XY-Wing

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XY-Wing

What It Is

XY-Wing uses three cells: a pivot with {X,Y}, and two wings {X,Z} and {Y,Z}. The pivot sees both wings. No matter pivot’s value, one wing becomes Z, so any cell seeing both wings cannot be Z.

When to Use

Mid-game when bi-value cells abound and simpler techniques stall.

How to Apply (Step-by-Step)

  1. Find a pivot bi-value cell {a,b}.
  2. Find two wings: one {a,c}, one {b,c}, each sharing a unit with the pivot.
  3. Verify pivot sees both; wings may not see each other.
  4. Eliminate c from any cell that sees both wings.
  5. Repeat as new XY-Wings appear.

Pivot {2,5}, wing1 {2,9}, wing2 {5,9}; any cell seeing both wings cannot have 9 because one wing must be 9.

See also

Scanning / Cross-Hatching Single Candidate (Naked Single) Single Position (Hidden Single) Naked Pairs / Triples / Quads Hidden Pairs / Triples / Quads Pointing Pairs / Triples (Locked Candidates Type 1) Box–Line Reduction (Locked Candidates Type 2) X-Wing Swordfish Jellyfish XY-Wing XYZ-Wing W-Wing Alternating Inference Chains (AICs) Forcing Chains / Forcing Nets Nishio Coloring Multi-Coloring Uniqueness Techniques (Unique Rectangle etc.) Fish Variants (Finned X-Wing, Sashimi etc.) ALS Techniques (ALS-XZ, ALS Chains) Sue de Coq Pattern Overlay / Template Method
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