Naked triple
The naked triple is a basic sudoku solving technique that you need to master.
Principle
A naked triple is a set of three cells belonging to the same row, column, or region, and whose set formed by their combined candidate values contains three distinct numbers in total.
Each cell of the naked triple can contain either all three candidate values, or only two of the three, as long as on the whole of the triplet the previous condition is respected (three distinct numbers in total).
In the grid solution, these three numbers will necessarily be in these three cells. Therefore, they can be eliminated as candidates from all the other cells of the row, column or region shared by the triplet.
The naked triple is therefore similar to the naked pair for three cells and three numbers. However, it is a little more difficult to spot because the cells do not systematically contain all three candidate values.
Examples
Example 1 : naked triple on column, the three cells of the triple contain the three candidate values
On column 4, cells A4, F4 et H4 have the three same candidate numbers : 1, 6 and 7. Therefore, these three numbers can be eliminated as candidates from all other cells of column 4, here B4, C4 and G4.
Example 2 : naked triple on column and region, the three cells of the triple contain two or three candidate values
Cells A4, B4 and C4 have three distinct numbers as combined candidates : 2, 4 and 5. These three cells belonging to both the same column (column 4) and the same region (region 2), the numbers 2, 4 and 5 can be eliminated as candidates from all other cells in that column (D4) and region (A6, B6 and C6).
Example 3 : naked triple on column, the three cells of the triple contain only two candidate values
On column 2, cells G2, H2 and K2 have as combined candidates three distinct numbers: 3, 5 and 7. These three numbers can therefore be eliminated as candidates from all the other cells of column 2, here A2 , B2 and C2.
Exercises
The sudoku grids below require, to be solved, to use the naked triple technique, as well as some naked pairs :
- Sudoku n°511 (Easy)
- Sudoku n°229 (Easy)
- Sudoku n°1027 (Medium)
- Sudoku n°467093 (Medium)
- Sudoku n°190423 (Medium)
You can also challenge yourself with our daily sudokus, the easy and medium levels regularly contain naked triples.