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au tough June 19, 2012

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arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Tue Jun 19, 2012 5:39 am Post subject: au tough June 19, 2012

Code:

*-----------*
|9..|3..|...|
|...|.5.|.4.|
|185|...|9..|
|---+---+---|
|.3.|..6|...|
|2..|.3.|..7|
|...|8..|.2.|
|---+---+---|
|..7|...|519|
|.4.|.7.|...|
|...|..9|..8|
*-----------*

Play/Print online

SudoQ

Joined: 02 Aug 2011
Posts: 127

Posted: Tue Jun 19, 2012 2:36 pm Post subject:

An extended WXYZ-Wing solves it... /SudoQ

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Tue Jun 19, 2012 2:44 pm Post subject:

SudoQ wrote:

An extended WXYZ-Wing solves it...

Help me with your wxyz wing. Confused

Here is a fancy xy-wing

Code:

*--------------------------------------------------------------------*
| 9 267 4 | 3 168 128 | 12678 58 1256 |
| 36 267 23 | 9 5 128 | 12678 4 126 |
| 1 8 5 | 467 46 247 | 9 36 236 |
|----------------------+----------------------+----------------------|
| 47 3 18 | 257 29 6 | 18 59 45 |
| 2 a59 168 |b145 3 b145 | 168 589 7 |
| 47 5-9 16 | 8 c19 157 | 136 2 13456 |
|----------------------+----------------------+----------------------|
| 68 26 7 | 246 2468 3 | 5 1 9 |
| 58 4 9 | 15 7 158 | 236 36 236 |
| 356 1 23 | 256 26 9 | 4 7 8 |
*--------------------------------------------------------------------*
(9=5)r5c2-(5=14)r5c46-(1=9)r6c5 => -9r6c2; stte

either r5c2 or r6c5 must be a 9

Play/Print online

Last edited by arkietech on Tue Jun 19, 2012 4:11 pm; edited 1 time in total

SudoQ

Joined: 02 Aug 2011
Posts: 127

Posted: Tue Jun 19, 2012 3:29 pm Post subject:

arkietech wrote:

Help me with your wxyz wing. Confused

Your solution seems to be identical to the one I found.
I also tried the puzzle in the XSUDO solver program
that showed a similar pattern, called "Extended WXYZ-Wing":

Code:

|---------------|----------------|-------------------|
| 9 267 4 | 3 168 128 | 12678 58 1256 |
| 36 267 23 | 9 5 128 | 12678 4 126 |
| 1 8 5 | 467 46 247 | 9 36 236 |
|---------------|----------------|-------------------|
| 47 3 18 | 257 29 6 | 18 59 45 |
| 2 9-5 168 |(145) 3 (145)| 168 589 7 |
| 47 (59) 16 | 8 (19) 17-5 | 136 2 13456 |
|---------------|----------------|-------------------|
| 68 26 7 | 246 2468 3 | 5 1 9 |
| 58 4 9 | 15 7 158 | 236 36 236 |
| 356 1 23 | 256 26 9 | 4 7 8 |
|---------------|----------------|-------------------|

/SudoQ

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Tue Jun 19, 2012 4:23 pm Post subject:

SudoQ wrote:

Your solution seems to be identical to the one I found.
I also tried the puzzle in the XSUDO solver program
that showed a similar pattern, called "Extended WXYZ-Wing":

(5=9)r6c2-(9=1)r6c5-(1=45)r5c46 => -5r6c2,r6c6; stte

A little different. I still don't see the "extended"

SudoQ

Joined: 02 Aug 2011
Posts: 127

Posted: Tue Jun 19, 2012 4:53 pm Post subject:

arkietech wrote:

A little different. I still don't see the "extended"

Me neither!
I borrowed the name from XSUDO, so I thought it was correct... Embarassed

/SudoQ

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Tue Jun 19, 2012 5:16 pm Post subject:

Extended must mean "extended form" Here is a guess

Code:

.-----------.----------.----------.
| * * WXYZ| . XZ . | YZ . . |
| . WZ . | . . . | . . . |
| . . . | . . . | . . . |
:-----------+----------+----------:

In a standard WXYZ-wing the pivot has the candidates WXYZ. In all possible options for the pivot cell, Z will be eliminated from the starred cells.

