XY-Wing Sudoku Strategy for Advanced Players

The XY-Wing technique is a powerful advanced Sudoku solving method that extends the concept of Y-Wing. This guide will help you understand and master this sophisticated elimination technique.

Understanding XY-Wing

XY-Wing is a three-cell pattern that uses bivalue cells to eliminate candidates. Unlike Y-Wing, XY-Wing specifically deals with cells that contain exactly two candidates each.

XY-Wing Structure

An XY-Wing consists of three bivalue cells:

• Pivot Cell (XY): Contains candidates X and Y
• Pincer Cell 1 (XZ): Contains candidates X and Z, shares a unit with pivot
• Pincer Cell 2 (YZ): Contains candidates Y and Z, shares a unit with pivot

The Logic Behind XY-Wing

The elimination logic works as follows:

1. If the pivot cell contains X, then Pincer Cell 1 must contain Z
2. If the pivot cell contains Y, then Pincer Cell 2 must contain Z
3. In both scenarios, Z must be true in one of the pincer cells
4. Any cell that can see both pincer cells cannot contain Z

How to Identify XY-Wing Patterns

Step 1: Find Bivalue Cells

Look for cells that contain exactly two candidates. These are your potential pivot and pincer cells.

Step 2: Locate the Pivot

Choose a bivalue cell as your pivot. This cell should have two candidates that appear in other bivalue cells.

Step 3: Find Pincer Cells

Look for two other bivalue cells that:

• Share a unit (row, column, or box) with the pivot
• Each contains one candidate from the pivot
• Both contain a common third candidate

Step 4: Apply the Elimination

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

XY-Wing Examples

Example 1: Basic XY-Wing

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

Example 2: Cross-Box XY-Wing

XY-Wing patterns can span multiple boxes, making them particularly useful in complex puzzles.

XY-Wing vs Y-Wing

While similar, XY-Wing and Y-Wing have key differences:

• XY-Wing: All three cells must be bivalue
• Y-Wing: Only the pivot cell must be bivalue
• XY-Wing: More restrictive but often easier to spot

Advanced XY-Wing Applications

Extended XY-Wing

In some cases, the XY-Wing pattern can be extended to involve more cells while maintaining the same logical structure.

Multiple XY-Wings

Complex puzzles may contain multiple XY-Wing patterns that can be applied sequentially.

Common Mistakes to Avoid

Mistake 1: Non-Bivalue Pincer Cells

Remember that in XY-Wing, all three cells must contain exactly two candidates each.

Mistake 2: Incorrect Unit Sharing

Ensure that pincer cells actually share a unit with the pivot cell.

Mistake 3: Wrong Elimination Target

Only eliminate the shared candidate from cells that can see both pincer cells.

Practice Strategies

• Start with puzzles that have many bivalue cells
• Look for XY-Wing patterns systematically
• Practice identifying the three-cell structure
• Verify eliminations before applying them

Related Techniques

XY-Wing is part of a family of advanced techniques:

• Y-Wing - Similar three-cell pattern
• XYZ-Wing - Extended version with trivalue cell
• XY-Wing Basics - Fundamental concepts