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2025-07-20T18:15:53Z

Created page with "The '''Remote Pairs''' technique uses a XY-Chain involving an even number of bivalue cells, and all the cells have the same two digits as their candidate..."

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The '''Remote Pairs''' [[technique]] uses a [[XY-Chain]] involving an even number of [[bivalue]] [[cell]]s, and all the cells have the same two [[digit]]s as their [[candidate]]. The chain can be seen as a series of [[Naked Pair]]s. Both digits may be [[eliminate]]d from any cell that is seen by both ends of the [[chain]].

In practice, Remote Pairs is rarely seen. However, when encountered, Remote Pairs is far more obvious than the typical [[XY-Chain]], and possibly more obvious than a [[X-Chain]] or [[XY-Wing]].

== How it works ==
The technique uses the fact that due to the series of links, the entire chain must contain an alternating series of digits. By considering each pair of cells with opposite [[parity]], except those directly linked, cells that can [[see]] both cells of such a pair cannot contain either of the two digits.

Here is a schematic example. The alternating digits are named '''X''' and '''Y'''.
{{grid|4=--|5=--|6=--|8=--|10=--|11=XY|12=--|13=--|14=YX|15=--|16=--|17=--|18=--|19=--|20=--|21=--|21=--|22=--|23=--|24=XY|25=--|26=YX|27=--|35=--|44=--|53=--|59=*|61=--|62=XY|63=--|65=*|69=*|70=YX|71=--|72=--|79=--|80=--|81=--}}
Candidates '''X''' and '''Y''' are already removed from the cells marked with a dash because of the naked pairs. The cells marked with * are possible eliminations for the Remote Pairs technique as they see two pairs of opposite parity (indicated by the '''XY''' and '''YX''' ordering).

== Example ==
This example comes from a possible [[solving path]] for [http://www.sudocue.net/olddaily.php?id=393&sol=0 Daily Nightmare of 2007 January 9].

[[Image:RemotePairExample.png]]

A chain of bivalue cells containing the candidates 2 and 7 can be identified: '''r5c3''' - '''r1c3''' - '''r3c2''' - '''r3c9'''. This results in the elimination of 7 from '''r5c9'''.

== Other techniques ==
There is a strong overlap between Remote Pairs and other solving techniques. The same eliminations can be performed by the following alternatives:
* [[Color Trap]] moves for both digits
* [[XY-Chain]]
* [[Nice Loop]]

== External links ==
* [http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143 Remote Pairs and Variants]
* [http://www.scanraid.com/AdvanStrategies.htm#RP Remote Pairs]

== See also ==
* [[Chain]] and [[Loop]]
* [[XY-Chain]]

[[Category:Chains and Loops]]
[[Category:Solving Techniques]]

Remote Pairs - Revision history

Rooted: Created page with "The '''Remote Pairs''' technique uses a XY-Chain involving an even number of bivalue cells, and all the cells have the same two digits as their candidate..."