SUDOKU SAMA
ExpertUsefulness: Medium

XY-Wing

A pivot cell {X,Y} sees two pincers {X,Z} and {Y,Z}. Whatever the pivot becomes, one pincer must be Z — so Z is eliminated from cells both pincers see.

The pivot cell has candidates 1 and 2. Two pincers share a house with it: one shows {1,3}, the other {2,3}.

patterneliminatesolved

How to spot it

  1. 1Find a pivot with two candidates {X,Y}.
  2. 2Find pincers {X,Z} and {Y,Z} it can see.
  3. 3Remove Z from any cell both pincers see.

When to use

When bi-value cells are plentiful — a workhorse of expert solving.

When not to

If the three cells don't share the right candidates, there's no wing.

Common mistake

Eliminating Z from cells only one pincer sees. Both must see the target.

Worked Example

An XY-Wing needs three cells: a pivot with exactly two candidates, {X,Y}, and two pincer cells it shares a house with — one showing {X,Z}, the other {Y,Z}. If the pivot turns out to be X, the first pincer can't also be X (they share a house), so it must be Z. If the pivot is Y instead, the second pincer is forced to Z the same way.

Either way — whichever value the pivot actually takes — one of the two pincers ends up holding Z. So any cell that shares a house with both pincers can't be Z either, since one of them is guaranteed to hold it. That third digit, Z, gets eliminated from every cell the two pincers have in common.