What are the chances of a puzzle being minimal...

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What are the chances of a puzzle being minimal...

Postby 999_Springs » Thu Jan 01, 2009 4:03 am

...if you are given the number of clues it has? Clearly it will decrease from 100% for a 17-clue puzzle to 0% for a 38-or-so-clue puzzle, but what happens in between?
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Postby StrmCkr » Thu Jan 01, 2009 6:59 am

the curve is formed based on cover set logic.

Code: Select all
{18-39 could be minimal}
100% at 17 clues
|                     

       100% at 39 clues. {chance to find this is extremly slim}.
|
0% -81 clues


http://forum.enjoysudoku.com/viewtopic.php?t=5469&postdays=0&postorder=asc&start=90

the perentage has variation depending
on the arrangment of all cover set logic.
the more sets covering the same logical forcing the same assertion = non-minimal.
Last edited by StrmCkr on Fri Jan 02, 2009 5:48 am, edited 3 times in total.
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Postby coloin » Fri Jan 02, 2009 4:22 am

A lot of work was done here by JPF,Ocean and Red Ed

http://forum.enjoysudoku.com/viewtopic.php?t=4771&postdays=0&postorder=asc&start=30

EDIT

From this I take it that if you reduce a solution grid to

43 clues ~ 50 % will be valid, [none will be minimal]

Generating minimal puzzles from a full grid - is relativly easy to get 22-28 clue minimal puzzles. Its difficult to produce a minimal puzzle with >28 clues !

Generating puzzles from other minimal puzzles with the same number of clues will give both minimal and non-minimal puzzles.

from making 20s-19s-18s-17s

10% of 20s are non minimal
5% of 19s are non-minimal
1% of 18s are non-minimal

taking a 24 clue minimal puzzle and making many others - 75% of these were non-minimal

30 clues - 99.9 % non-minimal

StrmCkr wrote:100% at 39 clues. {chance to find this is slim}.

"slim" should read "extremely slim" [ approx 1 in 10^30 perhaps]

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