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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Wed Dec 03, 2008 6:11 am Post subject: Does this have a name? |
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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 |
+-----------+-------------+-----------+
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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: 3854
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| Posted: Wed Dec 03, 2008 9:46 am Post subject: |
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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
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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
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[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: 5770
Location: Rochester, NY, USA
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| Posted: Wed Dec 03, 2008 4:47 pm Post subject: |
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| 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: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Dec 03, 2008 5:27 pm Post subject: |
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| 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: 3854
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| Posted: Wed Dec 03, 2008 8:01 pm Post subject: |
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| 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
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| Posted: Thu Dec 04, 2008 12:35 am Post subject: |
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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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