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WXYZ- WING

dailysudoku.com Forum Index -> Solving techniques, and terminology

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strmckr

Joined: 18 Aug 2009
Posts: 64

Posted: Thu Aug 20, 2009 7:56 am Post subject: WXYZ- WING

Quote:

This is an extension of XYZ-Wing that uses four cells instead of three. Each possible value of the hinge cell results in a Z value in one of the cells in the WXYZ-Wing pattern, thus leaving no room for a Z on any cell all four can 'see'.

Its name derives from the four numbers W, X, Y and Z that are required in the hinge. The outer cells in the formation will be Wz, XZ and YZ, Z being the common number

edit: this quote from scanraid.com should be amended.
w is required, but not all of the digits xyz are required in the hinge to function.

edit3: see collary located at the bottom of this post.

I have collected that limited data and complied a listing of all the variations i can identify here is that list:

Type 1:

Code:

. wz . | . . . | . . .
-Z wxyz -Z | . xyz . | . xyz .
. . . | . . . | . . .

Type 1a:

Code:

. wz . | . . . | -z -z -z
-Z wxy -Z | . xy . | . xyz .
. . . | . . . | . . .

Type 1b:

Code:

. wz . | . . . | -z -z -z
-Z wxy -Z | . . . | yxz yxz .
. . . | . . . | . . .

Type 2:

Code:

. xyz . | . . . | . . .
-Z wxyz -Z | . wz . | . . .
. xyz . | . . . | . . .

Type 2a:

Code:

. xyz . | -z -z -z | . . .
-Z wxy -Z | . wz . | . . .
. xy . | . . . | . . .

Type 2b:

Code:

. xyz xyz | -z -z -z | . . .
-Z wxy -Z | . wz . | . . .
. . . | . . . | . . .

Type 3:

Code:

. wz . | . . . | . . .
-z wxyz wxyz | . xyz . | . . .
. . . | . . . | . . .

Type 3a:

Code:

. wz . | -z -z -z | . . .
-z wxy wxy | . xyz . | . . .
. . . | . . . | . . .

Type 4

Code:

. xyz . | . . . | . . .
-z wxyz wxyz | . wz . | . . .
. . . | . . . | . . .

Type 4a

Code:

. xyz . | -z -z -z | . . .
-z wxy wxy | . wz . | . . .
. . . | . . . | . . .

Quote:

Collary:

1. WXYZ-Wings can be considered as a group of 4 cells and 4 digits, that has exactly one non-restricted common digit.

2. Not all candidates xyz may be presents in the cells where they are indicated.

I made a massive revision and deleted every case type reducing it to the 4 prime types with subset cases listed below, modified the collary

the original post which broke the above into each sub case arrangements has been moved to this post

Last edited by strmckr on Tue Jan 26, 2010 6:47 am; edited 1 time in total

wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Thu Aug 20, 2009 3:30 pm Post subject: Re: WXYZ- WING

strmckr wrote:

i figured id bring this with me over here from brief reading of many topics

this place seems to enjoy these types of solving methods and should be a nice addition for those not familiar with it.

this topic was originally posted

Here:

i have collected that limited data and complied a listing of all the variations i can identify here is that list:

Quote:

this quote from scanraid should be amended.
w is required, but not all of the digits xyz are required in the hinge to function.

I don't agree with your amendment. You seem to be taking a specific ALS with a name based on the wxyz being in the hinge and watering it down to cover all 4 cell ALS instances. Amongst other things you have usurped sue de coq. When you take a named and limited technique and apply it to higher orders of that method you wash out any meaning the name has.

It is correct to call an xy-wing a chain or an ALS. It not correct to call a 5 cell xy-chain an xy-wing.

The bulk of the post was useful for people inching in to Almost Locked Sets.

strmckr

Joined: 18 Aug 2009
Posts: 64

Posted: Thu Aug 20, 2009 8:10 pm Post subject:

Type 1c:

Code:

. wz . | . . . | . . .
-Z wxyz -Z | . yxz . | . yxz .
. . . | . . . | . . .

Type 2c:

Code:

. xyz . | . . . | . . .
-Z wxyz -Z | . wz . | . . .
. xyz . | . . . | . . .

the entire prospect of the wxyz wing is the usage of 4 digits(wxyz) spanning into 4 cells.

the fact the name is derived from an older definition of requirement is why i suggest amending it.

I have found countless reference post in the players form where wxyz-wings are quoted with the hinge not having all 4 digits in it.

further more the exploration of the wing its self lead me to finding that the requirement is not needed:

the requirement is

4 digits a bivalve cell (Wn) and 3 cells(wings and hinge) that through links sees the bivalve.

i view it as bent quad more then anything else.

where placements of digits leaves xy-wings,xyz wings, triples/pairs all causing reductions of z.

how ever if your paying attention to which case identity of the wxyz wing and where the candidates are specifically you can add in extra eliminations.

the content of the post is formed based on asking "what if specific digits are missing or moved from these two examples listed above".

the wxyz wing still functions regardless of all 4 candidates in the hinge:

hindsight: wxyz can be viewed as simplistic alx-xz rule, xy-chains, and in some case sue de coq.

this was not meant to usurp a singular technique as every other technique has more then 1 way to use\view it.

i would suggest viewing it more over as an exploration of how they function ie alternative method that can mimic others just as any other type can as well.

the entire list was hand complied from posts in the players forum and my own work.

p.s
su do cogs have been expanded to cover extremely complex als cases as well should i presume the same argument applies to them as well?

wapati

Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

Posted: Fri Aug 21, 2009 4:13 am Post subject:

strmckr wrote:

the entire list was hand complied from posts in the players forum and my own work.

Good job!

Quote:

su do cogs have been expanded to cover extremely complex als cases as well should i presume the same argument applies to them as well?

For me the defining characteristic of the sue de coq is the bi-value cell in the box that is not present outside the box and is not in the row/column of the externals. If you drop that requirement it is an ALS.

strmckr

Joined: 18 Aug 2009
Posts: 64

Posted: Tue Jan 26, 2010 6:48 am Post subject:

updated the thread simplified it

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