Naked Triples and Quads
A naked triple is three cells in a unit that, between them, use only three candidate digits. As with naked pairs, those three digits are reserved for those three cells, so they can be eliminated everywhere else in the unit. Quads extend the same idea to four cells and four digits. These techniques clear candidates in bulk and often crack a stalled hard board.
The subtlety that trips people up: each of the three cells does not need to contain all three digits. They only need to draw from the same pool of three. {2, 5}, {5, 8}, and {2, 8} form a perfectly valid naked triple even though no single cell shows all of 2, 5, and 8.
How a naked triple works
- the unit in focus
- the pattern
- a placement
- an elimination
Three cells in this column (amber) hold candidates drawn entirely from {2, 5, 8}. Whatever the exact arrangement, those three cells will consume the 2, the 5, and the 8 among themselves. So none of those digits can live anywhere else in the column, and they're struck from every other cell (red). One elimination like this can remove several candidates at once and immediately expose a placement.
Recognising the pattern
You're looking for any three cells in a unit whose combined candidates total exactly three distinct digits. The valid shapes are:
- Three cells each with the same three candidates: {2,5,8}, {2,5,8}, {2,5,8}.
- A mix of pairs and triples that overlap into three digits: {2,5}, {5,8}, {2,8} or {2,5,8}, {2,5}, {5,8}.
If the three cells together use a fourth digit, it isn't a triple. Counting the union of candidates is the reliable test: three cells, three digits total.
Naked quads
A naked quad is the same logic with four cells and four shared candidates. It's genuinely rare in everyday puzzles and tedious to scan for, so most solvers only reach for it on the hardest grids when nothing simpler is available. If you've mastered triples, you already understand quads — just add one cell and one digit.
A practical tip
Naked triples are easiest to find right after a round of naked pair eliminations, because those reduce candidate counts and make the three-cell groupings stand out. Look in units that are about half-solved, where several cells carry just two or three candidates. And remember the mirror: a hidden triple hides three digits among extra candidates, the same way a hidden pair does — act on the three cells themselves rather than the rest of the unit.
Play Sudoku Zen — six difficulties