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Colors - Thought I had it!
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kranser

Joined: 18 Aug 2005
Posts: 35
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PostPosted: Wed Nov 09, 2005 12:45 pm    Post subject: Reply with quote

rkral wrote:
kranser wrote:
And it also shows that Simple Sudoku opts to recolour the grid after a colouring rule 1 elimination - which sounds like a good idea to me

I may have mislead you by saying "the next coloring", but you're also jumping to a conclusion. There is no "opting to recolour" per se. For the next hint after the elimination of r4c5#1, Simple Sudoku first tries the simplest techniques. None yield eliminations until the "coloring rule 2" technique.


...and I presume that you call "coloring rule 2", "coloring rule 1", correct?

So instead of recolouring, you've found the best method to be for the colouring algorithm to stop looking for further eliminations from the current colors (despite the fact that more eliminations are possible) and look for other deduction methods - which turn out to require coloring again - but this time with slightly different cells colored?
*makes a note to include that in his solver*

If it does matter which order (and how) the coloring rules are applied, and the above implementation seems to work best, maybe this should be defined in the coloring technique definition - so that in theory the same eliminations will be found by all solvers that abide by the technique.

It bothers me that currently the coloring technique allows different implementations to find different eliminations (due to varying the way the rules are applied). As it means that possibly a sudoku will be found that requires coloring, but is unsolveable by some solvers due to the technique not being fully defined.

Maybe I'm being a but pedantic though, as ofcourse solvers that look for XY-Wing and XYZ-Wing before colouring will also get different colourings found (and some puzzles may not even need colouring to be solved after these techniques). So am I being slightly crazy by wanting the colouring rules to be prioritized?

Kranser.
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angusj
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Joined: 18 Jun 2005
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PostPosted: Wed Nov 09, 2005 1:46 pm    Post subject: Reply with quote

kranser wrote:
So am I being slightly crazy by wanting the colouring rules to be prioritized?

Ever so slightly Very Happy.
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byteman

Joined: 07 Nov 2005
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PostPosted: Wed Nov 09, 2005 9:07 pm    Post subject: Reply with quote

Quote:
Coloring highlights conjugate pairs. When A = 1, a cannot be 1, so A and a exclude each other.
There is an a in R4C1, sharing a row with R5C5 and R5C6.
There is an A in R6C4, sharing a box with R5C5 and R5C6.

"group" is the common name for row, column or box (anything that can only contain 9 different digits) see Gaby's list


Since either A or a contains digit 1, R5C5 and R5C6 would be eliminated in both situations.


I believe that you meant R4C5 and R4C6 - but thank you, that was very helpful.

Quote:
Every cell (square) is a member of three groups. As some look at it, every cell has 20 "buddies", 8 in its row, 8 in its column, and 4 more in its box (that weren't already counted as part of the row and column).


That "buddies" explanation was very helpful.

I think I do "have it" now - thanks everyone!
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