Naked Quad

A Naked Quad is the four-cell extension of Naked Pair and Naked Triple. When four cells in the same unit contain only candidates from a set of four digits, those digits can be eliminated from all other cells in that unit.

How It Works

The Mental Approach

Naked quads use cell-focused thinking — the same approach as pairs and triples:

Approach Question Technique
Cell-focused "What candidates does this cell have?" Naked Quad
Digit-focused "Where can this digit go in this unit?" Hidden Quad

The Pattern

Look for four cells in the same row, column, or box where:

Mixed Sizes Are Valid!

Like triples, not every cell needs all four candidates. Valid quads include:

The key rule: 4 cells with candidates from only 4 digits = Naked Quad

The Logic

If four cells collectively contain only {1, 5, 6, 8}, then:

How to Spot Naked Quads

Step-by-Step Scanning

  1. Count unsolved cells — Focus on units with 5-6 unsolved cells
  2. Find cells with limited candidates — Look for cells with 2-4 candidates
  3. Count the union — If 4 cells together have only 4 distinct digits, it's a quad
  4. Check for eliminations — Are any of these digits in the remaining cells?

When to Look

Naked quads are relatively rare. They typically appear in:

Example

Look at Box 1 (top-left) and ask: what candidates do these cells have?

Box 1 Analysis:

The union across all four cells is {1, 5, 6, 8} — four digits in four cells. This is a Naked Quad!

Note how R1C1 and R3C1 only have two candidates each. This is a "mixed size" quad — the pattern still works because the total distinct digits equals the number of cells.

Eliminations: Remove {1, 5, 6, 8} from other cells in Box 1:

puzzle: S9B0Z193016037N9E08065F5F7A1U027N9E040N1F091Q1M070805020N030701080506020904094Y4Y010402030705041010030907060108021N1M071F03080509430309024305040607075E5E094Y04010302
mode: guided
technique: Naked Quad
initial:
  layers:
    hints: true
steps:
  - text: >
      Box 1 has 8 unsolved cells. Look for cells with limited candidates.
    hint: subtle
    technique: NQ
    state:
      selection:
        cells: [R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C3]

  - text: >
      R1C1 has {1,5}. R2C1 has {1,5,6,8}. R2C2 has {1,5,6,8}. R3C1 has {1,6}. Notice R1C1 and R3C1 only have two candidates each!
    hint: obvious
    technique: NQ
    state:
      selection:
        cells: [R1C1, R2C1, R2C2, R3C1]
      focus:
        enabled: true
        digits: [1, 5, 6, 8]

  - text: >
      Together they contain only {1, 5, 6, 8} — four digits in four cells. This is a Naked Quad! Mixed sizes are valid.
    hint: obvious
    technique: NQ
    state:
      selection:
        cells: [R1C1, R2C1, R2C2, R3C1]
      focus:
        enabled: true
        digits: [1, 5, 6, 8]

  - text: >
      Eliminate {1,5,6,8} from other cells in Box 1: R1C2~1,5, R1C3~5, R2C3~5,6,8, R3C3~6.
    hint: detailed
    technique: NQ
    state:
      selection:
        cells: [R1C2, R1C3, R2C3, R3C3]
      focus:
        enabled: true
        digits: [1, 5, 6, 8]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Tips

  1. Start with small cells — Cells with 2-3 candidates are the best starting points
  2. Look for constrained boxes — Quads often appear in boxes with many solved cells
  3. Count systematically — Add up all distinct digits across cells with limited options
  4. Don't overlook pairs — A quad might include cells that look like parts of pairs

The Locked Set Family

Technique Cells Candidates
Naked Pair 2 2
Naked Triple 3 3
Naked Quad 4 4

The pattern continues theoretically to naked quints and beyond, but these are extremely rare in practice.

More Puzzles

Related Techniques