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XY-Wing (Y-Wing) Technique: 3-Cell Branching Logic & Visual Guide

Master the elegant XY-Wing (Y-Wing) strategy in Sudoku with clear 9x9 visual diagrams. Learn how a Pivot cell [X,Y] and two Wing cells [X,Z] and [Y,Z] eliminate candidates.

Unlike single-digit grid patterns such as X-Wing or Swordfish, XY-Wing (also known as Y-Wing) is a branching technique that links three bi-value cells (empty cells containing exactly two candidate numbers). Once you learn how to spot this three-cell triangle, you can break through tough Expert and Master puzzles without guessing.

1. The Three Roles in an XY-Wing

An XY-Wing is formed by three cells that each contain two candidates drawn from a trio of digits X, Y, and Z:

Pivot (Stem / Hinge): A cell with candidates [X, Y] that can "see" (shares a row, column, or 3×3 box with) both Wing A and Wing B.
Wing A (Pincer 1): Shares a unit with the Pivot and holds candidates [X, Z].
Wing B (Pincer 2): Shares a different unit with the Pivot and holds candidates [Y, Z].

Note: Wing A and Wing B do NOT share the same row, column, or box with each other—they only connect through the Pivot cell.

2. Concrete Visual Example (X=1, Y=2, Z=9)

Examine the partial 9×9 diagram below:

Row 2, Column 2 (R2C2) is the Pivot [1, 2].
Row 2, Column 8 (R2C8) is Wing A [1, 9] (shares Row 2 with the Pivot).
Row 7, Column 2 (R7C2) is Wing B [2, 9] (shares Column 2 with the Pivot).
Row 7, Column 8 (R7C8) sees BOTH Wing A (via Column 8) and Wing B (via Row 7).

.	.	.	.	.	.	.	.	.
.	[1, 2]	→	→	→	→	→	[1, 9]	.
.	↓	.	.	.	.	.	↓	.
.	↓	.	.	.	.	.	↓	.
.	↓	.	.	.	.	.	↓	.
.	↓	.	.	.	.	.	↓	.
.	[2, 9]	→	→	→	→	→	9✕	.
.	.	.	.	.	.	.	.	.

Why Can Candidate 9 Be Eliminated from R7C8?

Case A (Pivot R2C2 = 1): Since R2C2 is 1, Wing A (R2C8) in the same row cannot be 1, so Wing A must be 9.
Case B (Pivot R2C2 = 2): Since R2C2 is 2, Wing B (R7C2) in the same column cannot be 2, so Wing B must be 9.

Because at least one of the two Wings is guaranteed to contain 9, any cell that sees both Wings simultaneously (such as R7C8) can NEVER be 9!

3. Box-Line XY-Wing (Affecting Multiple Cells)

When the Pivot and one Wing share a 3×3 Box while the Pivot and the other Wing share a Row or Column, up to 4 or 5 cells can see both Wings at once. Always check both the row/column intersection and the 3×3 box intersection of the two Wings.

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