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Does this have a name?

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed Dec 03, 2008 6:11 am    Post subject: Does this have a name? Reply with quote

Consider this fragment:

Code:

+-----------+-------------+-----------+
| .  .   .  | .  .    .   | .   .  .  |
| .  .   .  | .  .    .   | .   .  .  |
| .  .   .  | .  .    .   | .   .  .  |
+-----------+-------------+-----------+
| .  .   .  | .  .    .   | .   .  .  |
| .  .   .  | .  .    .   | .   .  .  |
| 46 236 34 | 7  1    9   | 8   26 5  |
+-----------+-------------+-----------+
| 49 45  1  | 26 3679 367 | 357 8  29 |
| 89 58  2  | 19 4    137 | 37  35 6  |
| 3  7   6  | 29 5    8   | 1   24 49 |
+-----------+-------------+-----------+

Play this puzzle online at the Daily Sudoku site

Note the XY-Wing on 264 pivoted in r6c8. Nothing can be done with the pincers (4) in the usual way or with transport. But each 4 sees a 49 cell, creating pincers of 9 which solve r7c9. Does this pattern or technique have a name or is it just an isolated situation?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Dec 03, 2008 9:46 am    Post subject: Reply with quote

I'd call it a 5-cell XY-Chain:

Code:
 (9=4)r7c1 - (4=6)r6c1 - (6=2)r6c8 - (2=4)r9c8 - (4=9)r9c9 => [r7c9]<>9
  W Z      -  Z X      -  X Y      -  Y Z      -  Z W      =>  eliminations in W

It's also "#3" in the list of XY-Wing extensions I posted somewhere in these forums.

Code:
3-cell XY-Chain

             ** ** **
XY-Wing:     ZX-XY-YZ           =>  eliminations in Z
                ..                  pivot
             ..    ..               pincers


4-cell XY-Chain

             ** *   * **
Ext. #1:     ZX-XV-VY-YZ        =>  eliminations in Z


5-cell XY-Chain

             ** ** **
Ext. #2:     ZX-XY-YZ-ZW-WZ     =>  eliminations in Z
Ext. #3:  WZ-ZX-XY-YZ-ZW        =>  eliminations in W


3-cell XY-Chain w/Strong Link (transport)

             ** ** ** @...@
Ext. #4:     ZX-XY-YZ-Zw-vZ     =>  eliminations in Z

[Edit: lowercase letters indicate one-or-more candidates possible.]


Last edited by daj95376 on Wed Dec 03, 2008 8:09 pm; edited 2 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed Dec 03, 2008 4:47 pm    Post subject: Reply with quote

Thanks. Yes, I see that XY-Chain now, but my approach was through the XY-Wing and XY-Extension sounds good!
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arkietech



Joined: 31 Jul 2008
Posts: 1723
Location: Northwest Arkansas USA

PostPosted: Wed Dec 03, 2008 5:27 pm    Post subject: Reply with quote

An xy-chain requires cells with two candidates. Is this true of an xy-extension?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Dec 03, 2008 8:01 pm    Post subject: Reply with quote

arkietech wrote:
An xy-chain requires cells with two candidates. Is this true of an xy-extension?

An XY-Wing extension that uses an external strong link/transport is not restricted to bivalue cells. I updated extension #4 above to use lowercase letters to designate one-or-more candidates.
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Asellus



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

PostPosted: Thu Dec 04, 2008 12:35 am    Post subject: Reply with quote

Marty,

As you have described it, it is also a W-Wing. The 49 W-Wing is "activated" by the strong (inference) link of the <4> pincers of the XY Wing.
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