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A '''W-Wing''' is formed by a [[chain]] of four cells:
* '''A''': A cell with two [[candidate]]s '''W''' and '''X'''.
* '''B''': A cell with '''X''' as a candidate.
* '''C''': A cell with '''X''' as a candidate.
* '''D''': A cell with two candidates '''W''' and '''X'''.

It is required that '''A''' [[see]]s '''B''', '''C''' [[see]]s '''D''', and '''B''' and '''C''' has a [[strong link]] on the [[digit]] '''X'''. Then '''W''' can be [[eliminate]]d from any cell that is seen by both '''A''' and '''D'''.

Suppose '''T''' is a cell that is seen by both '''A''' and '''D''', and '''T''' contains '''W''' as a candidate. Then, the '''W-Wing''' can be written as follows in [[Nice Loop]] notation:
[T]-W-[A]-X-[B]=X=[C]-X-[D]-W-[T] => T<>W

== Example ==

[[Image:Wwing-example.png]]

In this [[grid]], note the '''r5c5''' and '''r6c3''' cells with the candidates '''2''' and '''7'''. Also, the green '''7''' candidates form a chain, with '''r5c8''' and '''r6c8''' forming a strong link (because '''r5c8''' and '''r6c8''' are the only cells with candidate '''7''' in this [[box]]). Hence, we can eliminate the digit '''2''' from all cells that are seen by both '''r5c5''' and '''r6c3''', i. e., those marked in red.

'''Doubly Linked W-Wing Example'''

In a doubly-linked W-Wing the identical pairs are linked to 2 digit conjugate pairs rather than a single digit conjugate pair as in the previous example. This is illustrated in the following example where the 17 cells r8c4 and r9c8 are linked to the 7 conjugate pair and the 1 grouped conjugate in box 7. This means that both 1 and 7 must occur either in r8c4 or r9c8. Each of these are conjugate with the 17 conjugates in box 7. Therefore 1 and 7 can be eliminated from other cells in rows 8 or 9. Candidate eliminations are indicated with a -.

Doubly Linked W-Wing Example
|-----------------+-----------------+-----------------|
| 5 67 3 | 9 2 68 | 4 178 16 |
| 4 167 168 | 5 67 3 | 678 9 2 |
| 89 2 689 | 17 4 168 | 678 5 3 |
|-----------------+-----------------+-----------------|
| 3 4 7 | 2 19 19 | 5 6 8 |
| 6 9 2 | 8 5 7 | 1 3 4 |
| 1 8 5 | 6 3 4 | 9 2 7 |
|-----------------+-----------------+-----------------|
| 2 5 4 | 3 1679 169 | 678 178 169 |
| 789 16 1689 | 17 -16-79 2 | 3 4 5 |
| 79 3 169 | 4 8 5 | 2 17 -169 |
|-----------------+-----------------+-----------------|

== External Link ==
* [http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2008 The W-Wing]

[[Category:Solving Techniques]]

W-Wing - Revision history

Rooted: Created page with "A '''W-Wing''' is formed by a chain of four cells: * '''A''': A cell with two candidates '''W''' and '''X'''. * '''B''': A cell with '''X''' as a candidate. * '''C''':..."