SudokuX (Diagonal Sudoku)

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Re: SudokuX (Diagonal Sudoku)

Postby Mathimagics » Wed Aug 08, 2018 10:21 pm

blue wrote:In return, I can confirm your result of 1,223,885,904 S-canonical forms for the SX grids.


A harmonious state of numerical concordance has been achieved! 8-)

I'm rebuilding my catalog from scratch, since the old one is not XCF'ed. The rebuild process is slightly sub-optimal, since I could make X-canonicalisation faster, as you described (thank you!), but since the job needs doing only once, it will probably finish well before I have the new CF function ready.

Cheers!

M
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SudokuX - Min Clue Puzzles

Postby Mathimagics » Mon Aug 27, 2018 11:11 am

Now that we have established the number of of SudokuX grids, and the number of EDX grids, we turn our attention to the minimum-clue questions.

Ruud's SudoCue website has a collection of 7193 x 12-clue puzzles (http://www.sudocue.net/minx.php). This formed the initial catalog.

I've been running an RMW (random morph walker), and when the "new grid find" rate had slowed to only one new grid per hour, it was terminated and a "backfill" process applied that filled in all {+1, -1} (PM1) morphs of the known puzzles.

The end result was a catalog of 15,626 puzzles on 12,010 EDX grids.

A "PM2 backfill" is in progress to expand the catalog by looking for {+2, -2} morphs. This is a slow process, and is expected to take about one week to complete. At the 2000 puzzle mark, this process has found over 5000 new grids/puzzles, so it looks as though the size of the catalog will at least triple.

The key questions, both of which remain open, are:

  • how many 12-clue puzzles are there?
An estimate at this stage looks difficult. We will probably get some idea of the size of the {+2, -2}-connected puzzle set in a week or so, when the initial PM2 job is finished and we start a second pass (on the new entries).

The size of the EDX grid pool (1.5 billion) means that an estimate based on sampling is going to be very difficult.

  • do any 11-clue puzzles exist?
All 12-clue puzzles found so far are minimal (otherwise you would cetainly hear about it!). This, and the low ratio of 12-clue puzzles / grids, suggest that an 11-clue puzzle is unlikely.
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Re: SudokuX (Diagonal Sudoku)

Postby Leren » Tue Aug 28, 2018 10:15 pm

I've been checking Mathimagics' work and can confirm his latest count of 26141 EDX 12 clue puzzles solving to 21699 EDX grids. And he's not finished yet. Awesome !

Ruud's catalog of 7193 puzzles contained some minlexing errors, and on fixing these, we found that he had 13 duplicate puzzles, reducing his EDX puzzle count to 7,180.

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Re: SudokuX (Diagonal Sudoku)

Postby blue » Thu Aug 30, 2018 9:51 am

Thanks Leren,

The "21699 EDX grids" part of your post, prompted me to find & fix a stupid bug in my "puzzle list" -> "ED grid count" code.
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Re: SudokuX (Diagonal Sudoku)

Postby Leren » Thu Aug 30, 2018 11:39 am

Whilst Mathimagics has not found an 11 clue puzzle yet, the following 11 clueset

......78............9.........................1.5.........4.....3....5.1....98

has just 2 ESX solutions

163452789457839126289671453394217865576984312812563974721345698938726541645198237
123456789457839162689271453394617825572984316816523974761345298938762541245198637

with the second of these, being the minlexed version, having 36 "siblings", that's 36 EDX 12 clue puzzles solving to it. I think we both tried a bit of a vicinity search to see if we could strike gold, but no luck.

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Re: SudokuX (Diagonal Sudoku)

Postby Leren » Fri Aug 31, 2018 5:27 am

Latest news from Mathimagics is that he has identified 45,296 12 clue EDX puzzles solving to 39,543 EDX grids. And no, he's not finished.

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Re: SudokuX (Diagonal Sudoku)

Postby Leren » Mon Sep 03, 2018 7:06 am

The latest update is that Mathimagics has increased the known 12 clue puzzle count to an incredible 73,258 EDX puzzles on 62,361 grids. The search is still not finished but no 11 clue puzzle found yet.

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