Sudoku technique
Naked Triple
Three cells in the same zone share only three possible digits between them — not necessarily all three in every cell. Those three digits are reserved for them: any other candidate elsewhere in the zone matching one of them gets eliminated. The naked pair, stretched to three.
A puzzle that requires it
Level Expert — the puzzle is shown twice: right below, and again in the demo that follows.
| 2 | 4 | |||||||
| 2 | 8 | 1 | 6 | |||||
| 1 | 7 | |||||||
| 4 | 7 | 6 | ||||||
| 6 | 8 | 9 | ||||||
| 3 | 6 | 7 | ||||||
| 3 | 4 | |||||||
| 9 | 4 | 2 | 8 | |||||
| 5 | 9 |
Demonstration
State of the grid right when the technique applies, after 6 earlier deductions.
Demo — watch first, you'll play right after.
- Technique's pattern
- Candidates removed
- Solved earlier
- Given (clue)
| 2 | 4 | 9 | ||||||
| 2 | 8 | 1 | 6 | |||||
| 1 | 3 8 | 2 | 7 | |||||
| 4 | 7 | 6 | ||||||
| 6 | 3 | 7 | 8 | 9 | ||||
| 5 | 3 | 6 | 7 | |||||
| 3 | 9 | 4 | ||||||
| 9 | 4 | 2 | 8 | |||||
| 5 | 9 | 7 |
Triplet nu
Ces 3 cases n'acceptent que 3, 7, 8. À elles trois elles épuisent ces chiffres : personne d'autre dans la zone ne peut les prendre.
Candidates removed:
- the 3, 8 from cell L3C4
- the 7 from cell L5C4
The Naked Triple extends the Naked Pair to three cells. Three cells of the same zone whose candidates, taken together, make up only three digits share those three digits between them. You can therefore erase them from every other cell of the zone: the Naked Triple eliminates elsewhere.
The principle
A zone is a row, a column or a box. Take three of its cells and combine their candidates. If that combination holds only three digits, say 2, 5 and 8, then those three cells share those three digits, one each. You do not know who takes what, but between them, they use them up.
In the other cells of the zone, 2, 5 and 8 are therefore impossible. Remove them from their notes. As with the Naked Pair, the cells of the triple do not change: the cleanup happens in the neighboring cells.
Key point: each cell of the triple does not need to contain all three digits. One cell may have only 2 and 5, another 5 and 8, a third 2 and 8. What counts is the total: three cells, and three digits in all, not one more.
How to spot it
You need candidate notes. In a zone, look for cells with few candidates, two or three. Pick three and check that the combination of their notes fits in three digits. If a fourth digit shows up, it is not a Naked Triple.
When you find one, erase the three digits from the other empty cells of the zone.
There is a shortcut. If a zone has only six empty cells left, a Naked Triple on three of them amounts to a Hidden Triple on the other three: the three remaining digits can only go in those other three cells. More generally, in a zone with n empty cells, a naked group of k cells always matches a hidden group of n − k cells.
A worked example
In one row, three cells have candidates 2 and 5 for the first, 5 and 8 for the second, 2 and 8 for the third. None contains all three digits, but their combination is 2, 5 and 8: a Naked Triple.
Elsewhere in the row, one cell has candidates 2, 5 and 9, another 4, 5 and 8. Remove the 2 and the 5 from the first: 9 remains. Remove the 5 and the 8 from the second: 4 remains. Two Naked Singles, which you can place.
Common mistakes
The most common mistake is to require three identical cells, each with the same three candidates. That exists, but it is only a special case. The Naked Triple is more often made of cells with only two candidates, as in the example above.
Another trap is to count a cell that brings in a fourth digit. One cell too many and the combination goes past three digits: there is no triple anymore. You also need three cells, not two: two cells sharing two digits form a Naked Pair, which you treat as such.
Finally, do not mix it up with the Hidden Triple. The Naked Triple is recognized by its cells and eliminates in the other cells of the zone. The Hidden Triple is recognized by its digits and cleans its own cells.
When to use it
The Naked Triple is expected at the Expert level, along with the Hidden Triple, the quads and the X-Wing. You should already master Naked and Hidden Pairs, whose reasoning it extends.
- Expert sudoku
- Technique: the Naked Pair
- Technique: the Hidden Triple
- How to solve a sudoku
- Learn the techniques
Frequently asked questions
Must every cell of a Naked Triple contain all three candidates?
No. It is enough that the combination of the candidates of the three cells makes exactly three digits. A cell can have only two, as long as the three cells together do not go past three digits in total.
What is the difference between a Naked Triple and a Hidden Triple?
The Naked Triple is recognized by its cells: three cells have only three candidates between them, and those digits disappear from the other cells of the zone. The Hidden Triple is recognized by its digits: three digits fit in only three cells, and the other candidates in those cells disappear.
Do the three cells have to be adjacent?
No. They only have to belong to the same zone, meaning the same row, the same column or the same box. Other cells can sit between them.
Does a Naked Triple place a digit?
No, it removes candidates from the other cells of the zone. Those eliminations can then leave a Naked or Hidden Single, which lets you place a digit.
Practice
Every technique helps remove candidates ; once a cell has only one left, you place it.
Three puzzles where Naked Triple is the key move, served right before the step, with a coach.
Puzzle 1
Expert
The technique is used once in this puzzle
Puzzle 2
Expert
The technique is used once in this puzzle
Puzzle 3
Expert
The technique is used twice in this puzzle
Puzzles change every day.