Sudoku Naked Triples Explained: Learn to Solve Puzzles Faster

Naked triples is a basic Sudoku solving technique that’s very similar to naked pairs. 

Both strategies can potentially help you complete your Sudokus faster and may become necessary to solve more challenging puzzles. The only difference is naked triples deals with three digits whereas naked pairs deals with only two. 

What is a naked triple in Sudoku?

Let’s first look at exactly what a naked triple is and how you can spot them before we move on to how they are useful. 

Simply put, a naked triple occurs when you have exactly three cells within a row, column, or 3×3 region where the only candidates are the same three digits or a subset of these three digits. 

For example, let’s consider the 3×3 region below. 

As the highlighting shows, the 1, 7, and 8 are the only candidates in three cells. This means they form a naked triple. 

If there were other candidates in these cells, then that would mean they would potentially form a hidden triple. The term ‘hidden’ refers to how the other candidates are ‘hiding’ this triple. 

As mentioned though, not all of the three cells that make up the hidden triple need to contain all three digits. They can potentially contain just a subset of the three digits. Such as in the slightly modified example below. 

The three highlighted cells in this example still form a naked triple as the set of three digits (1, 7, and 8) appears as the only candidates in three cells. 

At this point, it’s worth noting that this isn’t constrained to just 3×3 but also applies when you have a set of three digits being the only candidates in three cells of a column or row as well. Such as in the example below.

How to use naked triples to solve Sudoku puzzles

So now that you know what a naked triple is, the next question is: how does this help solve Sudoku puzzles?

The beauty of naked triples is that you can eliminate the digits that form the triple as candidates from all other cells in the row, column, or 3×3 region the triple occurs in. 

This is because if you were to place a 1, 7, or 8 in any other cell, you would not be able to legally fill the three cells that make up the triple.

If we take the 3×3 example from before, this means we can eliminate 1 and 7 as candidates from the top-left cell and 8 as a candidate from the center cell. 

Leaving us with the following candidates.

As you can see, by using the naked triple strategy, we have now revealed a naked single in the top-left cell, letting us place an extra digit in the grid. 

Hopefully, this demonstrates the power of naked triples. 

Just remember that you must have filled in ALL the possible candidates before you can use this strategy.