https://www.sudopedia.org/index.php?action=history&feed=atom&title=ALS-XY-ChainALS-XY-Chain - Revision history2026-04-29T05:34:06ZRevision history for this page on the wikiMediaWiki 1.34.1https://www.sudopedia.org/index.php?title=ALS-XY-Chain&diff=291&oldid=prevRooted: Created page with "An '''ALS-XY-Chain''' is a XY-Chain whose nodes are Almost Locked Sets. It is a generalization of the usual XY-Chain (whose nodes are bivalue cells), s..."2020-06-04T03:14:42Z<p>Created page with "An '''ALS-XY-Chain''' is a <a href="/wiki/XY-Chain" title="XY-Chain">XY-Chain</a> whose <a href="/wiki/Node" title="Node">nodes</a> are <a href="/wiki/Almost_Locked_Set" title="Almost Locked Set">Almost Locked Sets</a>. It is a generalization of the usual <a href="/wiki/XY-Chain" title="XY-Chain">XY-Chain</a> (whose nodes are <a href="/wiki/Bivalue" title="Bivalue">bivalue</a> <a href="/wiki/Cell" title="Cell">cells</a>), s..."</p>
<p><b>New page</b></p><div>An '''ALS-XY-Chain''' is a [[XY-Chain]] whose [[node]]s are [[Almost Locked Set]]s. It is a generalization of the usual [[XY-Chain]] (whose nodes are [[bivalue]] [[cell]]s), since each bivalue cell is itself an Almost Locked Set.<br />
<br />
The [[ALS-XZ]] rule is an ALS-XY-Chain of length two, while the [[ALS-XY-Wing]] is an ALS-XY-Chain of length three.<br />
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== Example ==<br />
The following example comes from a [http://www.sudoku.org.uk/SudokuThread.asp?fid=4&sid=6330 Eureka! forum post].<br />
. A46 . | . . . |D25 D258 .<br />
. . . | . . . | . . .<br />
. 27-4 . |C13 . . | . D1258 D1248<br />
------------------+------------------+------------------<br />
. . . | . . . | . . .<br />
. . B26 |C367 . . | . . .<br />
. A269 . | . . . | . . .<br />
------------------+------------------+------------------<br />
. A469 . | . . . | . . .<br />
. . . |C37 . . | . . .<br />
. . . | . . . | . . .<br />
<br />
There are four Almost Locked Sets, labeled '''A''', '''B''', '''C''' and '''D''' in the diagram. These Almost Locked Sets form a ALS-XY-Chain with the following links:<br />
* '''A''' and '''B''' has a [[restricted common]] 2.<br />
* '''B''' and '''C''' has a [[restricted common]] 6.<br />
* '''C''' and '''D''' has a [[restricted common]] 1.<br />
<br />
Since all [[cell]]s in '''A''' and '''D''' with [[candidate]] 4 see the cell '''r3c2''', we conclude that 4 can be [[eliminate]]d from '''r3c2'''.<br />
<br />
== Nice Loop Notation ==<br />
r3c2 -4- ALS:r167c2 -2- r5c3 -6- ALS:r358c4 -1- ALS:[r1c78,r3c89] -4- r3c2 => r3c2 <> 4<br />
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== Eureka Notation ==<br />
(4=692)ALS:r167c2 - (2=6)r5c3 - (6=371)ALS:r358c4 - (1258=4)ALS:r1c78,r3c89 => r3c2 <> 4<br />
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== See also ==<br />
* [[XY-Chain]]<br />
* [[Almost Locked Set]]<br />
* [[ALS-XZ]]<br />
* [[ALS-XY-Wing]]<br />
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[[Category:Solving Techniques]]<br />
[[Category:Chains and Loops]]</div>Rooted