Naked triples follow the naked pair idea, just one step bigger. Three cells in a unit lock three digits between them, and every other cell in the unit loses those digits as candidates.
How it works
Three cells in the same row, column or box form a naked triple if their combined candidate set covers exactly three digits. The cells do not all need to hold the full set. Patterns like {1, 2}, {2, 3} and {1, 3} count, and so do {1, 2, 3}, {1, 3}and {2, 3}.
Because the union is exactly three digits, those three digits must occupy those three cells in some order. Every other cell in the unit can have all three digits eliminated from its candidate list.
When to look for it
After naked and hidden pairs stop producing eliminations. Triples are the next sweep through the same units. Box units offer the most triples because boxes restrict three rows and three columns at once.
Full pencil marks are non-negotiable. Without them you cannot tell what the union of three candidate sets looks like.
Step-by-step example
- Pick a unit with at least four or five empty cells. Look at the candidate sets.
- Find three cells whose candidate sets together contain exactly three different digits.
- Confirm no fourth digit sneaks in. {1, 2}, {2, 3} and {1, 4} is not a triple. The union is {1, 2, 3, 4}.
- For every other cell in the unit, erase the three triple digits from its candidate list.
- Re-scan for singles. Triples usually produce one or two within a move or two.
Naked triple vs naked pair
Tips for spotting it
- Look for three cells in a unit where each holds two or three candidates and the union is three digits.
- Bivalue + bivalue + bivalue patterns are the cleanest. Train your eye on those first.
- Mark the three triple cells lightly so you do not lose track while sweeping the rest of the unit.
- Eliminations almost always create a single. Re-scan immediately.
Common mistakes
- Including a cell whose extra candidate is not in the triple set.
- Stopping at the find. The eliminations matter, not the spotting.
- Missing 2-2-2 triples because no single cell holds all three digits.
- Confusing the pattern with a hidden triple, which scans digits not cells.
Practise it
Hard puzzles on /play/hard/ regularly contain at least one naked triple. Mark every cell, then sweep each row, column and box looking for three-cell sets that cover three digits. Once you can spot 2-2-2 in your sleep, the rest of the intermediate techniques fall into reach.