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arkietech
Joined: 31 Jul 2008 Posts: 1832 Location: Northwest Arkansas USA

Posted: Mon Sep 03, 2012 5:14 pm Post subject: Half Mwing 


I am trying to identify what a half mwing is. The following puzzle, identified as a half mwing, located at
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
Code: 
++++
 59 45 1  47 6 79  2 3 8 
 7 34 8  5 34 2  1 9 6 
 69 36 2  1 8 39  5 7 4 
++++
 156 156 39  247 34A 8  347B 16 29 
 4 128 39  6 5 137  37 18 29 
 126 1268 7  24 9 13D  34C 168 5 
++++
 3 9 4  8 1 5  6 2 7 
 12 12 5  9 7 6  8 4 3 
 8 7 6  3 2 4  9 5 1 
++++
Either:
1. A is <3>.
Or:
2. A is <4>, C is <4>, D is <3>.
Any cell that sees both A and D cannot be <3>. In particular, we can take out <3> from R5C6.

I tried to put what I see in Eureka and get:
(3=4)r4c5r4c7=(43)r6c7=3r6c6 => 3r5c6
This looks like the classic mwing:
(X=Y)Y=(YX)=X
What am I missing? 

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

Posted: Mon Sep 03, 2012 5:38 pm Post subject: 


Quote:  What am I missing? 
Beats me. I'm no theoretician, but if I played and reported that move I'd call it an MWing. I wonder who'd correct me and say it's just a half. 

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keith
Joined: 19 Sep 2005 Posts: 3340 Location: near Detroit, Michigan, USA

Posted: Tue Sep 04, 2012 9:08 am Post subject: 


The original Mwing was built on the idea of a complementary pair:
Two cells, each XY, have the same solution, X or Y. Let's say it is X. Then, on either end you can add a strong link in Y:
XY ..... XY = Y or Y = XY ..... XY
and the end cells are pincers on Y.
The half Mwing does not need a complementary pair. All it needs is the following:
XY ..... aXY
where X in the first cell forces X in the cell containing aXY where a is any other candidates. Then you can add the strong link on Y:
XY ..... aXY = Y
and the end cells are pincers on Y.
It's a "half" wing because it only works one way. There is no requirement that X in aXY has any implication for the cell XY.
Over time, we've forgotten the distinction.
Keith 

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arkietech
Joined: 31 Jul 2008 Posts: 1832 Location: Northwest Arkansas USA

Posted: Tue Sep 04, 2012 11:33 am Post subject: 


keith wrote:  The original Mwing was built on the idea of a complementary pair:
Two cells, each XY, have the same solution, X or Y. Let's say it is X. Then, on either end you can add a strong link in Y:
XY ..... XY = Y or Y = XY ..... XY
and the end cells are pincers on Y.
The half Mwing does not need a complementary pair. All it needs is the following:
XY ..... aXY
where X in the first cell forces X in the cell containing aXY where a is any other candidates. Then you can add the strong link on Y:
XY ..... aXY = Y
and the end cells are pincers on Y.
It's a "half" wing because it only works one way. There is no requirement that X in aXY has any implication for the cell XY.
Over time, we've forgotten the distinction.
Keith 
The "half" mwing is a sis 3 like all other wings. The original must have been a sis 5?
Thanks Keith 

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


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