Jigsaw Layouts (Generate / Test)

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Re: Jigsaw Layouts (Generate / Test)

Postby tarek » Mon Dec 16, 2019 10:23 pm

coloin wrote:from a post way back bumblebeagle - it seems that the minimum clues is 8

Hatman posted several 8 clue puzzles that have the "Hands" Jigsaw regions arrangement. One of the regions, however, doesn't have contiguous cells.
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=753 is where he posted them but the images links are unfortunately broken. According to Hatman it was introduced first by Nikoli_Freak. I had at the time some experiments with the layout and found the Jigsaw regions force the formation of X diagonals and Old Lace group too.


[Edit: Found the image: this is one my puzzles ]
Last edited by tarek on Thu Dec 19, 2019 6:50 pm, edited 1 time in total.
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Re: Jigsaw Layouts (Generate / Test)

Postby Mathimagics » Tue Dec 17, 2019 4:35 am

@creint: You're right, of course - SAT is probably the fastest way to test a JL for validity ("has any solution"). I didn't realise this back then.

@tarek: Gareth Moore published (in his "SudokuXtra" magazine) several puzzles with toroidal jigsaw layouts.

coloin wrote:So there are 5,279,342 valid ED continuous JLs
[ and 13,638 invalid] :?: to clarify !
.... and each of these valid layouts may have 0,1 or more ED solutions

"Valid" means a layout has solutions, the invalid ones do not have solutions. See the hidden image in the very first post for a couple of innocent-looking, but invalid, layouts.

The counts I gave (13,638 invalid, 5,279,342 valid) refer to a restricted class of JL's. These are what I considered "nice" layouts - they are all symmetric, and have no partitions (no subset of regions forms a 9 x X rectangle).

Also, my actual catalog of valid "nice" JL's has only 3.5 million. I can't remember now - was this the result of a culling operation, ie removing duplicates (reflections/rotations)? Hmmm ...
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