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PostPosted: Sat Apr 13, 2019 4:10 am 
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Imagine, if you will, a movie called The Texas Chainsaw Zombie Massacre, in which the zombie killers are armed with weapons like this: AK-47 + chainsaw.

This puzzle was inspired by this wacky idea (no, I tell a lie, I only found the picture because I thought of the puzzle concept, then searched for "Chainsaw + AK-47", and to my amazement found that page!).

The puzzle is a standard Jigsaw Killer with "Anti-Knight" constraints. Anti-Knight means that no two cells that are a Knight-move apart can have the same value (a more elegant definition is that no two cells that are Manhattan distance 3 apart can be the same value).

This puzzle is "AK-47" since it also forbids any pair of cells that are a Knight-move apart from having a 4 in one cell and a 7 in the other. This additional constraint is redundant - it is not actually necessary to solve the puzzle, but knowing that the solution has this property may help with the solving process.

I constructed the puzzle this way so that it is still solvable by Sudoku Solver, which scores it as 0.9.
Attachment:
TJK-103-AK47.png
TJK-103-AK47.png [ 12.52 KiB | Viewed 6379 times ]


SS definition:
SumoCueV1=36J2+0J2+0J4=27J4+3J4+3J4=15J4+6J5+6J3+0J2+0J2+0J2+3J2+3J4+3J5+6J5=26J5+16J3=16J2+18J2=19J2+20J4+20J4+20J5+16J5+16J5+16J3+18J8=36J8+28J1+28J1=21J4+31J5=23J5=26J3+34J3+18J8+28J8+28J1+28J1+31J1+31J1+33J1+34J3+34J3=25J8+45J8=24J6+47J6=16J7+33J1+33J1+34J3+34J3+45J8=21J6+55J6+47J6+49J7+49J7=19J9+60J9+60J9+45J8+55J6+55J6+47J6=23J7=17J9+68J9=15J9+60J9+45J8+55J6+67J7+67J7+67J7+68J7+68J7+70J9+70J9


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PostPosted: Sat Apr 13, 2019 4:12 am 
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TJK-103-PF:
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PostPosted: Wed Apr 24, 2019 4:50 am 
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
This is a fairly easy puzzle; it should be P&P solvable but you may need a calculator at times unless you're exceptionally good at mental arithmetic.

I haven't done many Anti-Knight (AN) puzzles, but I found using this easy for this puzzle.

I decided fairly early not to use AN 4-7; it's slightly quicker using it but just as easy without it.

Here is my walkthrough for Texas Jigsaw Killer 103:
Anti-Knight (AN), also no 4-7 at Knight spacing, although that’s not required to solve this puzzle.

1a. 45 rule on R123 2 outies R45C1 = 4 = {13}, locked for C1, NR4C1 and 16(4) cage at R3C1
1b. R45C1 = 4 -> R3C12 = 12 = {48/57}, no 2,6,9
1c. Naked pair {13} in R45C1 -> no 1,3 in R45C3 (AN)

2a. 45 rule on NR4C1 using R45C1 =4, 2 remaining innies R45C2 = 16 = {79}, locked for C2, NR4C1 and 36(6) cage at R4C2, clean-up: no 5 in R3C1 (step 1b)
2b. 36(6) cage must contain 8 in R45C34, locked for NR4C3
2c. 9 in C1 only in R12C1, locked for NR1C1 and 36(6) cage at R1C1

3. 45 rule on R12 2 innies R2C89 = 12 = {39/48/57}, no 1,2,6

4a. 45 rule on C89 4 outies R1237C7 = 11 = {1235}, locked for C7
4b. 45 rule on C789 3 outies R689C6 = 3 = {123}, locked for C6
4c. 45 rule on NR7C7 2 outies R9C67 = 6 = [24]
4d. R9C67 = 6 -> R8C67 = 11 = [38]
4e. R6C6 = 1
AN eliminations:
R6C6 = 1 -> no 1 in R4C5 + R5C8 + R7C48 + R8C5
R8C6 = 3 -> no 3 in R6C5 + R79C4
R8C7 = 8 -> no 8 in R6C8 + R79C5
R9C6 = 2 -> no 2 in R7C7 + R8C48
R9C7 = 4 -> no 4 in R7C8 + R8C9
Naked triple {679} in R456C7 -> no 6,7,9 in R5C59
[I’ll leave those 4-7 eliminations for now, since SudokuSolver only scores this puzzle at 0.9.]

