Naked Triple Sudoku Strategy
Naked triples are an important intermediate Sudoku solving technique. This strategy helps you eliminate candidates and make progress when basic methods are no longer enough.
A naked triple occurs when three cells in a row, column, or 3x3 box contain only the same three candidates (in any combination), and no other candidates. Once you identify a naked triple, you can eliminate those three numbers as candidates from all other cells in that unit.
What is a Naked Triple?
A naked triple is present when exactly three cells in a unit (row, column, or box) contain only three specific candidates between them (for example, 2, 5, and 7), and no other candidates. These three numbers must be placed in those three cells, so they can be removed as possibilities from the rest of the unit.
How to Spot a Naked Triple
To find a naked triple, scan each row, column, or box for:
- Three cells that contain only the same three candidates (the cells may have two or three of the candidates each).
- No other cells in that unit contain those three candidates together.
- Once found, eliminate those three numbers as candidates from all other cells in the unit.
Example:
If three cells in a row have candidates {2,5}, {2,7}, and {5,7}, then 2, 5, and 7 form a naked triple. You can remove 2, 5, and 7 as candidates from all other cells in that row.
Why Use the Naked Triple Technique?
The naked triple technique is especially useful in medium and hard Sudoku puzzles, where simple elimination and singles are not enough. By mastering this strategy, you can break through tough spots and solve puzzles more efficiently.
Naked Triple Example
Let’s walk through an example of how to identify and use a naked triple.
Suppose you notice that in a particular box, three cells have candidates {1,3}, {1,5,3}, and {3,5}. Since only the numbers 1, 3, and 5 appear in these three cells, and no other candidates, you can eliminate 1, 3, and 5 from the candidate lists of all other cells in that box.
After applying the naked triple, check the rest of the unit for new opportunities—solving one naked triple can reveal others nearby.
Tips for Using Naked Triples
- Regularly scan each unit for groups of three cells with only three candidates between them.
- Each time you identify a naked triple, update the candidates for all affected cells.
- Naked triples can appear at any stage of the puzzle, so keep looking for them as you progress.
You’ve now learned how to spot and use the naked triple technique. Try it out in your next Sudoku game and see how much easier it is to solve challenging puzzles!