When three cells in a unit collectively contain exactly three candidates, those candidates can be eliminated from all other cells in that unit.
A Naked Triple is formed when three cells within the same row, column, or 3x3 box contain candidates drawn from exactly three numbers. Each individual cell may hold two or three of these candidates - the crucial point is that the total pool of candidates across all three cells is exactly three distinct numbers.
Consider three cells in a column with candidates [2, 5], [2, 9], and [5, 9]. Together, these cells cover exactly three numbers: 2, 5, and 9. Each number must go in one of these three cells, so 2, 5, and 9 can be eliminated from every other cell in that column. A variant like [2, 5, 9], [2, 5], and [5, 9] is equally valid - the first cell contains all three candidates while the others hold subsets.
This flexibility in how candidates are distributed among the three cells is what makes Naked Triples trickier to spot than Naked Pairs. For more terminology, see our Sudoku glossary.
Reach for Naked Triples when singles and pairs have stalled your progress. This commonly occurs in hard Sudoku puzzles and some medium puzzles with dense candidate distributions.
Naked Triples are particularly powerful because a single identification can eliminate candidates from up to six other cells in the unit, often triggering a cascade of singles. Combine with Pointing Pairs and Box-Line Reduction for maximum effectiveness. Visit our strategies overview for the complete solving progression, or learn fundamentals at how to play Sudoku.
Naked Triples is classified as an intermediate-level technique, sitting above pairs in complexity. Spotting them requires practice but the elimination logic is straightforward once understood.
Not needed - singles are sufficient
Occasionally needed for tougher medium puzzles
Regularly useful - a staple for hard puzzles
Part of the toolkit alongside advanced methods
A Naked Triple occurs when three cells in the same row, column, or box collectively contain exactly three candidate numbers (and no others). Each cell may have two or three of these candidates, but the total set of candidates across all three cells is exactly three numbers.
No. Each cell in a Naked Triple can contain two or three of the triple's candidates. For example, cells with {1,3}, {1,7}, and {3,7} form a valid Naked Triple for candidates 1, 3, and 7. The key requirement is that the union of all candidates across the three cells equals exactly three numbers.
A Naked Pair involves two cells with the same two candidates; a Naked Triple involves three cells whose combined candidates total exactly three numbers. Naked Triples are a natural extension of the pairs concept and follow the same elimination logic, but applied to three cells and three candidates.
Naked Triples are less common than Naked Pairs but appear regularly in hard and expert puzzles. They are an important tool for making progress when pairs alone are insufficient. Some medium puzzles also require triple-based eliminations.
The next extensions are Naked Quads (four cells, four candidates) and Hidden Triples. Most solvers find that mastering pairs and triples, combined with Pointing Pairs and Box-Line Reduction, is sufficient for the majority of hard puzzles.
Look at three cells in row 1: C1 has [2, 5, 8], C2 has [2, 5], and C3 has [5, 8].
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