XY-Wing Sudoku: How This Intermediate Technique Eliminates Candidates

By Michel

Sudoku a Day Blog ·

You have worked through naked singles, hidden singles, pointing pairs, and basic pair techniques. The grid is still stuck. This is exactly when XY-Wing tends to appear. It is the first technique that feels genuinely clever — a three-cell chain that forces an elimination across the board through pure logic. Once you understand the structure, you will start seeing it on almost every hard puzzle.

What Is the XY-Wing Technique?

XY-Wing uses three cells: one pivot and two pincers. Here is the structure:

  • Pivot: a cell with exactly two candidates, which we call X and Y.
  • Pincer 1: a cell that sees the pivot and contains candidates X and Z.
  • Pincer 2: a cell that sees the pivot and contains candidates Y and Z.

The pivot must be either X or Y:

  • If the pivot is X → Pincer 1 must be Z (because X is taken by the pivot).
  • If the pivot is Y → Pincer 2 must be Z (because Y is taken by the pivot).

In either case, at least one pincer must be Z. Therefore, any cell that sees both pincers cannot be Z and can have Z eliminated from its candidates.

Two cells "see" each other if they share the same row, column, or 3×3 box. A cell visible to both pincers simultaneously is in the elimination zone.

How XY-Wing Works — The Pivot and Pincers

Concrete example: The pivot at R4C5 has candidates {3, 7}. Pincer 1 at R4C9 has {3, 5}. Pincer 2 at R1C5 has {7, 5}. Here X=3, Y=7, Z=5.

  • Both pincers can see the pivot (they share the same row or column as the pivot).
  • Any cell that can see both pincers — meaning it is in the same row or column as both R4C9 and R1C5 — can have 5 eliminated.

In this case R1C9 sees both pincers (it is in row 1 with Pincer 2, and in column 9 with Pincer 1). Remove 5 from R1C9. That one elimination may be enough to unlock the rest of the grid.

Step-by-Step: How to Find XY-Wings

  1. Find all bi-value cells — cells with exactly two candidates. List them. These are your potential pivots and pincers.
  2. Pick a pivot. Take any bi-value cell with candidates {X, Y}.
  3. Find Pincer 1: look for a bi-value cell that the pivot can see, containing X and some third digit Z.
  4. Find Pincer 2: look for a bi-value cell that the pivot can see, containing Y and the same Z.
  5. Identify the elimination zone: cells that can see both pincers simultaneously.
  6. Eliminate Z from any cell in the elimination zone that currently has Z as a candidate.

XY-Wing vs Y-Wing: Are They the Same?

Yes. Y-Wing is an older name for exactly the same technique. Modern Sudoku notation uses XY-Wing to be more precise about the candidate labels involved (X, Y, and Z). If you see both names in solving guides, they refer to the identical three-cell elimination pattern.

XY-Wing vs XYZ-Wing: The Key Difference

In a standard XY-Wing, the pivot has exactly two candidates and does not share a box with both pincers simultaneously. In an XYZ-Wing, the pivot has three candidates — X, Y, and Z — and the elimination zone shrinks. With XYZ-Wing, only cells that can see all three cells (pivot, Pincer 1, and Pincer 2) have Z eliminated. This is a much more restricted zone, making XYZ-Wing harder to apply but occasionally necessary on the hardest grids.

When to Use XY-Wing

XY-Wing appears on hard and expert puzzles, typically after you have exhausted:

When none of those produce a move and you have multiple bi-value cells, scan for XY-Wing. It marks the transition from intermediate to genuinely advanced solving.

Want to practice? Try an expert puzzle on Sudoku a Day — XY-Wings appear regularly on those grids and the puzzle is solved without guessing.

Frequently Asked Questions

What is the XY-Wing technique in Sudoku?

XY-Wing is a three-cell elimination technique. A pivot cell has two candidates (X and Y). Two pincers each share one candidate with the pivot (X+Z and Y+Z). Because the pivot must be X or Y, at least one pincer must be Z. Any cell that sees both pincers cannot be Z.

What is the difference between XY-Wing and Y-Wing?

They are the same technique. Y-Wing is the older name; XY-Wing is the modern label. Both describe the same pivot-and-pincers elimination pattern.

What is the difference between XY-Wing and XYZ-Wing?

In XY-Wing, the pivot has two candidates. In XYZ-Wing, the pivot has three candidates (X, Y, Z). The XYZ-Wing elimination zone is narrower — only cells that see all three cells have Z eliminated, not just cells that see both pincers.

When should I use XY-Wing?

Use XY-Wing on hard and expert puzzles after exhausting singles, locked candidates, and basic pairs and triples. It is one of the first non-linear techniques and indicates you are moving into advanced solving territory.