Sudoku Hidden Triples Rule Explained with Examples

Hidden triples is a technique in Sudoku that lets you solve puzzles by eliminating candidates from the grid. 

This technique not only helps you solve simpler Sudoku puzzles quicker but can also become necessary to solve more difficult puzzles.

So let’s take a look at what a hidden triple is and how it’s useful. 

What is a hidden triple in Sudoku?

A hidden triple is when you have the same three digits (or a subset of them) as candidates in exactly three cells within the same row, column, or block. 

In addition to these three digits, you also have other possible candidates pencil marked in these cells along with the three digits that form the triple (otherwise it becomes a naked triple). 

To help explain this, let’s consider the hidden triple example below.

Are you able to spot the hidden triple? 

If you look closely, you’ll notice that digits 1, 5, and 7 only appear in three cells in the row: the 5th, 7th, and 9th cells. In fact, the 9th cell (the rightmost cell) only contains a subset of these three digits: 1 and 7. 

This hidden triple is highlighted below.

This would still be an example of a hidden triple if the 9th cell also contained a pencil marked 5. 

It would not, however, be a hidden triple if any of the digits 1, 5, or 9 were a candidate in any of the other cells. This would mean they appear in four or more cells and are therefore not a triple. 

One other thing to point out at this stage is that hidden triples can also occur within a column or 3×3 block. A row has just been used as an example in this case.

How to use hidden triples to solve puzzles

So now that you know what a hidden triple is, the next step is understanding how they help you solve Sudoku puzzles. 

In short, once you identify a hidden triple, you can immediately eliminate all other candidates from the three cells that contain the triple. 

So with the example above, we can eliminate the 3, 8, and 6 pencil marks from the highlighted cells. 

This is because the three digits 1, 5, and 7 must appear somewhere within these three cells. Meaning there’s no way any of these cells can contain any other digit as there’s this would leave no room for at least one of these digits in the row. 

This is a particularly powerful example too. 

By eliminating the extra candidates from the cells that form the hidden triple, there is now only one possible place for the 6 in this row. In other words, it’s revealed a hidden single and we can now place the 6. 

If you’re observant, you’ll also notice that after placing the 6 another hidden triple has been revealed with the 3, 4, and 8. 

This hidden triple example should demonstrate the power they have at letting you solve Sudoku puzzles. 

Just remember that the same logic applies to columns and 3×3 blocks, not just rows. 

Other types of hidden subsets

Hidden triples are only one type of what’s known as a hidden subset in Sudoku. 

There are also hidden singles, hidden pairs, and hidden quads. The same fundamental logic underpins all of these different types of hidden subsets, the only difference is the number of cells and digits they involve.