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 is an advanced Sudoku technique that uses a chain of three bi-value cells (cells with exactly two candidates) 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.

The technique works by creating a logical contradiction: if the target cell contained the elimination candidate, it would force an impossible situation in the Y-Wing chain.

Y-Wing Structure

Pivot Cell: AB ↗ Pincer 1: AC
↘ Pincer 2: BC

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

Elimination: Remove C from any cell that can "see" both pincers

The key insight is that regardless of which value the pivot takes, one of the pincers must contain the common candidate (C in this example).

How Y-Wing Works

1

Find a pivot cell

Look for a bi-value cell that can "see" two other bi-value cells.

2

Identify the pincers

Find two bi-value cells that each share one candidate with the pivot but not with each other.

3

Find the common candidate

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

4

Locate elimination targets

Find cells that can "see" both pincer cells and contain the common candidate.

5

Eliminate the candidate

Remove the common candidate from all target cells.

Example: Y-Wing in Action

Here's a practical example of a Y-Wing pattern with candidates 1, 5, and 9:

Y-Wing Pattern: Pivot (1,5) with Pincers (1,9) and (5,9)

3
6
8
2
4
7
1 9
12 5 9
12 5 9
7
12 45 9
12 45 9
3
8
6
12 45 9
12 45 9
12 45 9
12 45 9
12 45 9
12 45 9
12 456 789
12 45
123 45 8
123 456 78
123 456 78
123 456 78
12 456 89
123 45 789
123 45 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
12 456 89
123 45 789
123 45 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
12 456 89
123 45 789
123 45 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
12 456 89
123 45 789
123 45 789
123 456 789
123 456 789
123 456 789
1 5
123 456 789
123 456 789
12 456 89
123 45 789
123 45 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789
12 456 89
123 45 789
123 45 789
5 9
123 456 789
123 456 789
123 456 789
123 456 789
123 456 789

Y-Wing Analysis:

  • Pivot (orange): Row 7, Column 7 contains candidates (1,5)
  • Pincer 1 (blue): Row 1, Column 7 contains candidates (1,9)
  • Pincer 2 (blue): Row 9, Column 4 contains candidates (5,9)
  • Common candidate: 9 appears in both pincers but not the pivot
  • Target cell (pink border): Row 3, Column 4 can see both pincers and contains 9

Logic: If the pivot is 1, then Pincer 1 must be 9. If the pivot is 5, then Pincer 2 must be 9. Either way, one of the pincers must contain 9, so no other cell that can see both pincers can contain 9.

Elimination: Remove 9 from Row 3, Column 4 (and any other cells that can see both pincers).

Y-Wing Recognition Patterns

🔍 Key Recognition Features

  • Three bi-value cells: Each cell has exactly two candidates
  • Shared candidates: Pivot shares one candidate with each pincer
  • Different sharing: Each pincer shares a different candidate with the pivot
  • Common candidate: Both pincers share one candidate that's not in the pivot
  • Visibility: Target cells must "see" both pincers (same row, column, or box)

Step-by-Step Application

  1. Find bi-value cells: Identify cells with exactly two candidates throughout the grid
  2. Select potential pivots: Choose bi-value cells that can "see" other bi-value cells
  3. Check for valid pincers: Find two bi-value cells that each share one candidate with the pivot
  4. Verify the Y pattern: Ensure the pincers share a candidate not in the pivot
  5. Find target cells: Locate cells that can see both pincers and contain the common candidate
  6. Make eliminations: Remove the common candidate from all target cells

⚠️ Common Mistakes

  • Non-bi-value cells: All three Y-Wing cells must have exactly two candidates
  • Wrong candidate sharing: Each pincer must share exactly one candidate with the pivot
  • Incorrect eliminations: Only eliminate from cells that can see both pincers
  • Missing the common candidate: The elimination candidate must be in both pincers but not the pivot
  • Visibility errors: Check row, column, and box relationships carefully

🎯 Practice Exercise

To master Y-Wing recognition:

  1. Start with puzzles that have many bi-value cells
  2. Mark all bi-value cells on the grid
  3. For each bi-value cell, check if it could be a pivot
  4. Look for two other bi-value cells with the right candidate patterns
  5. Draw lines to visualize the Y pattern
  6. Practice identifying target cells that can see both pincers

Tip: Y-Wings often become visible after applying intermediate techniques that create more bi-value cells.

When to Use Y-Wing

  • When standard techniques (singles, pairs, pointing pairs, X-Wing) are exhausted
  • In advanced puzzles with multiple bi-value cells
  • When you notice potential chain patterns forming
  • Before attempting even more complex techniques like forcing chains

Related Techniques

  • X-Wing - Rectangular elimination patterns
  • Obvious Pairs - Foundation for creating bi-value cells
  • XY-Wing - Extended Y-Wing patterns with additional cells
  • XYZ-Wing - Y-Wing variation with three-candidate pivot
← Previous: X-Wing All Techniques Next: Swordfish →