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We have duplicated entries here for Remote Pairs and Remote Pair.

unkx80, I suggest they are merged under "Remote Pairs" with the example following the general illustration (which you will manage better than me!).

I was surprised that Ruud found that 5% of puzzles can involve a remote pairs exclusion. I guess this will usually be in the latter stages of the solution process.

Dpbobelisk 18:30, 4 February 2007 (CET)

Done.

--unkx80 19:39, 9 February 2007 (CET)

Definition is too restrictive

You do not need all the cells to have the same pair of candidates to make a remote pair elimination.

A remote pair is:

(a)XY==YX==XY==YX(A)

and any cell that "sees" both ends a and A cannot be X or Y. Necessarily, the chain is composed of strong links in both candidates. It must be comprised of an even number of cells connected by an odd number of links.

But, what if the strong links are only for one candidate?

(a)XY==WX==XZ==YX(A)

W and Z are anything - they do not have to represent a single candidate.

One of a and A must be X. AND, one must be Y! The eliminations for both chains are the same.

So, suppose you have two cells that have the same two candidates but are not a naked pair. If you can connect them by simple coloring on either of the candidates, and if the coloring chain has an uneven number of links (even number of cells), you can make the Remote Pair exclusions.

It seems to me this is a possibly useful rule when solving by hand. So far as programming is concerned, it is likely a special case of a number of chain types.

Keith