Lesson:Naked Triples
Similar to Naked Pairs, but with three cells and three candidates.
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💾 Saved locallyAbout This Lesson
Naked Triples extend the logic of Naked Pairs to three cells and three candidates. A Naked Triple exists in a unit (row, column, or box) when three cells collectively contain only three distinct candidate digits — in any combination. The key insight is the same as Naked Pairs: those three digits will be distributed among those three cells in some order, so no other cell in the unit can contain any of those three digits.
What makes Naked Triples more complex than Naked Pairs is that the three cells do not each need to contain all three candidates. One cell might have {1, 2}, another {2, 3}, and the third {1, 3} — the union is {1, 2, 3}, which is three digits in three cells. This pattern still qualifies as a Naked Triple, even though no individual cell is a simple bi-value cell with exactly {1,2,3}.
Naked Triples are relatively common on Hard-rated puzzles and above. Recognizing the various forms they can take — full triples, partial triples, and mixed triples — is an important skill for serious solvers.
How It Works — Step by Step
Step 1 — Find groups of 2–3 candidate cells with small candidate sets
Look for empty cells with only 2 or 3 candidates remaining. These cells are the most likely to form Naked Triples.
Step 2 — Check triplets in the same unit
Group three cells from the same unit. Find the union of all their candidates. If the union contains exactly three digits, you have a Naked Triple.
Step 3 — Eliminate from the rest of the unit
All three digits in the union can be eliminated from every other cell in the shared unit.
Step 4 — Follow up
The eliminations from a Naked Triple often directly create Naked Singles or Hidden Singles in the same unit or in intersecting units.
When to Use This Technique
After Naked Pairs and Hidden Pairs have been exhausted. On Hard and Expert puzzles, Naked Triples appear as a natural progression in the solve chain.
Worked Examples
In Column 4, three empty cells have candidates: R2C4 = {1, 5}, R5C4 = {1, 3}, R8C4 = {3, 5}. Union = {1, 3, 5} — exactly three digits in three cells. Naked Triple! Eliminate 1, 3, and 5 from every other empty cell in Column 4.
Frequently Asked Questions
Can a Naked Triple contain only two unique digits?
No. By definition, a Naked Triple requires a set of three cells whose union contains exactly three distinct digits. If only two distinct digits appear across the three cells, two of the cells form a Naked Pair and the third is redundant (it will be forced by another constraint).
Is a Naked Triple rarer than a Naked Pair?
Yes, considerably. Naked Pairs appear in most Hard puzzles; Naked Triples are less common and often more subtle to spot because of the variety of forms they can take.
Related Lessons
Ready to test your knowledge? Try applying this technique in our Hard Sudoku puzzles, Intermediate level course or explore Advanced Sudoku lessons. Keep training to improve your solve times and master the grid!
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