Y-Wing Sudoku Technique: Step-by-Step Guide

The Y-Wing technique is one of the most powerful advanced Sudoku solving methods. This comprehensive guide will teach you how to identify, understand, and apply Y-Wing patterns to solve even the most challenging puzzles.

What is the Y-Wing Technique?

The Y-Wing technique is a logical deduction method that uses three cells to eliminate candidates. It's called "Y-Wing" because the pattern resembles the letter Y when visualized on the Sudoku grid.

Basic Y-Wing Structure

A Y-Wing consists of three cells:

• Pivot Cell: Contains exactly two candidates (AB)
• Pincer Cell 1: Contains candidates (AC) and shares a unit with the pivot
• Pincer Cell 2: Contains candidates (BC) and shares a unit with the pivot

How Y-Wing Works

The logic behind Y-Wing is based on the following principle:

1. If the pivot cell contains A, then Pincer Cell 1 must contain C
2. If the pivot cell contains B, then Pincer Cell 2 must contain C
3. In both cases, C must be true in one of the pincer cells
4. Therefore, any cell that sees both pincer cells cannot contain C

Step-by-Step Y-Wing Identification

Step 1: Look for Bivalue Cells

Start by identifying cells that contain exactly two candidates. These are your potential pivot cells.

Step 2: Find Pincer Cells

For each bivalue cell, look for other cells that:

• Share a row, column, or box with the pivot
• Contain exactly two candidates
• Share one candidate with the pivot

Step 3: Check for Y-Wing Pattern

Verify that the two pincer cells share a common candidate that's different from the pivot's candidates.

Step 4: Apply the Elimination

Find cells that can see both pincer cells and eliminate the shared candidate from those cells.

Y-Wing Examples

Example 1: Basic Y-Wing

Consider a pivot cell with candidates (1,2), a pincer cell with (1,3), and another pincer cell with (2,3). Any cell that can see both pincer cells cannot contain 3.

Example 2: Complex Y-Wing

In more complex scenarios, the Y-Wing might span multiple boxes or have pincer cells in different units from the pivot.

Common Y-Wing Mistakes

Mistake 1: Incorrect Pincer Identification

Ensure that pincer cells actually share a unit with the pivot cell. Cells that don't share a row, column, or box cannot form a valid Y-Wing.

Mistake 2: Wrong Elimination Target

Only eliminate the shared candidate from cells that can see both pincer cells. Don't eliminate from cells that only see one pincer.

Mistake 3: Ignoring Unit Constraints

Remember that Y-Wing requires the pincer cells to share a unit with the pivot. This is crucial for the logical deduction to work.

Advanced Y-Wing Variations

W-Wing

The W-Wing is a variation where the pivot cell is replaced by a strong link between two cells.

Extended Y-Wing

In extended Y-Wing, the pattern can involve more than three cells while maintaining the same logical structure.

Practice Tips

• Start with puzzles that have many bivalue cells
• Look for Y-Wing patterns systematically
• Practice identifying the pivot and pincer cells
• Verify your eliminations before applying them

Related Techniques

Y-Wing is closely related to other advanced techniques:

• XY-Wing - Similar three-cell pattern
• X-Wing - Four-cell elimination pattern
• Swordfish - Extended X-Wing pattern