Hidden Triples
Three digits in deep cover.
Hidden Triples is the three-digit extension of Hidden Pairs, and the most elusive of the foundational hidden-set techniques. It occurs when three digits appear as candidates only within the same three cells of a row, column, or 3×3 box — nowhere else in that region — even though each of those three cells also lists other, unrelated candidates that obscure the pattern. The three cells don't need to each contain all three digits individually; it's enough that, collectively, the three digits never appear as candidates outside those three cells.
Because those digits must occupy exactly those cells, every other candidate sharing space with them in those three cells is impossible and can be eliminated. Spotting one means scanning a region for digits confined to two or three cells, then checking whether three such digits share exactly the same three-cell footprint. Rule out an obvious triple or a pointing triple in the same region first; they're cheaper to spot.
How It Works
A hidden triple exists when three specific digits appear as candidates only within the same three cells of a row, column, or box — and nowhere else in that region.
- Scan a region for digits that appear in two or three cells (not four or more).
- If three such digits all appear only within the same three cells, you have a hidden triple.
- The three digits must occupy those three cells — so every other candidate in those three cells is impossible. Eliminate them.
The three cells do not each need to contain all three digits. It is enough that the three digits collectively appear only within those three cells.
Example
Below board presents an example of a hidden triple on digits 2, 5, and 8, spread across three cells in a box.
No single cell here holds all three digits, and none of the three cells looks special at a glance — each carries other candidates too. But across the whole box, 2 appears only in two of these cells, 5 only in two, and 8 only in two, and all of that activity is confined to the same three cells. Together, 2, 5, and 8 must live here. Every other candidate sharing those cells can go.
On Evil Boards
Hidden triples are genuinely hard to find — three digits, any subset of which may appear in each of three cells, all camouflaged behind other candidates in a region of nine. Rule out the cheaper checks first: an obvious triple in the same region, or a pointing triple if the region is a box.