Naked Triples
Short answer: a naked triple is three cells in one unit whose candidates, pooled together, are just three shapes. Those three cells must use up those three shapes between them — so all three can be struck from every other cell in the row, column or box. It is the naked pair idea, one size up.
What a naked triple looks like
The three cells don't each need all three shapes — they just can't reach beyond them. Any mix works: {A,B}, {B,C}, {A,C}, or {A,B,C} with two-candidate partners. If the union of three cells' candidates is exactly three shapes, those cells form a naked triple.
Watch for the trap: three cells that each show two candidates are only a triple if their union is three shapes, not four or five. Pool the notes first, then count the distinct shapes.
How to use a naked triple
- Pencil in candidates. Note the remaining shapes for the empty cells in the unit you are examining.
- Find three cells over three shapes. Look for three cells whose candidates, taken together, use only three distinct shapes — each cell holding two or three of them.
- Lock the trio. Those three shapes are reserved for those three cells: between them they must take all three.
- Eliminate from the rest of the unit. Strike all three shapes from every other cell in the same row, column or box. Each removal can open a new single.
A naked triple is a naked pair scaled up — the same "these cells own these shapes" logic across three cells. The shape-tracking mirror, three shapes confined to three cells, is a hidden triple.
Naked triple vs naked pair
Only the size changes. A naked pair is two cells over two shapes; a naked triple is three cells over three shapes. The triple is trickier because the cells needn't each show the full set — you have to pool the candidates and count the distinct shapes before the pattern is clear.
Frequently asked questions
What is a naked triple in sudoku?
A naked triple is three cells in the same row, column or box whose candidates together add up to just three shapes. Those three cells must use those three shapes between them, so the shapes can be eliminated from every other cell in the unit.
Do all three cells need all three shapes?
No. Each cell needs two or three of the three shapes, and the union across the three cells must be exactly three. Combinations like {A,B}, {B,C}, {A,C} form a perfectly valid naked triple.
How is a naked triple different from a naked pair?
It is the same idea with one more cell and one more shape. A naked pair locks two shapes into two cells; a naked triple locks three shapes into three cells. Both eliminate those shapes from the rest of the unit.
Does a naked triple work in number sudoku?
Yes, identically. The shapes are just tokens, so a naked triple is the same deduction whether the unit holds the digits 1–9 or the nine form9 shapes.