A naked triple is three cells in the same row, column or box whose candidates, added together, use only three digits. None of the three cells needs to show all three; one might have two candidates, another three, as long as the combined set stops at three digits and no more. Since those three digits must fill those three cells between them, no other cell in the unit can hold any of the three.
The name follows the same logic as a naked pair, just one cell wider. Pairs are easier to see because both cells usually show exactly two marks. Triples take more scanning because the three cells rarely show the same three digits; more often it is two cells with two candidates each and a third cell with three, all drawn from the same pool of three digits.
You will not need this on Easy or most Medium boards. It becomes useful once a puzzle has enough empty cells packed into one row, column or box that singles and pairs alone cannot untangle it. Once you have practiced spotting pairs, the jump to triples is mostly patience: more cells to track, more candidates to add up, but the same underlying question of how many digits a group of cells can share.
Worked example
The same real puzzle position, viewed one row up. Step through to see a naked triple clear two other cells in row 1.
How to find a naked triple
Pick a unit with four or more empty cells and start listing candidates. Look for any three cells whose combined candidates total exactly three digits. A common shape is two cells with two candidates each that overlap on one digit, plus a third cell that has all three. Another is three cells each showing two of the same three digits in different combinations.
- The three cells do not all need three candidates. A cell with only two candidates can be part of a triple as long as both of its candidates belong to the trio.
- Count digits, not marks. Add up every distinct digit across the three cells. If the total is three, you have a triple. If it is four, keep looking elsewhere.
Once confirmed, erase those three digits from every other cell in that row, column or box. The three cells themselves keep only the candidates that belong to the trio.
Naked triple or hidden pair?
A hidden pair cleans up two cells by finding digits trapped inside them. A naked triple works the other direction: three cells are already narrow enough between them, and the cleanup happens everywhere else in the unit instead. Both remove clutter; they just point in opposite directions.
In a hard puzzle you often find both in the same pass. Scan a stuck row for hidden pairs first since there are only 36 digit pairs to check, then look for naked triples among cells with two or three marks if nothing turns up.
Common mistakes
- Counting the wrong way. Three cells with candidates {1,2}, {2,3} and {3,4} use four digits total (1, 2, 3 and 4), not three. That is not a triple, even though each cell shows only two marks.
- Forgetting a fourth cell also carries the digits. If a fourth empty cell in the unit has one of the three digits as a candidate, the elimination there is exactly the point; skipping it wastes the pattern you just found.
- Erasing from inside the triple. The three cells keep their own candidates as long as those candidates belong to the trio. Only cells outside the triple lose digits.
The crowded unit is where to look
Naked triples show up on Hard puzzles (28 to 32 givens) and beyond, usually after hidden pairs and pointing pairs have already been tried on a stuck unit. They tend to appear in the most crowded row, column or box on the board, the one with four or five empty cells left after everything easier has been placed.
If a puzzle feels stuck, count the empty cells in each row, column and box. The one with the most is the best place to look for a triple. It rarely appears on the first crowded unit you check, so be ready to try two or three before it clicks.
Hard boards carry 28 to 32 givens. When a row, column or box gets crowded and stuck, look for three cells sharing three digits.
Frequently asked questions
A naked triple is three cells in one row, column or box whose candidates together use only three digits. Since those three digits must fill those three cells, they can be erased from every other cell in the unit.
No. A naked triple can have cells with two or three candidates, as long as the combined set across all three cells never exceeds three digits.
The logic is identical, just with one more cell and one more digit. A naked pair uses two cells and two digits; a naked triple uses three cells and three digits.
Not directly. It removes candidates from other cells in the unit, which often creates a naked single somewhere else on a later move.
They show up on Hard puzzles and beyond, once naked and hidden singles, naked pairs and hidden pairs have already been used and a unit is still stuck.
Yes, noticeably. A pair needs two cells to line up on two digits; a triple needs three cells to line up on three, which happens less often. Expect to find fewer triples than pairs in any given puzzle.