Techniques / Subsets

Naked Triple

Also called Naked Triplet, Disjoint Subset of size 3.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Three squares in one group share the same three digits between them. Those digits fill those squares, so no other square in the group can use them.

The exact rule, for stronger players

The rule, stated exactly: For a house H, if three cells of H have candidate sets whose union has cardinality three, those three digits may be eliminated from every other cell of H. No individual cell need contain all three.

What it removes: Remove all three digits from all cells of H outside the triple.

Why it works: Three cells must hold three distinct digits. Their candidates are confined to a set of size three, so those three digits are distributed among exactly those cells and are unavailable elsewhere in H.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Naked Triple. r1c2, r1c3, r1c4 in r1 hold only 2, 4, 7 between them, so those 3 digits fill those cells and appear nowhere else in r1. — r1c2, r1c3, r1c4 in r1 hold only 2, 4, 7 between them, so those 3 digits fill those cells and appear nowhere else in r1.

Sudoku grid showing Naked Triple. r2c2, r2c4, r2c5 in r2 hold only 3, 6, 7 between them, so those 3 digits fill those cells and appear nowhere else in r2. — r2c2, r2c4, r2c5 in r2 hold only 3, 6, 7 between them, so those 3 digits fill those cells and appear nowhere else in r2.

Learn these first

Naked PairTwo squares in the same group both hold only the same two digits.

Related subsets

Hidden PairTwo digits in one group can only go in the same two squares.
Hidden QuadFour digits in a group can only go in the same four squares.
Hidden Subset (general form)Some numbers in a group have only a few homes left.
Hidden TripleThree digits in a group can only go in the same three squares.
Locked PairA pair that shares two groups at once, usually a row and a box.

How often does it come up?

Our rough estimate: moderately common. Frequently missed because the union rule does not require any cell to show all three digits.

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