From Sudopedia, the free Sudoku reference guide
Talk:X-Colors
From Sudopedia
- The original long post about the X-Colors technique has been copied to the main page and is removed from this discussion page to keep it short. However, the original post can be accessed through the page history.
Contents |
Extension
I thought that your article is well written, especially the examples. The only thing I might want to see fixed is the formatting of the article, but that is a small issue and I might attempt it later. Thanks for the great work!
A comment on the technique itself. I guess someone else must have figured it out already and posted this in some forum, but here goes anyway. I thought that X-Colors can be easily extended with the basic Pointing Pairs technique, although I am not sure whether this actually increases the power of X-Colors.
A contrived example, in the form of a fish diagram. The initial cluster is marked A and B:
. XA . | X X / | . . . . / . | / / X | . . . . / . | / / X | . . . --------+---------+-------- . / . | . . / | . . . . / . | . . / | . . . . / . | . . / | . . . --------+---------+-------- . / . | . . / | . . . . / . | . . / | . . . . XB . | . . X | . . .
We can "cancel" A from r1c4 and r1c5. Now the remaining cells in box 2 that can have A are r2c6 and r3c6, all located in column 6. By Pointing Pairs, r9c6 is not A. Because r9c2 is B, r9c6 is not B either. So we can eliminate the candidate from r9c6. Thus, we have replicated Empty Rectangle using this simple extension of X-Colors.
--unkx80 04:55, 1 December 2006 (CET)
I did some formatting and spelling corrections on your article. Hope it is okay with you.
--unkx80 20:46, 1 December 2006 (CET)
Thank you for the formatting, it is now much better understandable. And thanks for making corrections in my english... I do offer myself to make that work too... when Sudopedia in Spanish exists!!
On the example you mentioned, I think that X-Colors and Connecting Pairs are different techniques that, in some (maybe many) situations solve the same puzzles... but I don't think in Every Case. What I really like of X-Colors is that it is simple to define, and very powerful. The simple extension you mention, is really simple when you see it, but it is not as simple when you want to include it in the algorithm, at least it is not for me. If you can, please upgrade the definition, you're welcome... BTW, I have corrected one paragraph in the main article that, in some sense, can be erroneous or misinterpreted, so I have eliminated.
Pedro
I think I will leave your description of X-Colors as it is (except for, perhaps, additional language corrections). Rather, I will tack the extension at the end of the article and probably describe it via an example.
--unkx80 16:52, 2 December 2006 (CET)
X-Wing and X-Colors
Great your definition of "Augmented X-Colors"!! It gives new power to the technique that even I (the "discoverer" or maybe the "integrator" of the technique) didn't realized. I have slightly modified the paragraph when you mention the use of X-Wing together with X-Colors, because both actually makes the same eliminations. I expect you agree with that correction. Pedro.
Hmm... I can't prove or refute your claim right now, so lets leave it as it is right now. When I was running through examples for ER manually earlier, I thought I came across some examples that can make eliminations using X-Colors + X-Wing, but for some reason I didn't use them and forgot to record them, and didn't check whether these can be replicated using X-Colors alone. Anyway, a conceptual example that illustrates my idea follows:
. X1 . | . . . | . . . X X X | X / X | / / / . . . | . . . | . . . --------+---------+-------- / X / | X / X | / / / . . . | . . . | . . . . . . | . . . | . . . --------+---------+-------- . . . | / / / | . . . . . . | / X2 / | . . . . . . | X / X | . . .
If you color X1 with blue, then r2c123 and r3c1 cannot be colored with blue. Then an X-Wing appears at r24c46 and causes r9c46 to be not blue. Thus, X2 can be colored blue.
My two cents.
--unkx80 22:17, 2 December 2006 (CET)
Cluster size
The following sentence appears in the introduction.
- However, for the technique to be effective, you need a sizable color cluster to begin with.
Ruud and Pedro, can you verify whether this statement is true for most cases? The examples given make it seem that the initial cluster size is not very important, but I haven't used it enough to tell. Thanks.
--unkx80 22:27, 2 December 2006 (CET)
Credit Where is Due Please
I am getting peeved by the claims that X-Colors is the sole work of Pedro. His original work was faulty and had to be corrected. When this was done he was referred to the description of Weak Colouring where the banana skin concerned was described. He work therefore extended a method which had already been discovered, making it bifurcative in the process.
I don't particularly want to have my name in lights, but I don't believe that someone should be allowed to insinuate that he was the sole inventor, and the last edit to the article, "This technique is invented by Pedro Argal." has now gone a step too far as far as I am concerned.
Here are the original dicussions:
http://www.setbb.com/sudoku/viewtopic.php?t=1124&sid=b06a31bc63fa6a1895d14924fa0c842b&mforum=sudoku
http://www.sudoku.org.uk/cgi-bin/discus/show.cgi?tpc=2&post=6273#POST6273
I now provide a thumbnail description of Weak Coloring in a form which may be suitable to use as an Sudopedia entry. If an example is needed then the one used in my original piece. If someone would like to tidy it up and insert it in the most appropriate place I would be more than happy.
Description of Weak Colors deleted. It is now shown under it's own entry - thanks unkx80
David P Bird 4th Dec 3:13pm GMT
Hi David, I was the one who added the line "This technique is invented by Pedro Argal." I guess I am mistaken and I apologize, and I have deleted that line.
