XY-Wing: Three Cells That Trap a Candidate

XY-Wing is a beautiful logic pattern that uses three cells and three candidates to trap and eliminate a specific number. It's completely different from X-Wing despite the similar name!

What is an XY-Wing?

An XY-Wing consists of three cells with exactly two candidates each, forming a specific pattern:

• Pivot cell: Contains candidates (X, Y)
• Pincer 1: Contains (X, Z) and shares a region with the pivot
• Pincer 2: Contains (Y, Z) and shares a region with the pivot

When this pattern forms, you can eliminate Z from any cell that sees both pincers!

The Three-Cell Pattern

Think of it as a hinge:

• Pivot: The central cell with candidates (X, Y)
• Pincer 1: Sees the pivot, has (X, Z)
• Pincer 2: Sees the pivot, has (Y, Z)

The Logic: Why It Works

The pivot must be either X or Y:

• If pivot = X: Pincer 1 can't be X, so it must be Z
• If pivot = Y: Pincer 2 can't be Y, so it must be Z

Either way, Z appears in one of the pincers! Therefore, any cell that sees both pincers cannot be Z.

Example

Cells:

• Pivot (Row 3, Col 4): (2, 7)
• Pincer 1 (Row 3, Col 1): (2, 9) - shares row with pivot
• Pincer 2 (Row 5, Col 6): (7, 9) - shares box with pivot

Result: Any cell that sees both pincers can't be 9

How to Find XY-Wings

1. Find a bi-value cell (exactly 2 candidates) - this is your potential pivot
2. Look for cells with 2 candidates that share a region with it
3. Check if they form the XY-Wing pattern:
   • One pincer shares one candidate with pivot
   • Other pincer shares the other candidate
   • Both pincers share a third candidate (Z)
4. Find cells seeing both pincers - eliminate Z from them

The Visibility Rule

For elimination, a cell must "see" both pincers, meaning it must:

• Share a row, column, or box with Pincer 1, AND
• Share a row, column, or box with Pincer 2

This is often called the "victim cell" or "elimination cell."

Common Mistakes

• Confusing with X-Wing: XY-Wing uses cells with exactly 2 candidates, X-Wing uses row/column patterns
• Wrong elimination: Only eliminate from cells that see BOTH pincers
• Missing the shared candidate: Both pincers must have the same candidate Z
• Forgetting the pivot relationship: Pincers must see the pivot!

Pattern Variations

The pincers can connect to the pivot through:

• Same row
• Same column
• Same box
• Any combination!

This flexibility makes XY-Wings common but sometimes hard to spot.

Scanning Strategy

Systematic approach:

1. Find all bi-value cells (mark them!)
2. For each, treat it as a potential pivot
3. Look for cells that share one candidate
4. Check if they form the XY-Wing pattern
5. Search for elimination opportunities

Quick scan:

• Focus on cells with candidates like (2,7) in constraint-rich areas
• Look for cells with common candidates nearby

Frequency and Difficulty

XY-Wings are:

• More common than X-Wing
• Appear in medium-hard puzzles
• Easier to spot with practice
• Very satisfying when found!

Extended Elimination

Sometimes an XY-Wing eliminates candidates from multiple cells if they all see both pincers. This creates a powerful cascade effect!

Visual Recognition

Draw lines connecting:

• Pivot to Pincer 1
• Pivot to Pincer 2
• Look for cells in the "overlap zone" of both pincers

Practice Tips

1. Start by identifying all cells with exactly 2 candidates
2. Mark them on your grid
3. Look for the XY, XZ, YZ pattern
4. Use colored pencils to highlight connections
5. Don't rush - carefully verify each step

Common Candidate Patterns

XY-Wings often involve:

• Common numbers like (2,7), (4,9), (3,6)
• Candidates that appear frequently in the puzzle
• Cells in well-connected regions

Impact on Solving

XY-Wings typically:

• Eliminate 1-3 candidates
• Create hidden singles
• Unlock stuck puzzles
• Appear multiple times in hard puzzles

Related Techniques

• XYZ-Wing: Variation where the pivot has 3 candidates
• WXYZ-Wing: Four-cell extension
• Y-Wing: Alternative name for XY-Wing
• Remote Pairs: A chain-like extension of this concept

The Name Explained

"XY-Wing" comes from the candidate pattern:

• XY: The pivot cell
• Wing: The two pincer cells extending from it

Next Steps

You're mastering advanced techniques! Continue with:

• Simple Coloring - Alternating chains and colors
• Unique Rectangles - Using uniqueness constraints
• Forcing Chains - Following logical chains to conclusions