Anti-knight sudoku

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Postby evert » Tue Feb 12, 2008 1:29 am

Another AN-puzzle:
Code: Select all
750080000
000000000
003000600
000012009
000073000
000000000
000500100
900000000
000004000
evert
 
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Postby Pyrrhon » Thu Feb 21, 2008 11:27 am

List updated.

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Re: Anti-knight sudoku

Postby JFA » Tue Apr 09, 2019 7:23 pm

Hello, how many Anti-knight sudoku are there ? How I can calculate this number ?
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Re: Anti-knight sudoku

Postby Mathimagics » Wed Apr 10, 2019 8:31 pm

A good question! :cool:

I think the current situation is, nobody knows.

I doubt that the number can be calculated, some sort of enumeration is required.

A brute-force approach is out of the question - one would need to test all the ED grids (5,472,730,538), but also the 3,359,232 variants for every case, since these transformations don't preserve the AK property. We can only reduce this by a factor of 4, for rotation/reflection symmetries, but still the number of grids to test is enormous.

But these AK grids are likely to be very rare, since up to 8 extra eliminations can be associated with each cell (the central square has the full 8). Rarity seems to be confirmed by a random grid generator that tested over 1.5 billion grids before finding one anti-knight case … not very scientific, but it does suggest that an exact count is probably easily obtained ...
Last edited by Mathimagics on Wed Apr 10, 2019 11:01 pm, edited 1 time in total.
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Re: Anti-knight sudoku

Postby JFA » Wed Apr 10, 2019 9:33 pm

Yes I think adapt a fast Sudoku solver to solve in this mode is a good solution, but I don't have one. I hope you will succeed
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Anti-knight sudoku

Postby Mathimagics » Wed Apr 10, 2019 10:58 pm

Ok, that was fairly simple, really …

I decided not to bother with template generation, the grid count should be small enough to warrant an "all in one go" approach. So I just set the appropriate table for my solver, and gave it row 1 = "123456789" as the puzzle to be solved, asked for all solutions, and it came back 75s later with the answer 8,490,104.

My learned friend blue, or indeed anybody with a reasonably fast solver that can easily enforce the AK rules, should be able to confirm this figure.

ED grid count would probably be around 2.1 million?
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Re: Anti-knight sudoku

Postby JFA » Thu Apr 11, 2019 5:02 pm

Ok :) good job and very speed ..............., thank's
Beautiful method of resolution
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