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June 21 VH

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Jun 21, 2007 2:54 pm    Post subject: June 21 VH Reply with quote

Are the VH's getting easier, or have a learned something?

Today's VH had parallel pairs in columns 4 and 6 of rows 1 and 5,
requiring a 2 in R1C4, and rest was simple elimination.
Or was I lucky?

Earl[/b]
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jLo



Joined: 30 Apr 2007
Posts: 55

PostPosted: Thu Jun 21, 2007 3:28 pm    Post subject: Reply with quote

Quote:

Today's VH had parallel pairs in columns 4 and 6 of rows 1 and 5,
requiring a 2 in R1C4, and rest was simple elimination.
Or was I lucky?



At least 3 ways to go here. The UR you noted, an XY-wing, or a W-wing. All in the
same general area.
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Jun 21, 2007 3:49 pm    Post subject: June 21 Reply with quote

jlo,

Would you please show me the W wing.

Earl
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Thu Jun 21, 2007 4:06 pm    Post subject: Reply with quote

Hi Earl - it would be helpful if you could paste the grid. Marty has left some instructions in the Site Help forum.
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jLo



Joined: 30 Apr 2007
Posts: 55

PostPosted: Thu Jun 21, 2007 6:26 pm    Post subject: Reply with quote

Quote:

Would you please show me the W wing


Code:

+--------------+------------+--------------+
|          134 | 125     15 |      234 14  |
| 135 23   25  |            | 136      16  |
|          14  |     12     |      24      |
+--------------+------------+--------------+
| 35       256 | 79      23 | 57   69      |
|     49       | 15      15 |      49      |
| 345 2349 256 | 79      23 | 57       469 |
+--------------+------------+--------------+
|     34   13  |            | 134          |
| 134          | 12  123    | 1346 369 169 |
|              |     13     | 13           |
+--------------+------------+--------------+



W-wing with the 14's in R1C9,R3c3.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Thu Jun 21, 2007 10:12 pm    Post subject: Reply with quote

Yes it did seem easy. There were a couple of obvious x wings on 7's and 5's - and a Unique Rectangle of three 15's and a 152 on rows 1 and 5.

Where can I find an explanation for this W-Wing thing. I've been avoiding it because it seems to be a recent and contrived innovation. X,Y,Z are logical coordinates. W ain't.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Fri Jun 22, 2007 12:05 am    Post subject: Reply with quote

Quote:
Where can I find an explanation for this W-Wing thing. I've been avoiding it because it seems to be a recent and contrived innovation. X,Y,Z are logical coordinates. W ain't.


It was discussed in this thread:

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=1914
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Fri Jun 22, 2007 6:02 am    Post subject: Reply with quote

Could the W-wing be a variant on remote pairs ?
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Jun 22, 2007 11:23 am    Post subject: Reply with quote

I think it’s a matter of how broadly you want to look at it. As I see it, both are examples of double implication chains (= nice chains) with bivalue cells, say [xy], at the ends:

[xy] -x- a … d -x- [xy]

Because the labels at the ends are the same, here x, and both end links are weak, y may be eliminated from any common associate of the end cells. This applies irrespective of the links between cells a and d.

The distinctive feature of remote pairs is that all the nodes are of the [xy] type and all the links are weak:

[xy] -x- [xy] -y- … -y- [xy] -x- [xy]

In the case of the w-wing it is the shortness of the chain and a single strong link:

[xy] -x- a =x= b -x- [xy]

These characteristics make the patterns relatively easy to spot and use. I find a w-wing more quickly than an xy-wing but that may be because I rarely use pencil marks in intermediate puzzles.

Steve.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Fri Jun 22, 2007 11:55 am    Post subject: Reply with quote

Thanks Steve - it does depend on how you look at it.

The other thing more simplistically, is that the human eye is probably more easily drawn to pairs in the W-wing (even in different boxes) than the three bivalues in an X-Y. In an X-Y wing you still need to find all three bivalue squares to be sure that you have one.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Fri Jun 22, 2007 2:54 pm    Post subject: Reply with quote

I went back to look at the post explaining W Wings - like I was told to do (above). Found the first few posts confusing but kudos to TexCat for putting everything into a easy to follow diagram. (though still can't figure why he uses letters GW to denote a pair)

Also still not clear in above post from JLo how he eliminated the 2 from R3C3 to get a 14.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Jun 22, 2007 6:05 pm    Post subject: Reply with quote

I think this is the position you are referring to.

Code:
+-----------------------+
| 6 8 . | . 7 . | 9 . . |
| . . . | 4 9 8 | . 7 . |
| 9 7 . | 3 . 6 | 8 . 5 |
-------------------------
| . 1 . | . 4 . | . . 8 |
| 8 . 7 | . 6 . | 2 . 3 |
| . . . | . 8 . | . 1 . |
-------------------------
| 2 . . | 6 5 9 | . 8 7 |
| . 5 8 | . . 7 | . . . |
| 7 6 9 | 8 . 4 | . 5 2 |
+-----------------------+

In boxes 2 and 3, 2 can be placed only in the first and third rows. So in box 1 it must be in the second.

As to TexCat’s name for the pair, he may have had in mind George Woods, who first drew attention to the pattern on this site.

Steve
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