sudokly
Advanced technique

XYZ-Wing

An XYZ-wing extends XY-wing. The pivot holds three candidates {X, Y, Z}. The two wings are {X, Z} and {Y, Z}. Z can be eliminated from any cell that sees the pivot and both wings.

3

How it works

XYZ-wing is XY-wing with the pivot upgraded from bivalue to trivalue. The pivot still has X and Y, and now also Z directly.

Whichever digit the pivot resolves to, one of the three cells holds Z: the pivot itself, the X-Z wing, or the Y-Z wing. So Z is forced into one of those three cells.

Any cell that sees all three of them cannot be Z. That elimination is the payoff.

When to look for it

When XY-wing fails and a similar three-cell shape suggests itself with a trivalue pivot.

Tips for spotting the pattern

  • The eliminations are tighter than XY-wing because the cell must see all three of the pivot and both wings.
  • Bivalue wings only. The trivalue is the pivot.
  • Searching for both XY and XYZ patterns together is efficient.

Common mistakes

  • Bivalue pivot. That would be plain XY-wing, not XYZ.
  • Eliminating Z from cells that only see two of the three. They must see all three.
  • Confusing the shape with WXYZ-wing (four cells), which is a different and more advanced pattern.
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