TECHNIQUE · EXPERT
XY-Wing — three bi-value cells linked
Three cells with exactly two candidates each form an XY-XZ-YZ pattern. Any cell that sees both wings can be cleared of Z, even when X-Wing-style patterns are absent.
The logic
Let the pivot be {X, Y}, wing1 be {X, Z}, and wing2 be {Y, Z}. If the pivot resolves to X, wing1 becomes Z; if it resolves to Y, wing2 becomes Z. Either way, Z lands on one of the wings — so any cell seeing both wings cannot hold Z.
How to find it
Mark every bi-value cell. Pick one as a pivot and look at the other bi-value cells it sees. Search for the pair (X,Z) and (Y,Z) that completes the wing pattern.
- Mark every empty cell with exactly two candidates.
- Choose a pivot cell with candidates {X, Y}.
- Among bi-value cells visible to the pivot, find {X, Z} and {Y, Z}.
- Remove Z from any cell that sees both wings.
Different from X-Wing
X-Wing is a row/column candidate-grid pattern for a single digit. XY-Wing is a relationship between three bi-value cells. Both are Expert techniques but use very different scanning lenses.
Practice order
- Bi-value scanMark every empty cell with exactly two candidates.
- Pick the pivotChoose a {X, Y} cell as the pivot.
- Match wingsFind {X, Z} and {Y, Z} cells visible to the pivot.
- Eliminate ZRemove Z from any cell that sees both wings.
Walk through an XY-Wing
Step 1 of 4
Pick the pivot at (row 5, col 5) with candidates {1, 2}. We don't know which value it takes — but it must be 1 or 2.