Advanced Technique

Y-Wing

Master advanced chain-based elimination using a pivot cell and two pincers to eliminate candidates from target cells.

What Is a Y-Wing?

A Y-Wing (also called XY-Wing) is an advanced Sudoku technique that uses a chain of three bi-value cells to eliminate a candidate from one or more target cells. The pattern consists of a central "pivot" cell and two "pincer" cells that form a Y-shaped logical chain.

Key Insight

The technique works by creating a logical chain: no matter which value the pivot takes, one of the pincers must contain the common candidate. Therefore, any cell that "sees" both pincers cannot contain that candidate.

Y-Wing Structure

The Three Cells

Pivot Cell: {A, B}

The central cell with two candidates. It "sees" both pincers.

Pincer 1: {A, C}

Shares candidate A with the pivot. Has the common candidate C.

Pincer 2: {B, C}

Shares candidate B with the pivot. Has the common candidate C.

The Logic

Pivot: {A, B}

↗ Pincer 1: {A, C}

↘ Pincer 2: {B, C}

  • • If Pivot = A, then Pincer 1 = C
  • • If Pivot = B, then Pincer 2 = C
  • • Either way, one pincer must be C!

Eliminate C from any cell that can "see" both pincers

How Y-Wing Works

  1. 1

    Find a pivot cell

    Look for a bi-value cell (exactly two candidates, call them A and B) that can "see" two other bi-value cells.

  2. 2

    Identify the pincers

    Find two bi-value cells that share one candidate each with the pivot (AC and BC), where C is the common candidate not in the pivot.

  3. 3

    Find the common candidate

    Identify candidate C - the one that appears in both pincers but not in the pivot.

  4. 4

    Locate elimination targets

    Find cells that can "see" both pincer cells (share a row, column, or box with both).

  5. 5

    Eliminate candidate C

    Remove the common candidate from all target cells.

Example: Y-Wing in Action

Here's a Y-Wing with candidates 1, 5, and 9. The pivot has {1, 5}, Pincer 1 has {1, 9}, and Pincer 2 has {5, 9}:

Pivot

{1, 5}

Pincer 1

{1, 9}

Pincer 2

{5, 9}

Chain Logic:

If Pivot = 1:

Pincer 1 can't be 1, so it must be 9

If Pivot = 5:

Pincer 2 can't be 5, so it must be 9

Either way, one pincer is always 9!

Elimination

Any cell that can "see" both Pincer 1 and Pincer 2 (shares a row, column, or box with both) cannot contain 9, because one of the pincers will always be 9. Eliminate 9 from all such cells.

When to Use Y-Wing

Best Scenarios

  • ✓ Hard puzzles requiring advanced techniques
  • ✓ Many bi-value cells are present
  • ✓ Simpler techniques have been exhausted
  • ✓ Looking for chain-based eliminations

Common Mistakes

  • ✗ Pincers don't actually "see" the pivot
  • ✗ Wrong identification of the common candidate
  • ✗ Target cells don't see both pincers
  • ✗ Using cells with more than two candidates

Practice Tips

How to Find Y-Wings

  1. 1 Identify all bi-value cells on the grid
  2. 2 For each bi-value cell, check if it can be a pivot
  3. 3 Look for two pincers that complete the Y-Wing pattern
  4. 4 Find target cells and apply eliminations

Related Techniques

Previous: X-Wing All Techniques

Ready to Practice Y-Wing?

Look for chains of bi-value cells that create elimination opportunities in your next hard puzzle!

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