Sudoku Hidden Triples Technique and Examples

If you’re familiar with hidden pairs, you can build on that Sudoku technique and solve for hidden triples. Hidden triples occur when three cells within the same unit (row, column, or 3x3 block) share the same three repeated candidate numbers, or a subset of those numbers, that no other cells in that unit contain.

Hidden triples are similar to naked triples, except the cells contain other candidate numbers, which may make them hard to spot — hidden — at first. However, once you find this hidden set of triples, you can eliminate all other candidate numbers within these three cells because the cells must contain one of the three candidate options in that triple set.

With this Sudoku strategy, beginners can solve sudoku puzzles faster and advanced solvers can rely on this method to consistently work through more challenging puzzles, eliminating candidates and solving puzzles more efficiently.

How to Find Hidden Triples

Hidden triples differ slightly from the criteria for hidden doubles in that all three candidate numbers may not always appear in all three cells. One cell may simply have a hidden subset of those numbers. For example, consider if three cells in a 3x3 block have the following candidates:

  • 2, 3, 5, 7
  • 3, 5, 7
  • 1, 5, 7

As long as no other cells in that 3x3 block have a 3, 5, or 7, you’ve found a hidden triple because the third cell contains a subset (5, 7) of the triple (3, 5, 7). Since these candidates don’t appear in any other cell, only those three cells can possibly hold a 3, 5, or 7.

With that in mind, hidden triples must fit the following criteria:

  • Three cells within the same row, column, or 3x3 block share three candidate numbers or a subset of those numbers.
  • The three candidate numbers do not appear in any other cells within that unit.
  • Other candidates that are not part of the hidden triple appear in at least one of the three hidden triplet cells. In other words, like the example above, the second cell isn’t hiding the candidates, but because other candidates are in the first and third cells, this still qualifies as a hidden triple.

To identify hidden triples:

  1. Note all possible candidate numbers within each cell.
  2. Scan rows, columns, and blocks for three cells with the same three candidate numbers or a subset of those numbers.
  3. Ensure these numbers don’t appear in any other cell within that unit. For example, you find one cell within a row that has 2, 3, 5, and 7 as candidates; another cell has 3, 5, and 7 as candidates; and a third cell has 1, 5, and 7 as candidates. You need to be sure that 3, 5, and 7 are not candidates for any other cells in that row. If that’s the case, 3, 5, and 7 are the hidden triple.

Naked quads can contain hidden triples, so remember to scan the whole unit, whether it’s a row, column, or block, and look closely at cells that contain multiple candidates.

Hidden Triples Examples

Hidden triples offer a powerful strategy because they not only eliminate candidates in the three cells of the hidden triple, but they can also create chain reactions. By eliminating candidates, you narrow down possibilities for other cells, allowing you to find answers as well as eliminate candidates elsewhere in the puzzle.

Here are a few examples showing how they work in action.

Hidden Triples in a Row

example of a hidden triple in a row

In this example, you can find the hidden triple (3, 5, 7) in cells A2, B2, and H2. Although H2 is a subset (5, 7) of the triple, it contains at least two of the three hidden triple numbers, which makes it part of the hidden triple.

Verify it is a hidden triple by seeing if 3, 5, or 7 appear in any other cell in row 2. Because they don't, you can remove the 2 candidate in A2 and the 1 candidate in H2. Since these three candidate numbers (3, 5, 7) only appear in these three cells, they must be the only answers to those cells.

Hidden Triples in a Block

example of a hidden triple block

This example shows the hidden triple (2, 6, 9) in D1, E2, and F1 of the center block. Verify this by checking that 2, 6, or 9 don’t appear in any other cells in the middle 3x3 block. Now you can eliminate the following candidates: 5 in D1, 1 in E2, and 7 in F1.

You can see the chain reaction this technique created by looking at cells F2 and D3. Because 1 was eliminated from E2 and 7 was eliminated from F1, you’re left with a naked pair (1, 7) in F2 and D3. This allows you to eliminate 7 as a candidate from E3, making 5 the answer for that cell.

You can arrive at 5 as the answer for E3 in another way. After 5 was eliminated as a candidate from D1, that means E3 is the only possible cell in which 5 could be an answer for this block. Either way, using hidden triples not only helps eliminate candidates but can also create a cascade of elimination that results in answers for cells.

Hidden Triples in a Column

example of a hidden triple in a column

In this example, the hidden triple (4, 6, 9) appears in column C. Although C8 includes the candidates 4, 6, and 8, it does include a subset of the hidden triple (4, 6), which still makes it part of the hidden triple. Because 4, 6, and 9 must be the answers in cells C6, C8, and C9, you can eliminate the 8 and 1 candidates in those cells.

Hidden triples may sound like an advanced technique, but it builds off of hidden pairs and can be a reliable technique to unlock answers in intermediate or hard Sudoku puzzles. If you need more solving techniques, you can read our Sudoku blog and explore our archive for hundreds of free Sudoku games.