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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Tue Sep 08, 2009 2:02 am Post subject: Sept 8 VH |
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This one flies on either wing.
Solutions: 278 xy-wing; or 267 xyz-wing.
Early Earl |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Sep 08, 2009 11:58 am Post subject: |
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| Another wing: |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Sep 08, 2009 1:19 pm Post subject: |
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Another one step solution is a
| Quote: | | xy-wing 16-8 with vertex 16 inr2c3 and pseudocell 68 in box 7. |
Ted |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Tue Sep 08, 2009 2:38 pm Post subject: Sept 8 VH |
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Ted,
Perhaps many would appreciate a step-by-step solution of your xy-wings with pseudocells.
Earl |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Sep 08, 2009 9:51 pm Post subject: Re: Sept 8 VH |
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| Earl wrote: | Ted,
Perhaps many would appreciate a step-by-step solution of your xy-wings with pseudocells.
Earl |
Here is my code after basics. | Code: |
*--------------------------------------------------------------------*
| 18 258 129 | 4 3 6 | 7 129 1258 |
| 4 568 16 | 9 2 7 | 58 3 158 |
| 37 27 239 | 5 1 8 | 69 269 4 |
|----------------------+----------------------+----------------------|
| 6 3 8 | 2 9 4 | 1 5 7 |
| 2 4 5 | 6 7 1 | 3 8 9 |
| 9 1 7 | 3 8 5 | 2 4 6 |
|----------------------+----------------------+----------------------|
| 5 267 1236 | 8 4 29 | 69 12679 123 |
| 78 9 26 | 1 5 3 | 4 267 28 |
| 138 28 4 | 7 6 29 | 58 129 12358 |
*--------------------------------------------------------------------* |
The vertex or pivot of the xy-wing 16-8 is in r2c3, and pincer 18 is in r1c1. The second pincer, 68, is in box7 and is formed by the bivalue 26 in r8c3 and the bivalue 28 in r9c2. I believe that it was Keith who I first saw using the term pseudocell to identify the relationship between two bivalue cells containing a common digit, which is this case is the digit 2.
As for the xy-wing:
if the vertex r2c3=1, then pincer r1c1=8
if the vertex r2c3=6, then pseudocell pincer r8c3=2 and r9c2=8.
Thus, r12c2<>8 & r89c1<>8.
Alternatively, this configuration may be viewed as a 4-cell xy-chain:
(8=1)r1c1 - (1=6)r2c3 - (6=2)r8c3 - (2=8)r9c2.
Hope this helps clarify what I meant by "pseudocell". I am sure Keith or others could provide a better definition.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Sep 08, 2009 11:50 pm Post subject: |
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| Ted, that's very impressive. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Sep 09, 2009 1:55 am Post subject: |
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I first saw the term "pseudocell" used in terms of a UR, in particular a Type-3:
| Code: | +-----------+-----------+-----------+
| . . . | / . . | . . . |
| . . . | 34 . . | . . . |
| . . . | / . . | . . . |
+-----------+-----------+-----------+
| . . . | / . . | . . . |
| . . . | / . . | . . . |
| . . . | / . . | . . . |
+-----------+-----------+-----------+
| . 12 . | 123 . . | . . . |
| . . . | / . . | . . . |
| . 12 . | 124 . . | . . . |
+-----------+-----------+-----------+ |
Either R7C4 is <3> or <R9C4> is <4>. To any cell that sees them both*, they act like a "pseudocell" <34>. So, with R2C4 the pseudocell forms a pair, and you can eliminate <34> in any cell marked /.
* Not quite. See below.
Suppose you have: | Code: | +-----------+-----------+-----------+
| . . . | . . / | . . . |
| . . . | 35 . / | . . . |
| . . . | . . / | . . . |
+-----------+-----------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-----------+-----------+
| . 12 . | 123 . . | . . . |
| . . . | / . 45 | . . . |
| . 12 . | 124 . . | . . . |
+-----------+-----------+-----------+ |
Now the pseudocell is acting like the pivot of an XY-wing 35 - 34 - 45 and you can eliminate <5> from any cell marked /.
About the time this came up, I started using the term "pseudocell" in looking for four-cell chains as an extension of the XY-wing idea. For example, | Code: | +-----------+-----------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-----------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-----------+-----------+
| . 12 . | . . . | / 23 / |
| . . . | . . . | . . . |
| . / . | . . . | 14 . 34 |
+-----------+-----------+-----------+ |
<14> and <34> are a pseudocell <13> making an XY-wing 12 - 23 - 13 that eliminates <1> in the cells marked /.
My idea of the pseudocell was simply that it is a way to "collapse' two cells XY - YZ into one, XZ, and I find it a useful device to find chains, especially four-cell chains.
*Below.
It is not necessary that adjacent links see BOTH cells of the pseudocell. Consider this variation of the previous example:
| Code: | +-----------+-----------+-----------+
| . . . | . . . | . . . |
| . / . | . . . | . . 14 |
| . . . | . . . | . . . |
+-----------+-----------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------+-----------+-----------+
| . 12 . | . . . | . 23 . |
| . . . | . . . | . . . |
| . . . | . . . | . . 34 |
+-----------+-----------+-----------+ |
Neither <12> nor <14> sees both cells of the pseudocell in B9, <24>.
Best wishes,
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Sep 09, 2009 2:10 am Post subject: Re: Sept 8 VH |
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| tlanglet wrote: | | Earl wrote: | Ted,
Perhaps many would appreciate a step-by-step solution of your xy-wings with pseudocells.
Earl |
Here is my code after basics. | Code: |
*--------------------------------------------------------------------*
| 18 258 129 | 4 3 6 | 7 129 1258 |
| 4 568 16 | 9 2 7 | 58 3 158 |
| 37 27 239 | 5 1 8 | 69 269 4 |
|----------------------+----------------------+----------------------|
| 6 3 8 | 2 9 4 | 1 5 7 |
| 2 4 5 | 6 7 1 | 3 8 9 |
| 9 1 7 | 3 8 5 | 2 4 6 |
|----------------------+----------------------+----------------------|
| 5 267 1236 | 8 4 29 | 69 12679 123 |
| 78 9 26 | 1 5 3 | 4 267 28 |
| 138 28 4 | 7 6 29 | 58 129 12358 |
*--------------------------------------------------------------------* |
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Let me try to explain how I might have found this chain.
In C3 we have <16> and <26> that make a pseudocell (12). The question is, can we find two other cells so we have 1? - 12 - 2?, where ? is some candidate.
Note that 1? has to see the <1> in the pseudocell, 2? has to see the <2>.
By the way, any two adjacent cells in an XY chain can be regarded as a pseudocell. I am simply suggesting the idea is helpful to find short chains.
Best wishes,
Keith |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Wed Sep 09, 2009 10:13 pm Post subject: |
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I would call that a pincer transport since the 8 was transported, but my definition of a pincer transport is more liberal than others. You could also call it pincer coloring.
You could also use the 28 at r9c2 to eliminate 8 from r12c2 and r9c1.
Edit: Nevermind, I thought you used the 28 in box 9, which also works.
Last edited by gindaani on Fri Sep 11, 2009 2:01 pm; edited 1 time in total |
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Omari
Joined: 11 Sep 2009
Posts: 1
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| Posted: Fri Sep 11, 2009 12:49 pm Post subject: Daily Sudoku puzzles |
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It is so entertaining puzzle to play,So keep playing and enjoy Sudoku.....
Thanks & Regards
Omari Johnson |
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