Naked Triple
Three cells in a unit share three candidates between them.
The naked triple sudoku technique spots three cells in one row, column or box that between them use only three candidate digits — say 1, 2 and 3 and nothing else. Because those three cells must take exactly those three digits among themselves, the same three numbers can be struck from every other cell in the unit. It is the three-cell cousin of the naked pair, with one twist worth remembering: the cells do not each have to show all three digits — {1,2}, {2,3} and {1,3} form a naked triple just as {1,2,3} in all three would.
Worked example
In this board box 1 already holds the givens 4, 5, 6, 7, 8 and 9, so its only empty cells are R3C1, R3C2 and R3C3, and every one of them is limited to 1, 2 or 3. Those three cells therefore form a naked triple on {1,2,3}: whatever the order, they will consume all three of 1, 2 and 3 between them. That locks those digits out of the rest of row 3, so 1, 2 and 3 can be erased from R3C4, R3C5, R3C6, R3C7, R3C8 and R3C9. Because the triple happens to fill the whole of box 1 as well, there is nothing left to eliminate inside the box — the entire payoff lands along row 3.
When to use it
Reach for a naked triple once naked and hidden singles and naked pairs have stopped producing moves, and you are looking at a unit crowded with two- and three-candidate cells. Scan a single row, column or box and ask whether any three of its cells draw all their pencil marks from a shared pool of just three digits — a box or line with only a handful of empty cells (as here) is the easiest place to catch one. The tell is three cells whose candidates, when you union them, add up to exactly three numbers.
How to use it
- Find three linked cells. Find three cells in one unit whose candidates are drawn only from the same three digits (each cell may hold 2 or 3 of them).
- Confirm the triple. The union of their candidates must be exactly three digits — then those three digits are locked to those three cells.
- Eliminate from peers. Remove all three digits from the other cells in the unit.
Frequently asked questions
What is a naked triple in Sudoku?
A naked triple is three cells sharing one unit (a row, column or box) whose candidates between them contain only three different digits. Since those three cells are the only homes for those three digits within the unit, the digits must be placed there and can be removed as candidates from every other cell in that unit. In the example, R3C1, R3C2 and R3C3 are all confined to {1,2,3}, so 1, 2 and 3 come off the rest of row 3.
How do I spot a naked triple on the grid?
Pick one unit at a time and collect the candidate sets of its unsolved cells. If you can find three cells whose candidates together use exactly three distinct numbers, you have a naked triple. A quick shortcut is to look for units with few empty cells or clusters of two- and three-candidate cells: in this board box 1 has only three empty cells and all three are stuck on 1, 2 or 3, which is the pattern jumping straight out.
Do all three cells in a naked triple need all three candidates?
No, and that is the main thing that makes them harder to see than naked pairs. The three cells only need to share a common pool of three digits between them — valid shapes include {1,2}, {2,3}, {1,3}, or {1,2,3}, {1,2}, {2,3}, or all three showing {1,2,3}. What matters is that the union of the three candidate sets is exactly three digits; the elimination of those digits from the rest of the unit works the same either way.