Naked Triple Sudoku Technique Explained

Extending the Naked Pair concept to three cells

Naked Triple example in Sudoku

What is a Naked Triple?

A Naked Triple occurs when three cells in the same unit contain candidates from a set of exactly three numbers, with no other candidates present. These three cells "claim" those three numbers, allowing elimination from other cells in the unit.

Unlike Naked Pairs where both cells must have identical candidates, Naked Triples are more flexible – each cell can have two or three of the three candidates.

The Naked Triple Principle: If three cells in a unit contain only candidates from a set {A, B, C}, then A, B, and C MUST go in those three cells. Eliminate A, B, and C from all other cells in that unit.

The Flexibility of Naked Triples

A Naked Triple doesn't require all three cells to have all three candidates. Valid combinations include:

Full Triple

{1,2,3} + {1,2,3} + {1,2,3}

All three cells have all three candidates

Mixed Triple

{1,2} + {2,3} + {1,3}

Each cell has two of the three candidates

Partial Triple

{1,2,3} + {1,2} + {2,3}

Mix of two and three candidate cells

How to Find Naked Triples

Step-by-Step Process:

  1. Identify candidate cells: Look for cells with 2-3 candidates in a unit
  2. Group potential triples: Find three cells whose combined candidates form exactly three numbers
  3. Verify the pattern: Each cell must contain ONLY candidates from the set of three
  4. Make eliminations: Remove all three candidates from other cells in the unit

Example Analysis

Finding a Naked Triple

Consider a row with these candidates:

  • Cell A: {2, 5}
  • Cell B: {2, 5, 8}
  • Cell C: {5, 8}
  • Cell D: {1, 2, 5, 9}
  • Cell E: {1, 9}

Cells A, B, and C form a Naked Triple! Together they contain only {2, 5, 8}.

Elimination: Remove 2 and 5 from Cell D, leaving {1, 9}.

Why Naked Triples Work

The logic is the same as Naked Pairs, extended to three cells. If three cells can only contain numbers from a set of three, then those three numbers must go in those three cells (one number per cell). No other cell in the unit can contain any of those numbers.

Key Insight: The "mixed" form of Naked Triple (like {1,2} + {2,3} + {1,3}) is often harder to spot but equally valid. Each number appears in exactly two of the three cells, guaranteeing the triple relationship.

Common Mistakes

  • Extra candidates: If any cell has a candidate outside the set of three, it's not a valid Naked Triple
  • Missing the mixed form: Don't only look for cells with identical candidates
  • Incomplete counting: Ensure exactly three cells and exactly three candidates

Naked Triple vs Naked Pair

Naked Pair

2 cells with 2 candidates

Both cells must have identical candidates

Easier to spot

Naked Triple

3 cells with 3 candidates total

Cells can have 2 or 3 of the candidates

More flexible, harder to spot

Ready to Practice?

Download SudokuWorldTournament and master Naked Triples!

Download Free on App Store