Strategies for Number Puzzles of all kinds
  Print Version
Solvers
Puzzles
Basic Strategies
Tough Strategies
Diabolical Strategies
Extreme Strategies
Depreciated Strategies
Str8ts
Other
The Logic of Sudoku
  WXYZ-Wing

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.
WXYZ-Wing eg 1
WXYZ-Wing eg 1

In this example our four-value hinge is C3 marked in brown. The three outlier cells, marked in yellow each contain a 9 (our Z) plus one other number unique to themselves and the hinge. It's important that these extra numbers really are common only to the hinge and there are no pairs like 5/9 and 5/9 in two of the orange cells.

There is only one cell that all four of the WXYZ can see - C1. It has a 9 which can be removed. No matter what number is the final solution in the hinge, one of the WXYZ must be a 9.
WXYZ-Wing eg 1
WXYZ-Wing eg 1: Load Example or : From the Start

breakline

Comments...

Saturday 12-Jun-2010

... by: Strmckr

yes it is another way to view an Als-xz technique.

this same move can be viewed as this:

Almost Locked Set XZ-Rule: A=r2c3 {59}, B=r3c358 {4579}, X=5, Z=9 => r3c12<>9

for further extensions/ pattern variations to this technique visit my page
here:
http://forum.enjoysudoku.com/post200074.html#p200074



Saturday 8-May-2010

... by: Nassir M

also you could remove the 7s from c1 and c6 pls 4 from c1 and also to remove the 5 from A3 because the 5 is going to be either in B3 or C3.
Thanks

Tuesday 13-Apr-2010

... by: rich schrader

Isn't this strategy another way of interpreting an ALS?

Wednesday 10-Feb-2010

... by: Jeff Sanborn

What if the cell containing 4/9 were located at Row 1, Column 2 (instead of Row 3, Column 8).

Must there be one cell within the box and two cells in the row, or is it just a total of three cells that is important?

Furthermore, could you have a VWXYZ-wing if you had a hinge cell with five values and four outlying cells?

Andrew Stuart writes:
All the yellow cells must see the hinge - the brown cells.
Yes you could have a 5-cell VWXYZ-wing although I've not searched for one.

Thursday 21-Jan-2010

... by: LokiMomus

Is there a more generic strategy for this wxyz already mentioned? Couldnt find it, though I admit I havent read all strategies thoroughly. I don't have an example sudoku for this, but consider the given example and lets say row 3, column 5 has 379 as available options instead and i include an extra cell into the strategy, row 3, column 6, which has 379 as available options. Row 3, column 3 has instead the values 34579.

The theory still holds. Filling in the 9 in the yellow box will result in an invalid situation, so i can scratch the 9 in the yellow box.

In other words, the more generic requirement should be that there can be n cells of the same cellgroup as long as they have n+1 distinct symbols. (the +1 is for the symbol (9 in this case) that we are considering). The other rules stay intact.

The substrategy of wxyz-wing would be with n=1.

My question to you is: Is this strategy already mentioned on the site? If not, can it be solved by using multiple others?

Note:
This strategy can be even made more generic if there are more than 3 dimensions (special sudokus). In a traditional sudoku there are 3 dimensions (a cell is part of a horizontal cellgroup, a vertical cellgroup and a 3x3 cellgroup). A 4-dimensional sudoku would for example be a jigsaw sudoku on top of a traditional one.

Add your comments

A confirmation email will be sent to you after submitting.

Your Name

Email Address - required for confirmation (it will not be displayed here)

Your comment or question

Remember me


Please keep your comments relevant to this article. Email addresses are never displayed, but they are required to confirm your comments.

When you enter your name and email address, you'll be sent a link to confirm your comment. If you want to be remembered, the check box above will store a cookie with your name and email address on your computer.

Line breaks and paragraphs are automatically converted — no need to use <p> or <br> tags.



Article created on 11-April-2008. Views: 10108
This page was last modified on 17-March-2010, at 15:15.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Scanraid Ltd, 2010