## Anti-knight sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants
Another AN-puzzle:
Code: Select all
`750080000000000000003000600000012009000073000000000000000500100900000000000004000`
evert

Posts: 186
Joined: 26 August 2005

List updated.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

### Re: Anti-knight sudoku

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

Posts: 4
Joined: 08 April 2019

### Re: Anti-knight sudoku

A good question!

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.

Mathimagics
2017 Supporter

Posts: 1304
Joined: 27 May 2015
Location: Canberra

### Re: Anti-knight sudoku

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
JFA

Posts: 4
Joined: 08 April 2019

### Anti-knight sudoku

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?

Mathimagics
2017 Supporter

Posts: 1304
Joined: 27 May 2015
Location: Canberra

### Re: Anti-knight sudoku

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

Posts: 4
Joined: 08 April 2019

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