Hidden triple
Three digits whose only possible cells inside a unit are the same three cells — even if those cells still show other candidates. The digit-first sibling of the naked triple.
A hidden triple is three digits that, inside a single unit, can only legally go in the same three cells — even if those three cells still show other candidates. Once spotted, every other candidate in those three cells can be eliminated, because the three digits have nowhere else in the unit to live.
How to spot one
Pick a unit. For each unplaced digit, list its possible cells inside the unit. A hidden triple is three different digits whose possible-cell lists are all subsets of the same three cells.
Worked example: in column 5, the digit 2 can only go in (3, 5), (6, 5), and (8, 5); the digit 4 can only go in (3, 5) and (6, 5); the digit 9 can only go in (6, 5) and (8, 5). All three digits' candidate cells are subsets of {(3, 5), (6, 5), (8, 5)} — so 2, 4, and 9 must occupy those three cells. Any other pencil-mark currently in those cells (a 6, a 7) gets ruled out.
When you'll see it
Hidden triples are the rarest of the basic four pair-and-triple shapes (naked pair, hidden pair, naked triple, hidden triple). They show up on hard and expert puzzles where simpler eliminations have already fired. The reason they're hard to spot: each cell in the trio often still shows several extra candidates that haven't been ruled out yet, so the pattern doesn't pop visually — you have to lead with the digit-first count.
Why both shapes exist
Naked and hidden triples mirror each other the same way the naked pair and hidden pair do. The naked version says "these three cells contain these three digits between them, nothing else." The hidden version says "these three digits live in these three cells, nowhere else in the unit." Same logical claim, two angles, useful in different states of pencil-mark progress.
For a longer take on the symmetry between the two and how to scan for both, see Naked and hidden pairs and triples.
See also
- Naked triple— Three cells in the same unit whose candidates collectively use only three digits. Together they claim those digits across the unit and rule them out elsewhere.
- Hidden pair— Two digits whose only possible cells inside a unit are the same two cells — even if those cells still show other candidates. The digit-first sibling of the naked pair.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Naked and hidden pairs and triples
The mid-level extension of singles — how pairs and triples work, when each shows up, and the perspective shift that surfaces them.