## Psycho Killer Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Psycho Killer Sudoku

Great song, great band (Talking Heads), and hopefully a pretty decent puzzle!

Observe the grid below. It's an 11 x 11 Jigsaw layout, but it's strictly a 1 to 9 Sudoku Jigsaw, as it has 2 clue-cells in each row and column.

So the same rules apply: place 1 to 9 in each row, column and jigsaw region. The killer twist is that instead of cages, we have Kakuro clues. And of course there are 11 rows, columns, and jigsaw regions. More bang for your buck!

The clues give the total of the digits in a horizontal/vertical "run", and the run is defined in the standard Kakuro manner, ie it extends to the first grey cell or the edge of the grid, whichever comes first.

SudokuPK-Demo.png (17.8 KiB) Viewed 193 times

I believe that this has a unique solution (independent verification, by P&P or software, will be gratefully acknowledged!)

Have fun!

Note for programmers: this puzzle type is in fact very easy to configure in a DLX solver, or in a "house" solver like dobrichev's fsss2. My variant designation code is "PK" for now, ie SudokuPK (or should it be SudokuPJK, for Psycho Jigsaw Killer?)

[EDIT] Oops! forgot to provide the solution. You will find it two posts down, thanks to creint!
Last edited by Mathimagics on Fri Jan 25, 2019 10:44 pm, edited 1 time in total.

Mathimagics
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Location: Canberra

### Re: Psycho Killer Sudoku

.
I forgot to include the hint for getting started!
Hint: Show
Code: Select all
`Single at r1,c11Single at r11,c1Think Killer mode: "rule of 45" :)`

Mathimagics
2017 Supporter

Posts: 1433
Joined: 27 May 2015
Location: Canberra

### Re: Psycho Killer Sudoku

Single solution confirmed, no chains required.
How did you generate this one?
Random placement kakuro cells then random jigsaw group, then random solution, then a solution that gives empty grid with no givens?

Solution:
Hidden Text: Show
Code: Select all
`3 1   5 6   2 7 4 8 98 7 4 9 2 1 6   5 3  2 9   4 1 3   5 8 6 75 6 9 7 3 8 1   2   44 5 6 8 7 2   3 9   1  3 1 2 8 6 4 9 7 5  7   5 3   9 8 4 1 2 61   2   5 4 7 6 3 9 89 4 8 6   7 3 2   1 5  8 3   4 5 9 1 6 7 26 2 7 1 9   5 8   4 3`
creint

Posts: 129
Joined: 20 January 2018

### Re: Psycho Killer Sudoku

Thanks creint, nice job!

Sorry that I omitted SAT solvers from the "should be easy for …" list above!

The puzzle generation process used was:

a) Find a valid SudokuPK grid:

• select a random 2-holes per row/col pattern
• fill the grid in with a random but valid solution (a "Pseudo-Latin Square")
• find an 11 x 9 jigsaw pattern that matches this LS (the tricky bit), if so, then we have a valid SudokuPK grid

In the Kakuro world we prefer grid layouts to be symmetric (ie automorphic under 180-degree rotation) so both the 2-hole pattern AND the jigsaw pattern should have this property. This makes the 3rd step above especially tricky. Some grids don't have any jigsaw patterns, others have none with symmetry, so we need to to test a lot of random solutions for each pattern.

b) Test "Sums Only":

• this is a standard step for Kakuro puzzles: does the full set of sums for the given solution grid uniquely identify it?
• if so, we are done.
• otherwise we could permute the labels a few times, regenerate the sums, and try again. Or we can try another LS solution on this pattern, or restart from scratch with another 2-hole pattern.

c) Redundancy?
• we can of course toughen up the sums-only puzzle that we have created by removing clues, in the traditional manner

Pure Kakuro puzzles of course don't have any givens (they are against our religion), but I would certainly like to experiment here with puzzles that mix some givens with some SUMS, since we can skip step (b) altogether, and just take the grid as a SudokuPJ (Psycho Jigsaw?) from which we can reduce the givens in the conventional sense.

Or we can create a mix that is anywhere in between these two forms. There is an enormous range of puzzles that can be produced.

Mathimagics
2017 Supporter

Posts: 1433
Joined: 27 May 2015
Location: Canberra