Hidden triples are the rarest of the basic pair-triple family. They do not show up in every puzzle, but when they do they clear out a whole cluster of candidates in one move.
How it works
A hidden triple is three digits whose candidate positions within a row, column or 3x3 box are confined to the same three cells. The cells themselves can carry plenty of other candidates; the trick is that those three digits land nowhere else in the unit.
Since three digits must occupy three cells, the cells are committed to those digits. Every other candidate inside the three cells can be erased. The cleanup is dramatic when it fires.
When to look for it
After hidden pairs stop producing eliminations and the grid still has busy candidate sets. Hidden triples often hide inside boxes where six or seven digits are still in play.
A good signal: you spot a hidden pair, but a third digit also fits the same two cells (plus a third nearby). Check whether all three digits are confined to three cells total.
Step-by-step example
- Pick a unit. Boxes are best. List, for every digit still missing from the unit, which empty cells could hold it.
- Find three digits whose candidate-cell lists are all subsets of the same three cells. Say 2, 5 and 8 each appear only in the three highlighted cells above.
- The three cells must hold {2, 5, 8} in some order.
- Erase every non-triple candidate from those three cells. Other digits cannot live there anymore.
- The reduced cells often form a naked triple for a row or column, triggering further eliminations.
Hidden triple vs naked triple
Tips for spotting it
- Hidden triples in boxes are easiest. Scan boxes one digit at a time.
- Pick digits with sparse position counts (two or three cells in the unit). Their lists may overlap precisely.
- Pairs hint at triples. If two digits share two cells, look for a third digit that lives in three.
- Cleanup often produces a naked triple right after. Always re-scan.
Common mistakes
- Reading cell contents instead of digit positions. Scan by digit.
- Allowing a fourth digit to share the same three cells. That breaks the triple.
- Not stripping the extra candidates from the cells after spotting.
- Trying to apply the technique without full pencil marks.
Practise it
Hard and expert puzzles occasionally require hidden triples. Mark the grid fully and walk each box once looking for triples of digits with restricted homes. The skill carries over directly to X-wing and later chains, which also rely on digit-position scanning.