XY-Chain and Coloring in the same method ?

MotsCroises

Hi,

In order to explain some Sudoku with a XY-Chain with more than 3 candidates in some cells, I tried with another member of a Sudoku French forum to find a special case.

I found what looks like a XY-Chain, with a special case in the beginning (or in the end),

Then going deeper into the problem, I found a general explanation for this case.

You can look on my website (in French), for pictures Wink

:
http://www.mots-croises.ch/Manuels/Sudoku/XY-Color.htm

Or here, in English Google translation.

You can also have a look at the diagram (example):

I begin with a XY-Chain: (XY-Wing with more than 3 cells).

And in the chain, I switch from XY-Chain to Coloring (even number of cells).

And at the end, I continue with XY-Chain for the last cells (one cell or more).

My question is: according to you, is this a new solution method ? If not, what is the method's name?

Thanks in advance

Henri

Ruud · Site Admin

Hi Henri,

With coloring you only look at the placements of a single digit. Colors are applied where only 2 candidates exist in a row, column or box.

XY-Wing is a short forcing chain with candidates XY, XZ and YX, where both the XZ and the YZ cells share a house with the XY cell.

I have implemented an option in Sudo Cue to combine XY-Wings with coloring. This looks like what you're doing now, although I do not understand the French explanations....

Check this topic I started earlier on this forum: http://www.setbb.com/phpbb/viewtopic.php?t=340&mforum=sudoku

Ruud.

Edit: URL updated
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MotsCroises · Posted: Tue Dec 13, 2005 8:53 pm Post subject:

Ruud · Site Admin

MotsCroises · Posted: Tue Dec 13, 2005 9:32 pm Post subject:

Bob Hanson · Posted: Thu Dec 15, 2005 12:39 am Post subject:

What Ruud is saying, I think, is that there are "cycles" and there are
methods. You've described, I think, an interesting cycle that
involves an nice combination of "conjugate pairs" and "two-valued
cells." It's a bit too complicated to be very general or to get a fancy
name like "XY-Wing", I think.

It falls under the category "single strong chain with incompatibly weakly
linked node" or something like that. Moderately tricky. Keep looking
for these when you have a difficult puzzle. you will find them everywhere.

You can also take any puzzle and pop it into http://www.stolaf.edu/people/hansonr/sudoku pretty quickly and just see what's there of this type.
Click "All" to see everything that can be done with the current state
of the solution or "Solve" to watch it be completed. I like to then go
back and click on "snapshot" and maybe "Step" a bit through the
solution to learn what it was doing. NOT always obvious!
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr

rkral · Last edited by rkral on Fri Dec 16, 2005 5:55 pm; edited 3 times in total

MotsCroises

Bob Hanson · Posted: Fri Dec 16, 2005 5:47 pm Post subject:

I posted some ideas like this at the programmers forum:

http://www.setbb.com/phpbb/viewtopic.php?t=407&mforum=sudoku
http://www.setbb.com/phpbb/viewtopic.php?t=408&mforum=sudoku
http://www.setbb.com/phpbb/viewtopic.php?t=409&mforum=sudoku

They aren't particularly exciting. My point was, like yours, that you can
spot this sort of thing easily enough by hand if you know what to look for.
Sort of an extended "multicoloring technique". Or an application of
"supercoloring", I think.
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr