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M-Wing

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5065
Location: Rochester, NY, USA

PostPosted: Mon Mar 09, 2009 11:56 pm    Post subject: M-Wing Reply with quote

This is the BB SH from 6-18-08 after an X-Wing:

Code:

+-------------+----------+--------------+
| 12  4   5   | 6  37 8  | 123  9   237 |
| 3   7   28  | 5  9  1  | 28   4   6   |
| 9   18  6   | 34 2  47 | 135  358 357 |
+-------------+----------+--------------+
| 6   5   34  | 8  37 47 | 9    2   1   |
| 148 138 9   | 34 6  2  | 7    358 35  |
| 7   2   38  | 1  5  9  | 38   6   4   |
+-------------+----------+--------------+
| 248 38  7   | 9  1  6  | 2345 35  235 |
| 5   9   1   | 2  4  3  | 6    7   8   |
| 24  6   234 | 7  8  5  | 234  1   9   |
+-------------+----------+--------------+

Play this puzzle online at the Daily Sudoku site

Note the 34 cells in boxes 45. They can be connected by either 3s or 4s. If they're connected by 4s, each 3 pincer can be extended with the new pincers being in r3c4 and r4c5. This seems to work out so simply that I can't help but think that there is some simpler coloring to accomplish same, but I don't see it.

Does anyone?
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Tue Mar 10, 2009 5:06 am    Post subject: Re: M-Wing Reply with quote

Hi, Marty, and all. I'm Luke and this is my first post here. I saw the M-wing header and came right in and made myself comfortable!
Marty R. wrote:
This seems to work out so simply that I can't help but think that there is some simpler coloring to accomplish same, but I don't see it.
Does anyone?
When I was looking for the M-wing I noticed there's an X-wing on (3) in r69c37 that does some damage. I'm more interested in the M-wing, though.
Quote:
Note the 34 cells in boxes 45. They can be connected by either 3s or 4s.
I'm new to M-wings. W, X, Y, yes, M no. However, I think I see the set-up: complementary pairs connected by an even # of strong links on one of the candidates. In fact, the set-up holds true if either (3) or (4) supply the "strong links" component. What I can't find either way is what gets zapped! What is the elimination, or are you talking about an extended/combination M-wing of some kind that leads to an elimination? I've got a way of missing the obvious....

Thanks for your insight.
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Marty R.



Joined: 12 Feb 2006
Posts: 5065
Location: Rochester, NY, USA

PostPosted: Tue Mar 10, 2009 5:15 am    Post subject: Reply with quote

Hi Luke, welcome to the forum. I connected the pairs by the strong link on 4, so the 3 would be the pincer. There are no eliminations by extending just one 3. So I extended the 3 from r4c3 to r4c5 and the other from r5c4 to r3c4. The new pincers in r4c5 and r3c4 take out the 3s from r1c5 and r5c4.

Hope that make sense.

P.S. The M-Wing is discussed in the 3rd post in this thread.

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Tue Mar 10, 2009 5:39 am    Post subject: Reply with quote

Marty R. wrote:
There are no eliminations by extending just one 3.
Whew, glad for that, that's what I was looking for Smile.

So there is indeed an "extended" M-wing. Each (3) has a strong link extension, and the victim will be any candidate that can see both ends. Cool. The link you cited (and others) make no mention of this idea.

I like this. Learned something good already. Thanks.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Mar 10, 2009 5:53 am    Post subject: Reply with quote

Marty,

I don't understand what you're trying to say. r4c3 and r5c4 are not pincers of an M-Wing that I can see. The only M-Wing with <3> involving these cells that I notice is:
(3=4)r4c3 - (4)r4c6=(4-3)r5c4=(3)r3c4
So, the pincers are r4c3 and r3c4. You can use these to eliminate <3> from r3c7 (via the ERs in boxes 7 and 9), though I don't know if that is very helpful.

Also, pincers can not be transported to their conjugate pair companion. They must be transported via such a companion to another candidate.

Can you explain the structure of your M-Wing for me?

Luke,

Welcome!

(That X-Wing reduces the grid to a BUG+1.)
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Tue Mar 10, 2009 12:22 pm    Post subject: Reply with quote

Marty R. wrote:
Hi Luke, welcome to the forum. I connected the pairs by the strong link on 4, so the 3 would be the pincer. There are no eliminations by extending just one 3. So I extended the 3 from r4c3 to r4c5 and the other from r5c4 to r3c4. The new pincers in r4c5 and r3c4 take out the 3s from r1c5 and r5c4.

Looked at this again in the light of day. Only r1c5 can see both ends of your extended pincers, so that is the elimination. The other eliminations follow from there.

If M-wing can be extended with strong links, what about W-wing Question

Thanks for the welcome, Asellus! Or I should say, "Howdy, neighbor."
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Marty R.



Joined: 12 Feb 2006
Posts: 5065
Location: Rochester, NY, USA

PostPosted: Tue Mar 10, 2009 2:58 pm    Post subject: Reply with quote

Quote:
I don't understand what you're trying to say.

I don't either. After I shut down last night I was lying in bed thinking about this and realized that I was wrong. I was dreading booting up this morning and experiencing the embarrassment and humiliation of seeing my nonsense posted up there for the world to see.

Mea culpa. Embarassed Embarassed Embarassed

Quote:
If M-wing can be extended with strong links, what about
W-wing

If done correctly, pincers of W-Wings can be extended (transported), as can the pincers of XY-Wings. Pincer transport is something I learned just in the last year or so and it's an extremely valuable tool to have in one's arsenal.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Tue Mar 10, 2009 4:19 pm    Post subject: Reply with quote

Don't kick yourself. You've helped me get up to speed on M-wings, so it's all good.

I'll look into the "pincer transport" for W- and XY- wings as well. Thanks.
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