The Remote Pair – A Special XY-Chain

The remote pair comes your way with a blinking road sign. It is an XY-chain in which every bv along the chain contains the same two candidates, X and Y. The X and Y in the end cells are toxic.

Stephens remote pairThe way in which a remote pair stands out is evident in this example from Paul Stephens’ Mastering Sudoku Week by Week.

I mark a remote pair with the ©PowerPoint FreeForm shape, centering ends and corners on the XY cells. Such a chain of an even number of cells, i.e of odd length, is a remote pair. The two cells are toxic as if they were a naked pair in the same unit. You can confirm this behavior by considering X and Y separately as end candidates of an XY-chain. At all odd lengths (2, 4, 6, … cells), the toxic end cells are also known as conjugate pairs.


More 200 trick remotesHere is another instructive example from my review of Antoine Alary’s More Extreme Sudoku, puzzle 200. Two remote pair formations occur together, each removing a pair of candidates in the same cell, leaving a clue.

It came as I was showing how a technique reported by a blog reader solves Antoine’s “book’s most difficult” puzzle.

For continuity in learning advanced Sudoku methods, I now recommend going directly to the X-panel methods, starting with X-chains. This leaves out uniqueness methods, which do fit in with other bv scan techniques, but are not directly related to these methods. Fishing, X-chains and coloring are powerful methods which more directly extend the concepts of links, chains, and toxic sets beyond the bv field.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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2 Responses to The Remote Pair – A Special XY-Chain

  1. Big says:

    Would you give us the complete puzzle – 81 string would do?

    • Sudent says:

      I’d like to, but I can’t find it. The remote pair of the post was created by a solving mistake long since erased. But I do know of two nice remote pairs among the reviewed CrazyDad SuperTough’s. The one in book 5 is among the snapshots of post 3/26/13. The other one in book 5 I didn’t post, but you can download ST v5 b5 #5 and solve for it.

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