Colors Technique

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Colors Technique

Postby the Ghost » Sat Feb 07, 2015 12:14 am

I use Simple Sudoku and occasionally run across a "Colors Solution" offered by the hint that I don't understand and cannot find this pattern in the help index. Why is the box 1349 outlined in red shown as an "exclude 4" box?
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Sudoku Colors 1.jpg
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Re: Colors Technique

Postby JasonLion » Sat Feb 07, 2015 1:32 pm

Coloring looks for two groups of cells where either one color of cells all contain the digit, or the other color of cells all contain the digit. the colored groups are built up from conjugate pairs, pairs where either one cell contains 4 or the other cell contains 4. Conjugate pairs are connected together when one cell of a pair can see a cell of a different pair, in which case those two cells must be different colors. To "see" a cell means the cells share a house.

In your picture R2C45 can both "see" a cell of each color (in this case R2C9 and R3C6). Since one color or the other must contain 4, no cell which can see both colors can contain 4.

In the picture, there are actually three colors shown. The two colors used for coloring are the brighter green and the blue/cyan. They have also marked several cells in a paler green to show all of the remaining cells containing a pencil mark for 4 that are not yet colored.
Last edited by JasonLion on Sat Feb 07, 2015 4:35 pm, edited 1 time in total.
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Re: Colors Technique

Postby SteveG48 » Sat Feb 07, 2015 2:27 pm

Ghost, if you understand what Jason just said, you should notice that there is another cell that sees both colors. You can eliminate 4 from that cell as well. Can you spot it?
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Re: Colors Technique

Postby the Ghost » Sun Feb 08, 2015 4:16 am

JasonLion: thanks, that clears it up. Simple Sudoku has tremendous help, but didn't cover that case as far as I could find.
SteveG48: both R2C4 and R2C5 meet that criteria of seeing both R2C9 and R3C6.
the Ghost thanks you both
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Re: Colors Technique

Postby daj95376 » Tue Feb 10, 2015 11:31 pm

the Ghost wrote:JasonLion: thanks, that clears it up. Simple Sudoku has tremendous help, but didn't cover that case as far as I could find.

Simple Sudoku: F1 -> Index -> Colors -> Solving With Colors (halfway_down_long_article)


What Simple Sudoku doesn't do is tell you if a subset of its coloring pattern is a pattern that's been named beyond X-Wing and Swordfish. In your case, it's the Sashimi X-Wing in [c5+r7+c9] for value "4".

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