Naked Triple

Interactive Tutorial

A Naked Triple extends the Naked Pair concept to three cells. When three cells in the same unit contain only candidates from a set of three digits, those digits can be eliminated from all other cells in that unit.

How It Works

The Mental Approach

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

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

The Pattern

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

Mixed Sizes Are Valid!

Important: Not every cell needs all three candidates! This is a common point of confusion. Valid triples include:

The key rule: 3 cells with candidates from only 3 digits = Naked Triple

The Logic

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

How to Spot Naked Triples

Step-by-Step Scanning

  1. Find cells with limited candidates — Look for cells with 2-3 candidates
  2. Check for common digits — Do nearby cells share the same digits?
  3. Count the union — If 3 cells together have only 3 distinct digits, it's a triple
  4. Check for eliminations — Are any of these digits in other cells of the unit?

Using Focus Mode

Focus Mode makes spotting triples easier:

  1. Tap a digit to highlight where it appears
  2. Find digits that appear in few cells
  3. Check if those cells form a naked set

Example

Look at Box 4 (left middle box) and ask: what candidates do these cells have?

Box 4 Analysis:

The union across all three cells is just {1, 5, 8} — three digits in three cells. This is a Naked Triple!

Note how R5C1 only has two candidates. This is a "mixed size" triple — the pattern still works because the total distinct digits equals the number of cells.

Eliminations: Remove {1, 5, 8} from other cells in Box 4:

puzzle: S9B0209040501035U5U06062Q2Q08040203010903434306090702050443D5D50O0506D7D8480Z04A10O087N9V060O4J5HCP04077NBNB848070344010604B6B8050950500703054A4C01040Z0Z090208060307
mode: guided
technique: Naked Triple
initial:
  layers:
    hints: true
steps:
  - text: >
      Look for cells with limited candidates in Box 4 (left column).
    hint: subtle
    technique: NT
    state:
      selection:
        cells: [R4C1, R5C1, R6C1]

  - text: >
      R4C1 has {1,5,8}. R5C1 has just {1,5}. R6C1 has {1,5,8}. Notice R5C1 only has two candidates!
    hint: obvious
    technique: NT
    state:
      selection:
        cells: [R4C1, R5C1, R6C1]
      focus:
        enabled: true
        digits: [1, 5, 8]

  - text: >
      The union is only three digits: {1, 5, 8}. Three cells, three digits — this is a Naked Triple! Mixed sizes are valid.
    hint: obvious
    technique: NT
    state:
      selection:
        cells: [R4C1, R5C1, R6C1]
      focus:
        enabled: true
        digits: [1, 5, 8]

  - text: >
      Eliminate {1,5,8} from other cells in Box 4: R4C2~1,8, R4C3~1,8, R5C3~1,5, R6C2~1,5,8, R6C3~1,5,8.
    hint: detailed
    technique: NT
    state:
      selection:
        cells: [R4C2, R4C3, R5C3, R6C2, R6C3]
      focus:
        enabled: true
        digits: [1, 5, 8]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Tips

  1. Mixed sizes are common — Don't expect all three cells to have three candidates
  2. Start with small cells — Cells with 2-3 candidates are the best starting points
  3. Count the union — Add up all distinct digits across the cells
  4. Check multiple units — A triple in a column might also affect a box

The Subset Principle

Naked triples follow the same logic as pairs:

This scales to Naked Quad (four cells, four digits) and beyond.

More Puzzles

Related Techniques