SudokuW/SudokuWX (Windoku)

For fans of Killer Sudoku, Samurai Sudoku and other variants

SudokuWX: 9-clue Puzzles

Postby Mathimagics » Thu Aug 23, 2018 4:09 pm

.
I have found a 9-clue SudokuWX (WindokuX) puzzle:

Code: Select all
  +-------+-------+-------+
  | . . . | . . . | . 8 . |
  | . . . | . 7 . | . . . |
  | . . . | . . . | . 5 . |
  +-------+-------+-------+
  | . . . | 3 . . | . . . |
  | . 6 . | . . . | . . . |
  | . . . | . . 4 | . 2 . |
  +-------+-------+-------+
  | . . . | . . . | . . . |
  | . . . | . . . | . . 1 |
  | 7 . . | . . . | . . . |
  +-------+-------+-------+


I hope that tarek and other pencil-solvers have fun with this one! 8-)

I had thought that, since every 10-clue case found by the morph-walker so far is minimal, that 9-clue puzzles might be rare or non-existent, but these were found by checking morphs of the 10-clue puzzles, eg {-2, +1}. So 8-clue puzzles cannot be ruled out by any stretch!

Here are the first 5 x 9-clue puzzles found:
Hidden Text: Show
Code: Select all
.......8.....7...........5....3......6............4.2..................17........: 123456789456879312897132456942318675368725194571694823685241937234987561719563248
....................8...........7.........4.....5........8...32..........69......: 123456789457298361698371245214687593785139426936542817571864932342915678869723154
.......8.....7...........5....3......6............4.2.........7........1.........: 123456789456879312897132456942318675368725194571694823685241937234987561719563248
..3......4.......2...1...65...2...........9.....................7................: 123456789456789312789132465634298571817564923592317648345621897971845236268973154
..3......4...........1.2.65...2...........9.....................7................: 123456789456789312789132465634298571817564923592317648345621897971845236268973154
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Mathimagics
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Re: SudokuWX: 9-clue Puzzles

Postby tarek » Thu Aug 23, 2018 6:19 pm

Mathimagics wrote:.
I have found a 9-clue SudokuWX (WindokuX) puzzle:

Code: Select all
  +-------+-------+-------+
  | . . . | . . . | . 8 . |
  | . . . | . 7 . | . . . |
  | . . . | . . . | . 5 . |
  +-------+-------+-------+
  | . . . | 3 . . | . . . |
  | . 6 . | . . . | . . . |
  | . . . | . . 4 | . 2 . |
  +-------+-------+-------+
  | . . . | . . . | . . . |
  | . . . | . . . | . . 1 |
  | 7 . . | . . . | . . . |
  +-------+-------+-------+


I hope that tarek and other pencil-solvers have fun with this one! 8-)

Couldn't advance things here!!! congratulations for these discoveries
tarek
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SudokuW: 11-clue Puzzle

Postby Mathimagics » Fri Aug 24, 2018 3:45 am

.
Here is our first 11-clue SudokuW (Windoku) puzzle. I have found about 100 so far.

Code: Select all
  +-------+-------+-------+
  | . 2 . | . . . | . . 9 |
  | . . . | . . . | . . . |
  | . . . | . 3 . | . . 1 |
  +-------+-------+-------+
  | . . . | . . . | . . . |
  | 7 . 9 | . . . | . . . |
  | 5 . . | . . . | . . . |
  +-------+-------+-------+
  | 6 . . | . . . | . . . |
  | . . . | . . 1 | . 7 . |
  | . . . | . . . | . 4 . |
  +-------+-------+-------+


Solution:
Hidden Text: Show
[/code]
123456789467198235895237461284375916719682354536914827641723598952841673378569142
[/code]


For SudokuWX, I have found over 7000 9-clue puzzles on 3000 ED grids. No sign of existence of 8-clue puzzles, but I have an explicit 8-clue tester (using HSets) running that is testing each 9-clue grid.
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SudokuWX (WindokuX)

Postby Mathimagics » Sun Aug 26, 2018 1:24 pm

I stopped looking for 10-clue SudokuWX puzzles when it became apparent there were so many 9-clue puzzles. At that point I had found 30,554 of the 81,571 ED grids (37.4%) had 10-clue puzzles. This raises the interesting question "how many grids do NOT have 10-clue puzzles?". I will return to this question once the 9-clue puzzles have been identified.

For 9-clue puzzles, I have found 9616 grids (11.8%). A rough estimate of the number of grids with 9-clue puzzles is 27000 (33%) based on random sampling, using explicit HS-based grid testing. Only 100 grids were tested so the estimate error is likely to be relatively high.

I have also HS-tested half of the 9616 grids for 8-clue puzzles and none have been found.

The 9-clue search and 8-clue testing is ongoing.
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SudokuW/SudokuWX (Windoku)

Postby Mathimagics » Thu Sep 13, 2018 3:28 am

.
I have independent corroboration (twice in fact) of my figure for the number of SudokuW grids:

This was given by "aeb" here, and apparently confirmed by Red Ed.

https://homepages.cwi.nl/~aeb/games/sudoku/nrc.html

6,337,174,388,428,800 = 17,463,553,760 x 9!
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