Three cells whose candidates use at most three digits. Those digits are locked to those cells.
A Naked Triple is the logical extension of a Naked Pair. Three cells in the same unit have candidates drawn from exactly three digits. Those three digits must occupy those three cells, so you can remove all three digits from every other cell in the unit.
Here's the subtle part: each cell does NOT need to contain all three digits. Valid Naked Triples include {1,2,3}, {1,2,3}, {1,2,3}, but also {1,2}, {2,3}, {1,3} or even {1,2,3}, {1,2}, {2,3}. The only requirement is that the union of all candidates across the three cells contains at most three distinct digits.
Naked Triples appear in Medium and Hard puzzles. They're harder to spot than pairs because of the variety of configurations, but the elimination power is significant. You can clear three digits from up to six other cells in the unit.
Find three cells in a unit where the combined candidate set uses no more than three distinct digits. The three digits will be distributed across these cells in some combination. Every cell must be a subset of those three digits.
Once confirmed, remove all three digits from every other cell in the unit. The reasoning is identical to Naked Pairs: three digits in three cells means those digits are fully accounted for, with no room for them elsewhere.
A common configuration is the "incomplete triple" like {1,2}, {2,3}, {1,3}. Each cell has only two of the three digits, but together they cover exactly three digits in three cells. This is a valid Naked Triple and eliminates just as effectively.
Another common pattern: {1,2,3}, {1,3}, {2,3}. One cell has all three digits while the others have two each. Still valid. The three cells collectively account for digits 1, 2, and 3.
Example 1: Naked Triple in a Row
Look at row 2. Three cells (R2C3, R2C4, and R2C9) have candidates drawn from just three digits: {1, 4, 7}.
R2C3 has {1, 4}. R2C4 has {1, 7}. R2C9 has {4, 7}. Each cell holds a different pair from the same three digits. The union is {1, 4, 7}, exactly three digits in three cells. This is an "incomplete triple" where no single cell has all three digits.
Since 1, 4, and 7 must go in these three cells, they can be removed from all other cells in row 2. We eliminate 4 from R2C6, 7 from R2C7, and 4 from R2C8.
After eliminating, R2C6 is reduced to a single candidate: 2. That's a Naked Single we can place immediately.
Example 2: Naked Triple in a Box
Now look at box 2 (top-center). Three cells (R1C4, R1C5, and R2C5) contain candidates from the set {1, 3, 8}.
R1C4 has {1, 3}. R1C5 has {1, 3, 8}. R2C5 has {3, 8}. Notice that R1C5 has all three digits while the others have just two each, this is still a valid Naked Triple since the union is {1, 3, 8}.
Eliminate 1, 3, and 8 from all other cells in box 2: remove 8 from R1C6, 3 from R2C4, and 8 from R3C6.
R1C6 is reduced to {2}, another Naked Single. Naked Triples in a box can be harder to spot since the cells aren't necessarily in a straight line.
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