http://sudopedia.sudocue.net/index.php?action=history&feed=atom&title=W-Wing 2026-04-18T21:37:04Z Revision history for this page on the wiki MediaWiki 1.36.2 http://sudopedia.sudocue.net/index.php?title=W-Wing&diff=357&oldid=prev 2021-10-25T15:51:49Z

<p>Created page with &quot;A &#039;&#039;&#039;W-Wing&#039;&#039;&#039; is formed by a <a href="/index.php?title=Chain" title="Chain">chain</a> of four cells: * &#039;&#039;&#039;A&#039;&#039;&#039;: A cell with two <a href="/index.php?title=Candidate" title="Candidate">candidates</a> &#039;&#039;&#039;W&#039;&#039;&#039; and &#039;&#039;&#039;X&#039;&#039;&#039;. * &#039;&#039;&#039;B&#039;&#039;&#039;: A cell with &#039;&#039;&#039;X&#039;&#039;&#039; as a candidate. * &#039;&#039;&#039;C&#039;&#039;&#039;:...&quot;</p> <p><b>New page</b></p><div>A &#039;&#039;&#039;W-Wing&#039;&#039;&#039; is formed by a [[chain]] of four cells:<br /> * &#039;&#039;&#039;A&#039;&#039;&#039;: A cell with two [[candidate]]s &#039;&#039;&#039;W&#039;&#039;&#039; and &#039;&#039;&#039;X&#039;&#039;&#039;.<br /> * &#039;&#039;&#039;B&#039;&#039;&#039;: A cell with &#039;&#039;&#039;X&#039;&#039;&#039; as a candidate.<br /> * &#039;&#039;&#039;C&#039;&#039;&#039;: A cell with &#039;&#039;&#039;X&#039;&#039;&#039; as a candidate.<br /> * &#039;&#039;&#039;D&#039;&#039;&#039;: A cell with two candidates &#039;&#039;&#039;W&#039;&#039;&#039; and &#039;&#039;&#039;X&#039;&#039;&#039;.<br /> <br /> It is required that &#039;&#039;&#039;A&#039;&#039;&#039; [[see]]s &#039;&#039;&#039;B&#039;&#039;&#039;, &#039;&#039;&#039;C&#039;&#039;&#039; [[see]]s &#039;&#039;&#039;D&#039;&#039;&#039;, and &#039;&#039;&#039;B&#039;&#039;&#039; and &#039;&#039;&#039;C&#039;&#039;&#039; has a [[strong link]] on the [[digit]] &#039;&#039;&#039;X&#039;&#039;&#039;. Then &#039;&#039;&#039;W&#039;&#039;&#039; can be [[eliminate]]d from any cell that is seen by both &#039;&#039;&#039;A&#039;&#039;&#039; and &#039;&#039;&#039;D&#039;&#039;&#039;.<br /> <br /> Suppose &#039;&#039;&#039;T&#039;&#039;&#039; is a cell that is seen by both &#039;&#039;&#039;A&#039;&#039;&#039; and &#039;&#039;&#039;D&#039;&#039;&#039;, and &#039;&#039;&#039;T&#039;&#039;&#039; contains &#039;&#039;&#039;W&#039;&#039;&#039; as a candidate. Then, the &#039;&#039;&#039;W-Wing&#039;&#039;&#039; can be written as follows in [[Nice Loop]] notation:<br /> [T]-W-[A]-X-[B]=X=[C]-X-[D]-W-[T] =&gt; T&lt;&gt;W<br /> <br /> == Example ==<br /> <br /> [[Image:Wwing-example.png]]<br /> <br /> In this [[grid]], note the &#039;&#039;&#039;r5c5&#039;&#039;&#039; and &#039;&#039;&#039;r6c3&#039;&#039;&#039; cells with the candidates &#039;&#039;&#039;2&#039;&#039;&#039; and &#039;&#039;&#039;7&#039;&#039;&#039;. Also, the green &#039;&#039;&#039;7&#039;&#039;&#039; candidates form a chain, with &#039;&#039;&#039;r5c8&#039;&#039;&#039; and &#039;&#039;&#039;r6c8&#039;&#039;&#039; forming a strong link (because &#039;&#039;&#039;r5c8&#039;&#039;&#039; and &#039;&#039;&#039;r6c8&#039;&#039;&#039; are the only cells with candidate &#039;&#039;&#039;7&#039;&#039;&#039; in this [[box]]). Hence, we can eliminate the digit &#039;&#039;&#039;2&#039;&#039;&#039; from all cells that are seen by both &#039;&#039;&#039;r5c5&#039;&#039;&#039; and &#039;&#039;&#039;r6c3&#039;&#039;&#039;, i. e., those marked in red.<br /> <br /> &#039;&#039;&#039;Doubly Linked W-Wing Example&#039;&#039;&#039;<br /> <br /> 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 -. <br /> <br /> Doubly Linked W-Wing Example<br /> |-----------------+-----------------+-----------------|<br /> | 5 67 3 | 9 2 68 | 4 178 16 |<br /> | 4 167 168 | 5 67 3 | 678 9 2 |<br /> | 89 2 689 | 17 4 168 | 678 5 3 |<br /> |-----------------+-----------------+-----------------|<br /> | 3 4 7 | 2 19 19 | 5 6 8 |<br /> | 6 9 2 | 8 5 7 | 1 3 4 |<br /> | 1 8 5 | 6 3 4 | 9 2 7 |<br /> |-----------------+-----------------+-----------------|<br /> | 2 5 4 | 3 1679 169 | 678 178 169 |<br /> | 789 16 1689 | 17 -16-79 2 | 3 4 5 |<br /> | 79 3 169 | 4 8 5 | 2 17 -169 |<br /> |-----------------+-----------------+-----------------|<br /> <br /> == External Link ==<br /> * [http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2008 The W-Wing]<br /> <br /> [[Category:Solving Techniques]]</div>

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