WXYZ-Wing in Sudoku: The Complete Guide

What is a WXYZ-Wing?

A WXYZ-Wing is a rare and advanced Sudoku technique that extends the wing pattern family to four cells. It's the logical progression from XY-Wing (2+2 cells) and XYZ-Wing (3 candidates pivot) to a four-cell, four-candidate pattern.

The pattern consists of:

  • Pivot cell: Contains exactly four candidates {W, X, Y, Z}
  • Wing cell 1: Contains 2-3 candidates from {W, X, Y, Z} and can see the pivot
  • Wing cell 2: Contains 2-3 candidates from {W, X, Y, Z} and can see the pivot
  • Wing cell 3: Contains 2-3 candidates from {W, X, Y, Z} and can see the pivot

The Elimination Rule:

If one candidate (typically Z) appears in all four cells, and another cell can see all four pattern cells, you can eliminate that candidate from that cell. Why? Because the candidate must be placed in one of these four cells.

Example:

Pivot at Row 5, Col 5 with {2, 4, 6, 9}. Wing 1 has {2, 4, 9}, Wing 2 has {4, 6, 9}, Wing 3 has {2, 6, 9}. The common candidate 9 appears in all four cells. Any cell seeing all four cannot contain 9.

Why WXYZ-Wing Matters

  • It completes the wing technique family (XY → XYZ → WXYZ).
  • It solves rare situations in expert puzzles where nothing else works.
  • It demonstrates mastery of advanced pattern recognition.
  • It's one of the most sophisticated manual techniques.
  • Finding one is a badge of honor among Sudoku enthusiasts.

How to Spot a WXYZ-Wing

  1. Find a pivot cell with four candidates.
    Look for cells with exactly four candidates like {1,3,5,8} or {2,4,6,9}. Call these W, X, Y, and Z.
  2. Look for three wing cells.
    Find three cells that each have 2-3 candidates drawn only from {W,X,Y,Z}.
  3. Verify visibility.
    The pivot must be able to "see" all three wing cells (same row, column, or box).
  4. Identify the common candidate.
    Find which candidate appears in all four cells (pivot + three wings). This is typically Z.
  5. Find elimination targets.
    Look for cells that see all four cells in the pattern.
  6. Eliminate.
    Remove the common candidate from any cell that sees all four pattern cells.

WXYZ-Wing in the Wing Family

The wing techniques form a progression:

  • XY-Wing:
    • Pivot: {X, Y} (2 candidates)
    • Wings: {X, Z}, {Y, Z}
    • Rarity: Occasional
  • XYZ-Wing:
    • Pivot: {X, Y, Z} (3 candidates, includes Z)
    • Wings: {X, Z}, {Y, Z}
    • Rarity: Rare
  • WXYZ-Wing:
    • Pivot: {W, X, Y, Z} (4 candidates, includes Z)
    • Wings: Three cells with 2-3 candidates from {W,X,Y,Z}
    • Rarity: Extremely rare

Each adds complexity but follows the same logical principle.

Step-by-Step Example

Let's identify a theoretical WXYZ-Wing:

Pattern cells:

  • Pivot: Row 5, Col 5 contains {1, 3, 7, 9}
  • Wing 1: Row 5, Col 2 contains {1, 7, 9} (shares row with pivot)
  • Wing 2: Row 2, Col 5 contains {3, 7, 9} (shares column with pivot)
  • Wing 3: Row 6, Col 6 contains {1, 3, 9} (shares box with pivot)

Verification:

  • ✓ Pivot has four candidates: {1, 3, 7, 9}
  • ✓ Wing 1 has {1, 7, 9}—subset of pivot candidates
  • ✓ Wing 2 has {3, 7, 9}—subset of pivot candidates
  • ✓ Wing 3 has {1, 3, 9}—subset of pivot candidates
  • ✓ Common candidate across all four: 9
  • ✓ Pivot sees all three wings (row, column, box)

The Logic:

Candidate 9 must go in one of these four cells. If another cell can see all four cells, it cannot contain 9 because 9 is locked to these four positions.

Elimination:

Any cell that sees all four pattern cells (through row, column, and box relationships) cannot contain 9. For example, Row 2, Col 2 (if it sees Row 5/Col 2, Row 2/Col 5, and potentially the pivot and Wing 3 through complex visibility).

