Hidden Triple Sudoku Technique
Among the hardest patterns to see by eye, because the three cells can be carrying five or six candidates and look nothing like a set.
Also called: hidden triplet, hidden three.
What a hidden triple is
Three digits within a unit have, between them, only three cells left where any of them can go. Those cells must take those digits, so every other candidate in them is wrong.
As with hidden pairs, the digits do not each need all three cells available — one may fit in two of them, another in a different two. What counts is that no fourth cell can host any of the three.
The elimination happens inside the three cells rather than outside them, which is what makes it easy to overlook: nothing about the rest of the unit changes.
How to spot one
- Work by digit. For a unit, list which cells can still hold each missing digit.
- Look for three digits whose combined cell lists cover exactly three cells. That is the pattern.
- Most productive in units with four to six empties. With more than that the counting is slow and a naked pattern usually surfaces first anyway.
Worked example
| Column 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| Row 8 | 124 | 235 | 136 | 45 | 46 | 56 | 7 | 8 | 9 |
Solid digits are already placed. Small digits are the candidates still available in that cell.
- Count homes per digit: the 1 fits only in cells one and three, the 2 only in cells one and two, the 3 only in cells two and three.
- Three digits — 1, 2 and 3 — between them reach only three cells. Those cells must take them.
- Strike everything else from those cells. They become {1,2}, {2,3} and {1,3}, and the row is resolved into two clean triples.
What it eliminates
Every candidate other than the three digits, inside the three cells that form the triple.
When you need it
On the same grids as naked triples, and usually worth trying second — the naked version is faster to see when both are present.
Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.