Naked Triples extends the Naked Pairs concept to three cells and three candidates. A Naked Triple occurs when three cells in the same row, column, or box collectively contain exactly three candidate digits, with each cell holding a subset of those three digits. Importantly, not every cell needs to contain all three candidates -- as long as the union of candidates across the three cells produces exactly three distinct digits, the pattern qualifies.
For example, cells with candidates {2, 5}, {2, 8}, and {5, 8} form a Naked Triple on digits 2, 5, and 8. Between the three cells, these three digits must be distributed in some order, which means 2, 5, and 8 can be eliminated from all other cells in the shared unit. This type of Naked Triple where no single cell contains all three candidates is sometimes harder to spot but is equally valid.
Naked Triples appear in medium to hard puzzles and are a natural progression from Naked Pairs. The challenge lies in recognizing that three cells can form a triple even when individual cells contain only two of the three candidates. Developing the ability to spot these partial triples is a significant step forward in your solving capability and sets the foundation for understanding Naked Quads and other higher-order subsets.
Try It Yourself
Walk through each step of the naked triples technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look at row 4 (index 3). Three cells at positions (3,0), (3,1), and (3,2) are empty. Identify the candidates for each cell by checking which digits are missing from the row, column, and box.
Step-by-Step Guide
Ensure all pencilmarks are up to date in the grid.
In a row, column, or box, find cells with two or three candidates.
Select three cells and compute the union of all their candidates.
If the union contains exactly three distinct digits, you have a Naked Triple.
Eliminate those three digits from all other cells in the same unit.
Check if any cells are now resolved to a single candidate.
Continue scanning other units for additional Naked Triples.
Three friends agree to share three dishes at a restaurant. Even though each person only wants two of the three, those three dishes are reserved for the group and nobody else at the table can order them.
When three cells in a unit collectively contain at most three distinct candidates, those three cells define a closed system: three positions that must be filled by exactly three digits. By the pigeonhole principle, the three digits are fully consumed by the three cells, leaving none available for other cells in the unit. Even if individual cells hold only a subset of the three digits, the combinatorial possibilities across all three cells can only be satisfied by those digits, making any occurrence elsewhere a guaranteed contradiction.
When to use: Use Naked Triples when you see three cells in a unit whose combined candidates total exactly three distinct digits. Remember that each cell need not contain all three -- partial overlap counts.
Common Mistakes to Avoid
Thinking every cell in the triple must contain all three candidates. A cell with only two of the three digits is still part of the triple.
Check the UNION of candidates across all three cells. If the union has exactly three distinct digits, it is a valid Naked Triple regardless of individual cell sizes.
Missing a triple because one cell has only one candidate (a naked single that is also part of the triple).
Even a cell with a single candidate can be part of a Naked Triple. The key is that the union of all three cells' candidates equals exactly three digits.
Accidentally including a fourth cell in the analysis, which would make it a quad, not a triple.
Be precise about which three cells you are grouping. If you need four cells to cover the candidates, check for a Naked Quad instead.
More Examples
See naked triples applied in different puzzle configurations to strengthen your pattern recognition.
Row Naked Triple
Highlighted cells show the naked triples pattern
Practice Puzzles
Apply the naked triples technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Three cells in a unit collectively contain exactly three candidates
- Action:
- Eliminate those three candidates from all other cells in the unit
- Look for:
- Three cells whose combined candidate sets yield exactly three digits