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Morniura SudokuGuide

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.

Example: pivot (row 5, col 5) {1, 2}, wings (row 5, col 2) {1, 3} and (row 2, col 5) {2, 3}. Cell (row 2, col 2) sees both wings and loses 3.7231312
Example: pivot (row 5, col 5) {1, 2}, wings (row 5, col 2) {1, 3} and (row 2, col 5) {2, 3}. Cell (row 2, col 2) sees both wings and loses 3.

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

  1. Bi-value scanMark every empty cell with exactly two candidates.
  2. Pick the pivotChoose a {X, Y} cell as the pivot.
  3. Match wingsFind {X, Z} and {Y, Z} cells visible to the pivot.
  4. Eliminate ZRemove Z from any cell that sees both wings.

Walk through an XY-Wing

Step 1 of 4

XY-Wing walkthrough37231312
XY-Wing walkthrough

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.