Naked Triple

The pattern

Three cells in the same unit whose candidates, taken together, use exactly three digits. No cell has to hold all three — what matters is that the union of their candidate lists has size three.

Those three digits fill those three cells in some order, so they can be erased from every other cell in the unit.

The shapes it comes in

• Three cells of (4,7,9), (4,7,9), (4,7,9) — the obvious case.
• Two-candidate cells that interlock: (4,7), (7,9), (4,9).
• Mixed sizes: (4,7), (4,7,9), (7,9) — still exactly three digits in total.
• Not a triple: (4,7), (7,9), (2,9) — four digits between them, so nothing is locked.

How to find one

Scan a unit for cells with two or three candidates and ignore the rest. Collect the digits they use. If three of those cells cover exactly three digits, the triple is there. Counting the union is the whole technique — the individual cells can look unremarkable.

Units with five or six empty cells are the sweet spot: fewer cells to compare, and the elimination still hits something.

Why it is valid

Three cells, three digits, and each digit appears once per unit. If an outside cell took one of the three, the remaining two digits would have to cover three cells, which is impossible. The argument is the same as for the naked pair, one size up.