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stevieboy
Joined: 25 Jan 2008
Posts: 31
Location: Michigan
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 Posted: Fri May 09, 2008 1:46 pm Post subject: |
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WOW!! What a discussion I've seemed to spark!
OK, it's the next day, and I've just read nataraj's patient words-of-wisdom (and, the others as well)...can't thank you all enough for the interest you're all showing on the May 8th vh.
First of all, I "thought" that I had read SOMEWHERE that "my" method was legitimate, but, wasn't sure where.
NOW, I've found the link:
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
Chapter 3 in this link explains (I believe) what I was trying to express; if it doesn't, then please tell me why - the "beginning" point of my link, and my "ending" point are not an exact pair, and all the the links in-between are strong "one or the other" pairs (the Row 8 2's, upwards to the Row 3 5's, and left to the other 5 or 3)...the common 5's between the beginning and end points (Box 4, C1) can be eliminated, just like it's done in the Chapter 3 example.
I believe I'm correct, aren't I?
I've honestly seen this type of thing in almost all the puzzles I've been solving in the last couple of weeks - and, I've been 100% correct when viewing the results!
BTW, nataraj, I hadn't yet made the eliminations necessary to see the
XY-Wing you described; but, you're right, it's there. (And), I didn't notice, but, now see the W-Wing.
AGAIN, A MAJOR THANK YOU!!! |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri May 09, 2008 8:19 pm Post subject: |
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stevieboy,
The reference you provide is to a discussion of the M-Wing, which involves something called a remote complementary pair. But, that isn't what you're dealing with here.
However, the M-Wing got its name from the fact that it is a simple application of Medusa Coloring. Medusa involves coloring the conjugate links among various digits and finding eliminations of digits that are "trapped" by the opposing color polarities. In your sequence of links, you don't seem to be paying attention to these polarities. Using the color marks may help you see this.
You may also want to read up a bit on Medusa. Here is a link. (You could search for others.) I suggest you first read about basic coloring at this link. There, another concept known as a color "wrap" is explained as well.
Now, here's your grid, as much as I can reconstruct it from your comments, with the links you mention color marked (per Medusa):
| Code: | +------------------+-------------+--------------+
| 8 6 4 | 2 7 9 | 3 15 15 |
| 1 2 9 | 6 5 3 | 4 7 8 |
| 3g5r 7 3r5g | 1 8 4 | 6 2 9 |
+------------------+-------------+--------------+
| 35 1 7 | 34 6 2 | 9 8 45 |
| 256 45 8 | 9 34 7 | 1 345 26 |
| 269 49 23 | 5 1 8 | 7 34 26 |
+------------------+-------------+--------------+
| 7 3 6 | 8 9 5 | 2 14 14 |
| 2r59 59 2g5r | 34 34 1 | 8 6 7 |
| 4 8 1 | 7 2 6 | 5 9 3 |
+------------------+-------------+--------------+ |
(As nataraj noted, the <5>s at r58c1 can be removed due to the 35 Naked Pair in r34c1. But, we'll ignore that.)
You claim that your links allow removal of the <5>s at r45c1. Let's look. In order to be "trapped," the <5> at r4c1 must "see" both a 5r and a 5g. It can see 5r in r3c1; but it cannot see any 5g. It could also be trapped if it shared its cell with any green digit and sees that 5r. But, that's not the case either. So, based only on your set of links, there is no elimination.
The same arguments hold for the <5> in r5c1.
Let's see what happens if we continue coloring available links (i.e., expand the Medusa cluster):
| Code: | +------------------+-------------+--------------+
| 8 6 4 | 2 7 9 | 3 15 15 |
| 1 2 9 | 6 5 3 | 4 7 8 |
| 3g5r 7 3r5g | 1 8 4 | 6 2 9 |
+------------------+-------------+--------------+
| 3r5g 1 7 | 3g4r 6 2 | 9 8 45 |
| 2-56 #4g5r 8 | 9 #3r4g 7 | 1 3g45 26 |
| 269 4r9g 2r3g | 5 1 8 | 7 3r4g 26 |
+------------------+-------------+--------------+
| 7 3 6 | 8 9 5 | 2 14 14 |
| 2r-59 5g9r 2g5r | 3r4g 3g4r 1 | 8 6 7 |
| 4 8 1 | 7 2 6 | 5 9 3 |
+------------------+-------------+--------------+ |
Not surprisingly, the <5>s in that Naked Pair have opposite colors and eliminate the other <5>s in c1. (But, we didn't need Medusa for that!)
Now, look at the <4> in r5c5 (marked 4g, as it happens... but ignore that for the moment). It sees 4r in r4c4 and r8c5. And, it sees 4g in r5c2. So, it is trapped and can be eliminated. (Notice that this just our XY Wing elimination.)
However, you can also note that there are two 4g values in r5 (marked #). This is a Medusa Wrap: There cannot be two values of the same polarity in a single house (or a single cell), so ALL g values are false and ALL r values are true. (This isn't really remarkable: just trapping that 4g in r5c5 causes an equivalent cascade of determinations.)
Having, I hope, helped you learn about using those multi-digit end-to-end links a bit more reliably, I should say this: Most sudoku solvers consider the use of Medusa in puzzles that can be solved with common advanced techniques such as the various "fish" and "wing" techniques, etc., to be overkill. Certainly, spotting one of those XY Wings in this puzzle is probably a lot easier than doing all the Medusa color marking. |
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