XY-Wing (Y-Wing) Technique in Sudoku
An elegant 3-cell pattern connecting a central Pivot cell with two Pincer wings. By testing both outcomes of the pivot, candidate Z is eliminated from all intersecting cells.
Interactive XY-Wing Trainer (Pivot at R3C3)
Pivot R3C3 has {1, 2}. Pincer 1 (R3C8) has {1, 5}. Pincer 2 (R7C3) has {2, 5}. Click Solve to eliminate 5 from R7C8 which sees both pincers.
The 3-Step XY-Wing Formula
Locate Bi-Value Pivot
Find a cell with exactly two candidates, labelled {X, Y}.
Find Two Pincers
Find two cells visible from the pivot having {X, Z} and {Y, Z}.
Eliminate Z at Intersection
Any cell sharing a row, col, or box with BOTH pincers cannot contain Z.
Frequently Asked Questions
What is an XY-Wing (Y-Wing) in Sudoku?
An XY-Wing is an advanced solving technique using three bi-value cells (cells with exactly 2 candidates). One cell acts as the 'Pivot' with candidates {X, Y}. Two other cells act as 'Pincers' that can see the pivot, containing candidates {X, Z} and {Y, Z}. Regardless of whether the pivot turns out to be X or Y, one of the pincers is guaranteed to be Z. Therefore, any cell that can see BOTH pincers cannot be Z.
What does it mean for a cell to 'see' another cell in Sudoku?
A cell 'sees' another cell if they share the same row, the same column, or the same 3×3 box. Two cells that see each other can never contain the same number.
How difficult is it to spot an XY-Wing?
XY-Wings become easy to spot once you scan for bi-value cells. Look for cells with 2 candidates, then check their shared houses for matching pairs of {X, Z} and {Y, Z}.
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