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| MotsCroises
| Joined: 08 Dec 2005 | Posts: 10 | : | | Items |
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Posted: Tue Dec 13, 2005 8:20 pm Post subject: XY-Chain and Coloring in the same method ? |
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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 :
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 |
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| Ruud Site Admin
| Joined: 17 Sep 2005 | Posts: 708 | : | Location: Netherlands | Items |
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Posted: Tue Dec 13, 2005 8:39 pm Post subject: |
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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 _________________ Meet me at sudocue.net
Last edited by Ruud on Mon Jan 09, 2006 10:23 pm; edited 1 time in total |
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| MotsCroises
| Joined: 08 Dec 2005 | Posts: 10 | : | | Items |
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Posted: Tue Dec 13, 2005 8:53 pm Post subject: |
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Ruud wrote: | 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. |
Hi Ruud,
Yes, but it's not an XY-Wing, but a XY-Chain (for the beginning), I think that can be a forcing chain but not sure for the name...
You can just look at: XY-Chain for my diagram.
Thanks |
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| Ruud Site Admin
| Joined: 17 Sep 2005 | Posts: 708 | : | Location: Netherlands | Items |
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Posted: Tue Dec 13, 2005 9:11 pm Post subject: |
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Henri wrote: | You can just look at: XY-Chain for my diagram. |
I see. Most people just call that just a forcing chain.
You can indeed combine these techniques. One of the best implementations is Bob Hanson's 3D Medusa technique. Other people do similar things and call it "ultracolouring" or "supercolouring". Search for these terms and you will find lots of info.
Ruud. _________________ Meet me at sudocue.net |
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| MotsCroises
| Joined: 08 Dec 2005 | Posts: 10 | : | | Items |
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Posted: Tue Dec 13, 2005 9:32 pm Post subject: |
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Ruud wrote: | You can indeed combine these techniques. One of the best implementations is Bob Hanson's 3D Medusa technique. Other people do similar things and call it "ultracolouring" or "supercolouring". |
Thanks,
I'm not 100% sure it's the same method… If it's possible to have others confirmations… |
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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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Posted: Thu Dec 15, 2005 12:39 am Post subject: |
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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 |
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| rkral
| Joined: 21 Oct 2005 | Posts: 233 | : | | Items |
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Posted: Fri Dec 16, 2005 5:09 pm Post subject: Re: XY-Chain and Coloring in the same method ? |
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MotsCroises wrote: | My question is: according to you, is this a new solution method ? If not, what is the method's name? |
See bilocation/bivalue plot: description and exercise at the Player's Forum.
Your illustration contains a "nice loop".
.......... Code: |
Nice loop:
[r2c8]-Z-[r2c4]-A-[r4c4]-B-[r6c6]=C=[r6c3]=C=[r1c3]=C=[r3c1]=C=[r7c1]=C=[r8c2]-D-[r8c8]-Z-[r2c8]
With double implication chains:
r1c3<>C => r6c3=C => r6c6=B => r4c4=A => r2c4=Z => r2c8<>Z
r1c3=C => r3c1<>C => r7c1=C => r8c2=D => r8c8=Z => r2c8<>Z
... and since either r1c3=C or r1c3<>C, then r2c8<>Z |
The symbol '=' indicates a bilocation link (conjugate pair), and '-' indicates a bivalue link. While it's obvious the '-' would be used between two bivalued locations, I'm unsure of which symbol to use at bilocation/bivalue junctions. (You're looking at my first nice-loop equation. )
In general, I agree with Ruud's statement that your illustration is an example of a forcing chain.
Last edited by rkral on Fri Dec 16, 2005 5:55 pm; edited 3 times in total |
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| MotsCroises
| Joined: 08 Dec 2005 | Posts: 10 | : | | Items |
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Posted: Fri Dec 16, 2005 5:36 pm Post subject: Re: XY-Chain and Coloring in the same method ? |
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rkral wrote: | In general, I agree with Ruud's statement that your illustration is an example of a forcing chain. |
Thanks Rkral,
I think for Ruud it's more a 3D Medusa technique. After some private mails from Bob Hanson, I think it's a simplified version of 3D Medusa.
In my site, you can see the opposite version with this diagram:
(Coloring-Forcing Chain-Coloring in French)
For me it's an interesting help, for a real Sudoku player (not a computer). Because when you look for a Coloring or XY path, you often found just 1 or 2 cells with the same candidate but with/without a needed value. With this explanation, it's possible to know how to use it…
But it's only my point of view |
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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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