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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Mon Sep 03, 2012 5:14 pm Post subject: Half M-wing |
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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.
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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: 5770
Location: Rochester, NY, USA
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| Posted: Mon Sep 03, 2012 5:38 pm Post subject: |
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| 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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Sep 04, 2012 9:08 am Post subject: |
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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: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Sep 04, 2012 11:33 am Post subject: |
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| 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? 
Thanks Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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