XY-Wing Technique
advancedThree bi-value cells forming a pivot-and-wings pattern for eliminations
The XY-Wing is one of the most elegant advanced techniques. It uses three cells, each containing exactly two candidates, arranged so that a common digit can be eliminated from any cell that sees both "wings."
Understanding the Concept
You need three bi-value cells: a Pivot and two Wings.
The Pivot has candidates {X,Y}. Wing 1 has {X,Z}. Wing 2 has {Y,Z}. The shared digit Z is the elimination target.
The Pivot must see (share a row, column, or box with) both Wings. The Wings do NOT need to see each other.
Reasoning: If the Pivot is X, then Wing 1 (which sees the Pivot) cannot be X, so Wing 1 must be Z. If the Pivot is Y, then Wing 2 must be Z. Either way, at least one Wing is Z.
Therefore, any cell that sees BOTH Wings cannot be Z — because one of the Wings already holds Z.
This is also called a "Y-Wing" in some references.
Examples
XY-Wing: Pivot {3,7}, Wings {3,9} and {7,9}
Pivot at R4C4 has candidates {3,7}. Wing 1 at R4C8 has {3,9} (same row as pivot). Wing 2 at R7C4 has {7,9} (same column as pivot). The elimination digit is 9. Any cell seeing both wings cannot be 9. Cell R7C8 sees Wing 1 (same column 8) and Wing 2 (same row 7) — eliminate 9 from R7C8.
Pro Tips
- •Start by scanning for bi-value cells (cells with exactly 2 candidates)
- •The Pivot must see both Wings — check shared rows, columns, and boxes
- •The Wings must share exactly one candidate (Z) — this is the elimination digit
- •Eliminations happen only in cells that see BOTH Wings simultaneously
- •XY-Wings are more common than fish patterns and well worth mastering
