Naked triple

Three cells whose candidates union to three values lock them in the unit

How to use it

Three cells in one unit whose candidates union to exactly three symbols. The cells do not need two candidates each — a cell may carry two or three of the symbols — as long as no fourth symbol appears in the group. The three symbols are then confined to the three cells, and every other cell of the unit loses all three.

Scan units that still have exactly three cells with two or three candidates left; overlapping marks make triples easy to miss, so look for three cells whose union is small rather than for identical marks.

Why it is sound

Three cells of a unit whose candidates lie inside {x, y, z} must take exactly x, y and z (pigeonhole: three symbols confined to three cells). No other cell of the unit can hold any of the three in any solution.

A worked example

Of row 1's five empty letter cells, three — r1c1, r1c4 and r1c5 — carry only the candidates B, C and E between them. Three letters, three cells: whatever the arrangement, those cells consume B, C and E for the row. So the other cells of the row lose them: B and E are struck from r1c2, C and E from r1c3. The cells' marks may overlap (one may hold all three letters, others only two) — the lock comes from the union size, not from identical marks. The strike leaves r1c3 with the letters A and D; a line-transversal deduction then removes D there, the cell takes A, and a pair hidden single settles its digit.