Naked Triple Sudoku Technique

The same logic as a naked pair, one size up — and much easier to miss, because the three cells rarely look alike.

Also called: naked triplet, naked three.

What a naked triple is

Three cells in one unit whose candidates, taken together, form a set of exactly three digits. Those three digits are consumed by those three cells, so they can be cleared from everywhere else in the unit.

The trap is expecting all three cells to show all three digits. They do not have to. {1,2}, {2,3} and {1,3} is a perfectly good naked triple on {1,2,3}, and so is {1,2}, {2,3} and {1,2,3}.

What matters is the union, not the individual lists: three cells, and no more than three distinct digits between them.

How to spot one

Ignore cells with four or more candidates — they cannot take part.
Collect the two- and three-candidate cells in a unit and look for three whose union has size three. With only a handful of cells this is quick by eye.
Any two cells forming a naked pair are worth extending: check whether a third nearby cell draws only from those two digits plus one more.

Worked example

	Column 1	2	3	4	5	6	7	8	9
Row 6	12	23	13	145	246	356	7	8	9

Solid digits are already placed. Small digits are the candidates still available in that cell.

Row 6 holds 7, 8 and 9, so digits 1 to 6 are spread across the six empty cells. No two cells share an identical pair, so there is no naked pair to take.

The first three cells show {1,2}, {2,3} and {1,3}. No cell holds all three digits, but between them the union is exactly {1, 2, 3}.
Those three digits are therefore used up by those three cells, in some order you do not need to determine.
Strike 1, 2 and 3 from the rest of row 6. The remaining cells fall to {4,5}, {4,6} and {5,6} — themselves a naked triple on {4,5,6}.

What it eliminates

All three digits of the triple, from every cell in the unit outside the three that form it.

When you need it

From around 34 clues down. Triples are what tends to be left when pairs and locked candidates have already been mined out.

Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.

Play a puzzle All solving techniques How to play Sudoku

Related techniques

Naked Pair Sudoku Technique — The first technique that eliminates candidates instead of placing digits — and the gateway to everything above it.
Hidden Triple Sudoku Technique — Among the hardest patterns to see by eye, because the three cells can be carrying five or six candidates and look nothing like a set.
X-Wing Sudoku Technique — The step where Sudoku stops being local. Everything before this works inside one unit; the X-Wing needs four cells in four different ones.

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