Extended form of the WXYZ-Wing

Code:

.-----------.----------.----------.
| * * * |XYZ . XYZ | . . . |
| . WZ . | * WX * | . . . |
| . . . | . . . | . . . |
:-----------+----------+----------:

Z'S can be removed from starred cells

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Tue Jun 19, 2012 10:17 pm Post subject:

I don't agree with any of the "names" submitted for the two patterns under discussion for this grid.

Accepting that a wing is any chain with three strong links separated by two weak links. At best, what I see are two wings with a single ALS strong link in each.

Code:

Wing with an ALS for the pseudo-vertex cell:
+-----------------------------------------------------------------------+
| 9 267 4 | 3 168 128 | 12678 58 1256 |
| 36 267 23 | 9 5 128 | 12678 4 126 |
| 1 8 5 | 467 46 247 | 9 36 236 |
|-----------------------+-----------------------+-----------------------|
| 47 3 18 | 257 29 6 | 18 59 45 |
| 2 (59) 168 | (145) 3 (145) | 168 589 7 |
| 47 5-9 16 | 8 (19) 157 | 136 2 13456 |
|-----------------------+-----------------------+-----------------------|
| 68 26 7 | 246 2468 3 | 5 1 9 |
| 58 4 9 | 15 7 158 | 236 36 236 |
| 356 1 23 | 256 26 9 | 4 7 8 |
+-----------------------------------------------------------------------+
# 87 eliminations remain

(9=5)r5c2 - (54=41)r5c46 - (1=9)r6c5 => r6c2<>9

Code:

Wing with an ALS for a pseudo-pincer cell:
+-----------------------------------------------------------------------+
| 9 267 4 | 3 168 128 | 12678 58 1256 |
| 36 267 23 | 9 5 128 | 12678 4 126 |
| 1 8 5 | 467 46 247 | 9 36 236 |
|-----------------------+-----------------------+-----------------------|
| 47 3 18 | 257 29 6 | 18 59 45 |
| 2 9-5 168 | (145) 3 (145) | 168 589 7 |
| 47 (59) 16 | 8 (19) 17-5 | 136 2 13456 |
|-----------------------+-----------------------+-----------------------|
| 68 26 7 | 246 2468 3 | 5 1 9 |
| 58 4 9 | 15 7 158 | 236 36 236 |
| 356 1 23 | 256 26 9 | 4 7 8 |
+-----------------------------------------------------------------------+
# 87 eliminations remain

(5=9)r6c2 - (9=1)r6c5 - (1=45)r5c46 => r5c2,r6c6<>5

As an aside point:

Here's what I consider to be the proper notation for reading the first chain from l-to-r:

Code:

(9=5)r5c2 - (5=41)r5c46 - (1=9)r6c5 => r6c2<>9

However, here's what I consider to be the proper notation for reading the first chain from r-to-l:

Code:

(9=5)r5c2 - (54=1)r5c46 - (1=9)r6c5 => r6c2<>9

If this chain had been part of a loop, then we have a scenario where the ALS quasi-resembles an ERI (Empty Rectangle Intersection) with two interpretations. That's why I wrote the first chain the way I did.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Wed Jun 20, 2012 10:01 pm Post subject:

daj95376 wrote:

I think the wxyz-wing and extended wxyz-wing terms are OK for these two patterns. These names pre-dated the use of the wing term for patterns with three strong links, except for the xy-wing, of course.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Jun 21, 2012 3:15 am Post subject:

[Withdrawn: I've been working from a misconception of *-Wing for a very long time. My apologies.] Last edited by daj95376 on Thu Jun 21, 2012 4:36 pm; edited 1 time in total

aran

Joined: 19 Apr 2010
Posts: 70

Posted: Thu Jun 21, 2012 3:53 pm Post subject:

daj95376 wrote:

ronk wrote:

Well, I'm not buying it. A WXYZ-Wing -- even extended -- should have four distinct candidate values in the vertex ... and none of these patterns qualify.

Given that all XY XYZ WXYZ wings are particular instances of ALS X-Z logic, the important notion would seem to be ALS rather than the actual distribution of the ALS candidates over the ALS cells.
Under this view, there would be no requirement for any vertex cell in a WXYZ to contain all 4 candidates, nor any need to draw a distinction between WXYZ and extended-WXYZ, all that changes being the distribution of the same candidates over the same cells.
Accordingly under this approach, the above :
{1459}r5c246
{19}r6c5
ie {9451} {19} =><9>r6c2
would qualify as WXYZ.

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