5a. 15(3) cage at R8C8 = {456} (only remaining combination, cannot be {159} which clashes with R7C7) -> R8C8 = 4, R9C89 = {56}, locked for R9 and NR7C7, clean-up: no 8 in R2C9 (step 3)
5b. R7C7 = 1
5c. R9C1 = 8, clean-up: no 4 in R3C2 (step 1b)
5d. 9 in R9 only in R9C345, locked for NR6C5
5e. 8 in NR6C5 only in 16(3) cage at R6C5 = {358} -> R7C5 = 3
5f. R8C5 = 6 (hidden single in NR6C5)
5g. R9C2 = 3 (hidden single in R9)
AN eliminations:
R7C5 = 3 -> no 3 in R5C4
R8C5 = 6 -> no 6 in R6C4 + R7C3
R8C8 = 4 -> no 4 in R6C9
Naked pair {58} in R6C5 + R7C6 -> no 5 in R4C6 + R68C4
Naked triple {235} in R123C7 -> no 2,5 in R2C5, no 3,5 in R2C9, clean-up: no 7,9 in R2C8 (step 3)

6. R4C4 = 3 (hidden single in NR4C3), R45C1 = [13]
6a. 36(6) cage at R4C2 = {345789} (only remaining combination) -> R4C3 + R5C34 = {458}, locked for NR3C4
6b. R5C5 = 2
6c. 2 in R4 only in R4C89, locked for NR1C9
6d. Naked triple {679} in R5C267, locked for R5, 6 also locked for NR4C3
6e. Naked triple {458} in R5C348, locked for R5, 4 also locked for NR4C3
6f. R5C9 = 1
6g. 4 in C5 only in R1234C5, locked for NR1C3
AN eliminations:
R4C4 = 3 -> no 3 in R2C3
R5C5 = 2 -> no 2 in R37C4 + R6C3
R5C9 = 1 -> no 1 in R3C7
6 in R5 only in R5C67 -> no 6 in R3C6
6 in C7 only in R45C7 -> no 6 in R4C9
Naked triple 4,5,8 in R4C3 + R5C34 -> no 4,5,8 in R7C3

7. Naked triple {279} in R7C389, locked for R7
7a. R3C3 = 3 (hidden single in NR1C1)
7b. R1C7 = 3 (hidden single in NR1C3)
7c. Naked pair {25} in R23C7, locked for NR1C8, clean-up: no 7 in R2C9 (step 3)
AN eliminations:
Naked pair {25} in R23C7 -> no 5 in R3C5, no 2,5 in R3C9

8. 45 rule on R12 3 outies R3C789 = 14 = {248} (cannot be {257} because 2,5 only in R3C7) = [284], R2C789 = [539], R5C8 = 5, R9C89 = [65], R6C78 = [97]
8a. R147C8 = [129], R146C9 = [683], R4C3 = 5
8b. Naked pair {67} in R5C67, locked for R5 -> R45C2 = [79], R45C7 = [67], R5C6 = 6
8c. R3C12 = [75], R3C456 = [619], R4C56 = [94], R2C6 = 7, R9C5 = 7
8d. R1C34 = [72] (hidden pair in NR1C3)
8e. Naked triple {458} in R1C56 + R2C5, locked for 27(6) cage at R1C4 -> R2C4 = 1, R9C34 = [19], R8C4 = 7, R78C3 = [29], R8C12 = [51]
8f. R7C3 + R8C23 + R9C2 = [2193] = 15 -> R7C2 = 6 (cage sum)
AN eliminations:
R4C6 = 4 -> no 4 in R2C5 + R5C4

and the rest is naked singles.

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


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