389} must be in R12C9 (R12C9 cannot be {28} which clashes with R34C9 + R5C9, killer ALS block), no 3 in R12C8

19. 5 in C9 only in R67C9, locked for 15(4) cage at R6C8 and NR5C7

20. 3 in C8 only in R67C8, locked for 15(4) cage at R6C8
20a. 3 in NR5C7 only in R7C78, locked for R7, clean-up: no 7 in R6C1 (step 4)

21. 28(4) cage at R1C6 = {4789/5689}, 22(4) cage at R1C8 (step 18b) = {1489/1678/2389}
21a. Caged X-Wing for 8 in 28(4) cage and 22(4) cage, no other 8 in R12

22. 8 in R34 only in 20(4) cage at R3C1 and 20(4) cage at R3C3, which must each contain 8

23. R1C7 + R34C8 (step 17) = {459/567}, CPE no 5 in R34C7
23a. 45 rule on NR1C7 using R34C9 = 5 (step 3), 2 outies R34C7 = 1 innie R1C7 + 4
23b. R1C7 = {45} -> R34C9 = 8,9 -> no 4 in R34C9

24. Hidden killer pair 4,5 in R1C345 and R4C6 for NR1C3, R4C6 = {45} -> R1C345 must contain one of 4,5
24a. Killer pair 4,5 in R1C345 and R1C7, locked for R1, clean-up: no 1,2 in R2C1 (step 2)

25. Hidden killer pair 1,2 in R1C345 and R34C7 for NR1C3, R34C7 cannot contain both of 1,2 (because of 22(4) cage at R3C7), R1C345 cannot contain both of 1,2 (which would clash with R1C1) -> R1C345 contains one of 1,2 and R34C7 contains one of 1,2
25a. Killer pair 1,2 in R1C1 and R1C345, locked for R1

26. R1C7 + R34C8 (step 17) = {459/567}
26a. R34C7 = R1C7 + 4 (step 23a)
26b. Consider placements for R1C7
R1C7 = 4 => R1C7 + R34C8 = {459}
or R1C7 = 5 => R34C7 = 9 = {27/36} => R1C7 + R34C8 = {459} (cannot be {567} which clashes with R34C7)
-> R1C7 + R34C8 = {459}, locked for NR1C7, clean-up: no 1 in R34C9 (step 3)
26c. Naked pair {23} in R34C9, locked for C9 and NR1C7
26d. R5C9 = 4 (hidden single in C9)
26e. 8 in C9 only in R12C9, locked for NR1C7
26f. 1 in NR1C7 only in R2C89, locked for R2
26g. 2,3 in R2 only in R2C2345, locked for NR1C2, no 2,3 in R1C2 + R3C4 + R4C234

27. 23(4) cage at R3C5 = {3479/3569}, R34C9 = {23}
27a. Caged X-Wing for 3 in 23(4) cage and R34C9, no other 3 in R34

28. 23(4) cage at R3C5 = {3479/3569}, R1C7 + R34C8 = {459} with 9 in R34C8
28a. Caged X-Wing for 9 in 23(4) cage and R1C7 + R34C8, no other 9 in R34

29. Naked quad {6789} in R1C2689, locked for R1

30. 15(4) cage at R1C4 = {1239/1257/1347/1356/2346}
30a. Killer quad 6,7,8,9 in 15(4) cage, R2C67 and R2C89, locked for R2
30b. Max R1C3 + R2C23 = 12 -> min R1C2 = 7
30c. 19(4) cage at R1C2 = {2359/3457} (cannot be {1459} which clashes with R2C1), no 1
30d. 3 in R12 only in 19(4) cage and 15(4) cage -> 15(4) cage = {1239/1347/1356/2346}
[3 in R12 is an alternative way to eliminate {1459} from 19(4) cage.]

31. R67C2 + R9C3 (step 7) = {489/579/678}
31a. 5 of {579} must be in R67C2 (R67C2 cannot be {79} which clashes with R1C2), no 5 in R9C3

32. 9 in C1 only in R57C1, 9 in C3 only in R59C3 -> grouped X-Wing for 9, no other 9 in NR1C1 and NR6C1

33. R1C2 = 9 (hidden single in C2), placed for NR1C2
33a.19(4) cage at R1C2 (step 30c) = {2359} (only remaining combination), no 4

34. 25(4) cage at R6C2 = {4678} (only remaining combination)
34a. Caged X-Wing for 4,8 in 25(4) cage and R6C5 + R7C45, no other 4,8 in R67, clean-up: no 2,6 in R67C1 (step 4)
34b. Naked quad {4678} in 25(4) cage, CPE no 4,6,7,8 in R9C3 using NR6C1 -> R9C3 = 9, placed for NR6C1, R89C9 = [97]
34c. R67C1 = 10 (step 4) -> R6C1 = 3, R7C1 = 7, both placed for NR6C1
34d. Naked quad {2468} in R7C2345, locked for R7
34e. Naked pair {13} in R7C78, locked for R7 and NR5C7 -> R67C9 = [65], R67C8 = [13], 1 placed for NR6C6, R7C6 = 9, placed for NR6C6
34f. R7C67 = [91] = 10 -> R6C67 = 7 = {25}, locked for R6 and NR6C6
34g. R2C6 = 9 (hidden single in NR1C3)
34h. R5C1 = 9 (hidden single in C1)
34h. R6C3 = 7 (hidden single in R6), placed for NR6C3

35. Naked pair {48} in R89C8, locked for C8, NR6C6 and 22(4) cage at R8C7 -> R5C78 = [82]
35a. R1C7 = 4 (hidden single in NR1C7) -> 28(4) cage at R1C6 = {4789}, 7,8 locked for C6 and NR1C3
35b. Naked pair {26} in R34C7, locked for C7 and NR1C3 -> R6C67 = [25], R9C7 = 3, placed for NR6C3, R8C7 = 7

36. R1C1 = 2 (hidden single in R1), R2C1 = 4 (step 2), both placed for NR1C1

37. R12C9 = [81], R12C6 = [78], R12C8 = [67]
37a. 19(4) cage at R1C2 (step 33a) = {2359}, 2 locked for R2

38. 2 in NR6C1 only in R89C2, locked for C2
38a. R2C3 = 2 (hidden single in R2)

39. R9C3 = 9 -> 16(4) cage at R8C3 = {1249}, locked for NR6C3, 2 locked for C4

40. R9C3 = 9 -> R78C2 = 12 (step 7) = {48}, locked for C2, NR6C1 and 25(4) cage at R6C2 -> R7C3 = 6, placed for NR6C3, R9C56 = [85], R5C3 = 3, R1C3 = 5, R2C2 = 3, R2C45 = [56], R4C6 = 4

41. Naked pair {18} in R34C3, locked for C3 and 20(4) cage at R3C3 -> R8C3 = 4

42. Naked pair {12} in R89C4, locked for C4 -> R1C45 = [31]

43. R34C3 = {18} = 9 -> R34C4 = 11 = [47]

44. 8 in C1 only in R34C1, locked for NR1C1 -> R3C3 = 1, placed for NR1C1

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


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PostPosted: Sun Dec 28, 2014 3:47 am 
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 47 by Ed (November 2014) here

Puzzle Diagram:
Image
Code: Select, Copy & 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 |
+-------+-------+-------+

Quote:
Ed: 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.

Andrew: 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

Ed:
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.


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.
Andrew's walkthrough:
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.
Ed's walkthrough:
[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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