127.0.0.1 at 15:15, 25 October 2021

2021-10-25T15:15:36Z

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	Here is a schematic example. The alternating digits are named '''X''' and '''Y'''.		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=--}}		{{grid\|4=--\|5=--\|6=--\|8=--\|10=--\|11=XY\|12=--\|13=--\|14=YX\|15=--\|16=--\|17=--\|18=--\|19=--\|20=--\|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).		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).

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

2021-10-25T15:13:59Z

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

New page

The '''Remote Pairs''' [[solving 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

127.0.0.1 at 15:15, 25 October 2021

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