I suggest that your description on Weak Coloring be put in a separate article. Not feeling too well right now, so I leave it to someone else to do this work.
--unkx80 17:06, 4 December 2006 (CET)
I consider this issue closed, but I would like a to add a general remark.
Solving techniques are often the work of many contributors, using different names and introducing them in different discussion platforms. So far, I have avoided crditing specific people in Sudopedia, even when I knew who came up with the original concept. An external link to such an introduction should be sufficient.
--Ruud 19:08, 4 December 2006 (CET)
1) yes, you seem to be right, and X-Wing seems that it is possible to link with X-Colors in a form very seemed with Finned Fish. I haven't found examples of that, but after reading your post, it seems you're right... and I was, then, wrong. If I get any example of that, I will provide it. Thanks again.
Ruud: To begin with, you need at least a cluster of two conjugated cells. It is a "sizable" cluster (of size 2). The definition inserted in the main article surely suggest that you need a lot of colored cells to be effective, and, in some example you can see that only three colored cells can make an elimination. I will agree with any solution you choose for the main article, in order to get the definition as clear as possible.
David: I am sorry for not mentioning all the work made months ago, by yourself and others, that complete the technique, but I agree with the administrator that a link to the original article will suffice. BTW, when I publish for the first time my discoverings, I didn't know about your Weak Coloring technique, that works in the same direction. You are right, probably you were the first one in publish your Weak Coloring. Your credit for it. I agree again with the main idea that most of the techniques shown here are the result of individual discoverings and a lot of common work.
You said you were preparing the definition of Weak Coloring, this will be good. My suggestion is, if you think X-Colors covers the same situations than Weak Coloring, then it would be good to link them and explain that fact. Pedro
About Bifurcation on X-Colors
I have been reading a little on bifurcation, and someone says that X-Colors is a bifurcative technique (David had mentioned it, and some others that know very much than me seem to agree with it).
Well, I don't see it. Sorry. Its algorithm is completely defined, and, given any position, and following strictly the steps, only one position arises. Using X-Colors you don't need bifurcation in the sense given in this sudopedia. You don't make any choice between two different candidates. Look at the examples. I don't see were the bifurcation is made. If all but one cell are peers of cells colored "A", then you can color this cell "A". No doubt. Concise, precise. If this sentence is false, you cannot color any cell. Step 4 is too well defined: if the conditions marked there are true, you can eliminate a candidate, or trueing a candidate in a cell, in the terms defined. If the conditions are not true, you can make any elimination, etc. Again: no doubt, precise, concise. I am a computer (software) specialist, and this algorithm has not trace of trial&error, or bifurcation. It is perfectly well defined an can be easily implemented in a software program.
Why do you say X-Colors is bifurcative? Caution: I am not saying you are not right!! I only say I don't understand why do you say that. Regards.
Pedro
Thanks
Unkx80 Thank you for dealing with my moan so quickly, somehow I missed that it was you that made the insertion, otherwise I would have phrased it differently! Sorry you're not well, I trust it's not Sudopedia burn out!
Pedro, Thanks for your friendly reply. I also agree that Ruud's policy to avoid crediting individuals is best, as readers can soon find that out by following the links.
You must be a quick reader because I gave my write-up above in 12 lines which you must have missed! But an example needs adding to show it in operation.
As it happens I don't have problems with bifurcation myself provided it is done methodically as in X-colors. One of the reasons why X-colors is classed as bifurcative is that the inference chains you must follow to decide what cells in a unit see a colored cell can be branched. In your example #4 the cell at r1c7 can be colored because the other cells in the same unit are seen by two different colored cells (twice! - for both box and row). This changes it from a coloring chain into a coloring net - like Nishio. In Weak Coloring each additional cell is colored using hinge mechanisms arising from just one previously colored cell so it should always be a single chain. (Note though, in one diagram, several chains might exist.) I can't remember if there was another reason someone else found when you were looking at the extensions to it.
Thank you, David. I did read your 12 lines (I knew them before), but what I meant was that maybe it would be good to begin a complete new chapter for Weak Coloring, instead of describing it in the discussion page of X-Colors, that's all!
And about bifurcation, you're right in the things you say... but I continue not seeing why X-Colors could be marked as bifurcative. In the example #4, you can actually color r1c7 both because it is the only cell in its row not been a peer of green cells and becasue it is the only cell in its box not been a peer of green cells. Perfect. It is green becuase it is doubly green. No problem. Note that the two prior asserts are connected by an OR operation. So, if one of them is true, the OR operation is true, and, if both are true, the OR operation is true too. Implementing the algorithm, probably you first check one house of the cell (let's say row), then other one (let's say column) and finally the restant house (box). Whenever you find that it is an exception cell, you color it and stop the proccess for this cell. Or maybe you continue and re-color again the cell. No difference.
And the fact that several networks can be found in a single position, yes, you are right again, but this sentence is true too with Simple Colors... and I have never seen anyone saying Simple Colors is not an "acceptable technique".
Anyway, the discussion in futile. If X-Colors (or any other technique) is useful to solve Sudokus, people will use it; if it is not useful, for any reason, will not be used and will be forgotten... Life is change. A pleasure to talk with you all, as always. Pedro Argal
David, not your fault for not being able to tell who made the insertion, because I did not login when I made that insertion. Anyway, Ruud's point is taken - obviously I never lurked around in the forums enough.
--unkx80 18:44, 5 December 2006 (CET)
