Hidden Triples is the three-candidate extension of Hidden Pairs. A Hidden Triple occurs when three candidate digits appear in exactly three cells within a row, column, or box, but those cells also contain additional candidates that obscure the pattern. Once you identify the hidden triple, you can remove all non-triple candidates from those three cells, simplifying the grid considerably.
The difficulty with Hidden Triples lies in detection. Unlike Naked Triples where you look for cells with small candidate lists, Hidden Triples require you to track where specific digits can appear within a unit. You must find three digits that are confined to the same three cells, even though those cells might each contain five or six candidates total. The triple is hidden among all those extra candidates, which is why systematic scanning of digit distributions is essential.
Hidden Triples are less common than Hidden Pairs but substantially more powerful when they appear. A single Hidden Triple can eliminate many candidates at once, often unblocking a puzzle that seemed stuck. Mastering this technique requires practice with candidate counting and develops the analytical mindset needed for advanced Sudoku solving. It pairs naturally with Hidden Pairs analysis and serves as preparation for recognizing even rarer hidden subsets.
Try It Yourself
Walk through each step of the hidden triples technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Examine box 1 (rows 0-2, columns 0-2). Several cells are empty. List all the candidates for each empty cell in this box to uncover the hidden pattern.
Step-by-Step Guide
Select a row, column, or box and list all candidate digits that still need to be placed.
For each candidate, note exactly which cells in the unit can contain it.
Look for three candidates that each appear in only three cells and the same three cells.
Verify that all three digits are confined to exactly those three cells in the unit.
Remove all other candidates from those three cells, keeping only the triple digits.
Check whether the simplified cells create new singles or enable further techniques.
Scan other units for additional hidden triples.
Three specialty tools can only hang on three specific hooks in your workshop, but those hooks are cluttered with other gear. Once you realize only those hooks can hold those tools, you clear away everything else to make the assignment obvious.
Every digit in a unit must be placed in exactly one cell. If three digits each have candidates in only three cells, and those are the same three cells, then those three cells are the only way to satisfy all three placement requirements. Three cells can hold exactly three digits, so those cells are fully allocated to the triple. Any additional candidates in those cells are impossible -- assigning one would displace a triple digit, leaving it with no valid cell in the unit.
When to use: Use Hidden Triples when you cannot find Naked Triples but suspect that certain digits are restricted to a small number of cells. Track digit placements within a unit: if three digits can only go in three cells, you have a Hidden Triple.
Common Mistakes to Avoid
Failing to check all three digits thoroughly. You might identify two digits confined to three cells but miss that the third digit also fits only those cells.
Systematically list all unplaced digits in a unit and the cells where each can go. Compare the cell sets to find three digits sharing the same three cells.
Removing the triple digits from the cells instead of removing the non-triple candidates.
The Hidden Triple digits STAY in the cells. You remove all OTHER candidates from those three cells, not the triple digits themselves.
Confusing Hidden Triples with Naked Triples. Hidden Triples have extra candidates in the cells; Naked Triples do not.
If the three cells contain only three candidates total (the triple digits), it is a Naked Triple. If they contain additional candidates beyond the triple, it is a Hidden Triple.
More Examples
See hidden triples applied in different puzzle configurations to strengthen your pattern recognition.
Box Hidden Triple
Highlighted cells show the hidden triples pattern
Practice Puzzles
Apply the hidden triples technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Three candidates appear in only three cells within a unit
- Action:
- Remove all other candidates from those three cells
- Look for:
- Three digits confined to the same three cells in a unit