Naked and hidden triples in sudoku
Triples are pairs grown by one, and the growth hides them. Three cells in a unit drawing from the same three digits lock all three up, but the cells rarely show their full hands, so the eye slides past. Learning to verify a suspected triple, instead of trusting a glance, is a defining habit of hard-tier play.
The naked triple
Look at the marked column. Three highlighted cells show 2-5, 5-8 and 2-8. No cell holds all three digits, and the union across the cells is exactly 8. Three cells, three digits between them, fully claimed:
The counting argument runs like the pair’s. Three digits must fill three cells that accept nothing else, so the digits are consumed, order unknown. The column’s other open cells kept a 2, a 5 and an 8 penciled in, and those candidates now point at futures that cannot happen:
Both cleaned cells drop to a single candidate here, which is the triple’s usual gift: it rarely solves its own cells and often solves its neighbors.
Verifying a suspect
The test is the union. Gather the candidates across the three suspect cells and count distinct digits. Three digits, genuine triple. Four digits, nothing, however similar the cells look:
Run the union check on complete marks only. A stale candidate inflates the union and hides a real triple; a forgotten one shrinks it and invents a false triple. Auto notes rebuilds the truth in one tap, and the auto-remove default keeps it current as you place.
Hidden triples
Three digits confined to the same three cells of a unit form the hidden version, buried under other candidates the way hidden pairs are. The eliminations invert: a naked triple cleans the rest of the unit, a hidden triple cleans the extra candidates out of its own three cells. Hunt them by counting homes per digit and shortlisting anything with two or three, then checking for three digits sharing three cells.
Triples sit on the hard rung of our ladder beside hidden pairs and the X-wing, and every hard puzzle here needs at least one move from that shelf. The union check is the skill; the rest is patience with your own pencil marks.
Frequently asked questions
What is a naked triple in sudoku?
Three cells in one row, column or box whose candidates draw from the same set of three digits. Those digits must fill those cells in some order, so every other cell in the unit loses all three as candidates.
Do all three cells need all three candidates?
No, and this is the detail that hides most triples. Cells showing 2-5, 5-8 and 2-8 form a full naked triple on 2, 5 and 8, even though no cell shows all three. The test is whether the union of candidates across the three cells stays within three digits.
What is a hidden triple?
Three digits confined to the same three cells of a unit, buried under other candidates. The digits own those cells, so the extra candidates penciled in them can be erased. It is the pair logic scaled up: count homes per digit and watch for three digits sharing three cells.
How common are triples?
Common enough to grade on. Our hard tier requires hidden pairs, triples or an X-wing at the toughest point of every puzzle, so a hard stall on this site has a fair chance of being a triple waiting in your pencil marks.