The Reality of WXYZ-Wing

Let's be honest about this technique:

  • Extremely rare: Most expert solvers have never encountered one in actual solving.
  • Hard to spot: With four cells and complex visibility requirements, it's very difficult to recognize.
  • Often avoidable: Many puzzles with potential WXYZ-Wings can be solved using other advanced techniques.
  • Theoretical importance: It completes your understanding of wing patterns, even if rarely used.
  • Diminishing returns: The complexity-to-frequency ratio makes it impractical for regular use.

Strategies for Spotting WXYZ-Wing

  1. Don't actively hunt for them
    WXYZ-Wings are so rare that searching wastes time. They're more of a "last resort" technique.
  2. Start with four-candidate cells
    If you do search, look for cells with exactly four candidates as potential pivots.
  3. Check visibility carefully
    The pivot must see all three wings. This geometric constraint is restrictive.
  4. Look for the common candidate
    All four cells must share at least one candidate. If they don't, it's not a WXYZ-Wing.
  5. Use after simpler wings
    Only consider WXYZ-Wing after XY-Wing and XYZ-Wing searches come up empty.

Common Pitfalls

  • Wrong pivot: The pivot must have exactly four candidates, not three or five.
  • Missing visibility: All three wings must be visible from the pivot cell.
  • Wing cells with wrong candidates: Each wing must only contain candidates from the pivot's set.
  • No common candidate: At least one candidate must appear in all four cells.
  • Wasting time: Don't spend hours searching for WXYZ-Wings. They're too rare.

Why WXYZ-Wing Sets the Stage

WXYZ-Wing represents the practical limit of wing techniques:

  • It completes your theoretical knowledge of wing patterns
  • It demonstrates that patterns scale logically (2→3→4)
  • It shows why humans rarely go beyond four cells (complexity grows exponentially)
  • It prepares you for other advanced techniques that involve multiple cell relationships
  • It proves that even the most obscure patterns follow consistent logical principles

Quick Recap

Technique Cells Pivot Candidates Rarity Difficulty
XY-Wing 3 2 Occasional Advanced
XYZ-Wing 3 3 Rare Advanced
WXYZ-Wing 4 4 Extremely Rare Advanced

Final Thought

WXYZ-Wing is Sudoku's "legendary creature"—few have seen one, but knowing it exists completes your toolkit. Found a four-candidate cell with three visible wings sharing a common candidate? You might have spotted the rarest wing pattern in Sudoku!

Frequently Asked Questions

What is a WXYZ-Wing in Sudoku?

A WXYZ-Wing is a rare advanced Sudoku technique involving four cells: a pivot cell with candidates {W,X,Y,Z} and three wing cells with three candidates each from the set {W,X,Y,Z}. If any cell can see all four cells of the WXYZ-Wing, you can eliminate candidate Z from that cell. It's the four-cell extension of XYZ-Wing.

How do I spot a WXYZ-Wing?

To spot a WXYZ-Wing: 1) Find a cell with exactly four candidates {W,X,Y,Z} as your pivot, 2) Look for three wing cells each with 2-3 candidates from this set, 3) Verify the pivot sees all three wing cells, 4) Identify one candidate (Z) that appears in all four cells, 5) Eliminate Z from cells that see all four pattern cells.

What's the difference between WXYZ-Wing and XYZ-Wing?

XYZ-Wing uses three cells with a pivot containing three candidates. WXYZ-Wing uses four cells with a pivot containing four candidates. Both follow the same logic pattern but WXYZ-Wing is much rarer and harder to spot. WXYZ-Wing extends the wing family to its practical limit for human solvers.

Why is WXYZ-Wing important?

WXYZ-Wing is important because it completes the wing technique family (XY→XYZ→WXYZ), it solves rare situations in expert puzzles where nothing else works, it demonstrates mastery of pattern recognition, and it's one of the most advanced manual techniques.

When should I look for WXYZ-Wing?

Look for WXYZ-Wing only after exhausting all simpler techniques including XY-Wing and XYZ-Wing. Focus on cells with exactly four candidates as potential pivots. This technique is extremely rare—many expert solvers never encounter one. Don't spend too much time searching for it.

Ready to advance? Check out our complete strategy guide for more techniques.

Related Strategies

Once you've mastered WXYZ-Wing, these techniques build naturally:

  • XYZ-Wing - The three-cell predecessor to WXYZ-Wing
  • XY-Wing - The foundation of all wing techniques
  • X-Wing - Different pattern family but similar logic
  • Swordfish - Advanced fish pattern
  • Naked Quads - Four-cell subset technique

Practice WXYZ-Wing

Next up: Try other expert techniques like Jellyfish or coloring methods (coming soon).

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