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Half M-wing

 
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arkietech



Joined: 31 Jul 2008
Posts: 1708
Location: Northwest Arkansas USA

PostPosted: Mon Sep 03, 2012 5:14 pm    Post subject: Half M-wing Reply with quote

I am trying to identify what a half m-wing is. The following puzzle, identified as a half m-wing, 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    1-37 | 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)r4c5-r4c7=(4-3)r6c7=3r6c6 => -3r5c6

This looks like the classic m-wing:

(X=Y)-Y=(Y-X)=X

What am I missing?
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Marty R.



Joined: 12 Feb 2006
Posts: 5122
Location: Rochester, NY, USA

PostPosted: Mon Sep 03, 2012 5:38 pm    Post subject: Reply with quote

Quote:
What am I missing?


Beats me. I'm no theoretician, but if I played and reported that move I'd call it an M-Wing. I wonder who'd correct me and say it's just a half.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Tue Sep 04, 2012 9:08 am    Post subject: Reply with quote

The original M-wing 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 M-wing 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: 1708
Location: Northwest Arkansas USA

PostPosted: Tue Sep 04, 2012 11:33 am    Post subject: Reply with quote

keith wrote:
The original M-wing 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 M-wing 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" m-wing is a sis 3 like all other wings. The original must have been a sis 5? Confused

Thanks Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5122
Location: Rochester, NY, USA

PostPosted: Tue Sep 04, 2012 3:43 pm    Post subject: Reply with quote

To my untrained eye, this Half M-Wing looks similar to what Nataraj described as a Generalized M-Wing. Did I read that correctly?

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2908
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