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Naked Triples

Three cells, three digits — even when no single cell shows all three.

A naked triple is three cells in the same row, column or box whose candidates, taken together, are only three digits. Each cell does not need to show all three — {1,2}, {2,4} and {1,4} is a perfectly good triple. Because the three digits must fill those three cells, they can be removed from every other cell in the unit.

Worked example

The three highlighted cells hold only {1,2}, {2,4} and {1,4}. Together they use up 1, 2 and 4, so those digits are crossed out of the other empty cells in the row (shaded).

How to apply it

1

Write pencil marks for every empty cell in the unit.

2

Look for three cells whose candidates all come from the same set of three digits.

3

Check that none of the three cells contains a fourth digit.

4

Remove those three digits from every other cell in that row, column or box.

When to use it

Naked triples appear on hard and expert puzzles. They are easy to overlook when a cell shows only two of the three digits, so check combinations of two-candidate cells whenever pairs fail. The same idea extends to naked quads.

Frequently asked questions

Does every cell in a naked triple need three candidates?
No. A cell can show two or three of the digits — what matters is that the three cells together contain no more than three different digits.