WXYZ-Wing

A WXYZ-Wing is the four-cell extension of XYZ-Wing. It involves four cells containing exactly four distinct digits, where one digit (the "non-restricted" digit) can be eliminated from cells that see all its instances.

How It Works

The Pattern

A WXYZ-Wing requires:

1. Four cells that together contain exactly four distinct digits (W, X, Y, Z)
2. A hinge cell (typically a quad-value cell with all four digits)
3. Three wing cells that contain subsets of the four digits
4. One non-restricted digit — a digit whose cells don't all see each other

The Non-Restricted Digit

The key to WXYZ-Wing is finding the non-restricted digit:

• For each of the four digits, look at which cells contain it
• If all cells containing that digit can see each other, it's "restricted"
• If NOT all cells can see each other, it's "non-restricted"

The Logic

The non-restricted digit MUST appear in at least one of its cells. Since those cells don't all see each other, any cell that sees ALL of them cannot contain that digit.

Example

Look for cells with 3-4 candidates and ask: which cells can form a WXYZ-Wing?

In this puzzle, find four cells containing exactly four distinct digits.

puzzle: S9Bc38jb7bn0b04070c4j050db70307b60b064302030g5f0z5e83b70407918582038408041v8i900c040h01829g3m7n08049u069w830l03030l456r0r6q1m05094b074j5e09031m4302bf830602174i0c5v5v
mode: guided
technique: WXYZ-Wing
initial:
  layers:
    hints: true
steps:
  - text: >
      WXYZ-Wing uses four cells containing exactly four distinct digits. Look for cells with 3-4 candidates.
    hint: subtle
    technique: WXY
    state:
      selection:
        cells: [R4C3, R4C4, R4C6, R6C1]

  - text: >
      R4C3 {1,2,5,9}, R4C4 {5,9}, R4C6 {1,9}, R6C1 {2,5}. Together: four cells with digits {1,2,5,9}.
    hint: obvious
    technique: WXY
    state:
      selection:
        cells: [R4C3, R4C4, R4C6, R6C1]

  - text: >
      Check which digit is non-restricted: 9 appears in R4C3, R4C4, R4C6 — but R4C6 doesn't see the others!
    hint: obvious
    technique: WXY
    state:
      selection:
        cells: [R4C3, R4C4, R4C6]

  - text: >
      Since 9 is non-restricted, eliminate it from cells seeing ALL instances. R4C2 sees all three, so R4C2~9.
    hint: detailed
    technique: WXY
    state:
      selection:
        cells: [R4C2]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

The Wing Family

Each step adds one cell and one digit, with similar elimination logic.

Finding WXYZ-Wings

Step 1: Find Potential Hinges

Look for cells with 3-4 candidates. These are potential hinges that can connect to wings.

Step 2: Find Compatible Wings

From the hinge, find other cells whose candidates are subsets of the potential four digits.

Step 3: Check Total Digits

Ensure the four cells together have exactly four distinct digits.

Step 4: Identify Non-Restricted Digit

Check each digit to find which one's cells don't all see each other.

Step 5: Find Eliminations

Any cell seeing ALL instances of the non-restricted digit can have it eliminated.

How to Spot WXYZ-Wings

Quad-Value Cell Focus

The key to spotting WXYZ-Wings is finding cells with 3-4 candidates — potential hinges:

Step-by-Step Scanning

1. Scan for multi-value cells — Look for cells with 3-4 candidates as potential hinges
2. Group cells by digits — Find four cells that share exactly four digits
3. Check digit visibility — For each digit, do all cells containing it see each other?
4. Identify non-restricted — The digit whose cells DON'T all see each other
5. Eliminate — Remove from cells that see ALL instances of that digit

Why "Non-Restricted"?

A digit is "restricted" when all its cells see each other — it must appear in one specific cell. A digit is "non-restricted" when its cells don't all see each other — it COULD be in multiple places. The non-restricted digit must be in one of its cells, so any cell seeing all instances cannot contain it.

Complexity

WXYZ-Wing is expert-level because:

• Must find four cells with exactly four digits combined
• Must correctly identify the non-restricted digit
• Must verify which cells see all instances
• Patterns span multiple boxes and units

Tips

1. Start with XYZ-Wing — Master the three-cell version first
2. Look for quad-value cells — These are good hinge candidates
3. Check digit visibility — The key is finding the non-restricted digit
4. Use the hint system — WXYZ-Wings are difficult to spot manually
5. Focus on congested areas — Where many candidates overlap

More Puzzles

• WXYZ-Wing ex. 1
• WXYZ-Wing ex. 2
• WXYZ-Wing ex. 3
• WXYZ-Wing ex. 4
• WXYZ-Wing ex. 5

Related Techniques

• XYZ-Wing — Three-cell version
• Y-Wing — Simpler three-cell pattern
• Naked Quad — Four cells with four digits (different logic)