Naked Triple

A Naked Triple (also called an Obvious Triple) is the naked pair's bigger sibling. Where a naked pair locks two digits into two cells, a naked triple locks three digits into three cells - and clears those digits from everywhere else in the unit. It's a pure elimination technique, and once you're comfortable with pairs it's the natural next step.

What is a Naked Triple?

A Naked Triple appears when three cells in the same unit (row, column or box) together contain only three candidates between them - no others. The clever part: each cell doesn't have to show all three. Any mix works, as long as the three cells use just those three digits:

  • {3, 8}   {3, 9}   {8, 9} - three cells, only the digits 3, 8 and 9
  • {3, 8, 9}   {3, 8}   {8, 9} - also a valid triple

Because those three digits must fill those three cells (in some order), they are claimed - and can be removed from every other cell in the unit.

Step by step

  1. Fill in your pencil marks. Like all subset techniques, a naked triple is invisible until every candidate is on the board.
  2. Find two or three cells with small candidate lists in one unit - two or three candidates each.
  3. Check the union. If three cells use only three distinct digits between them, you have a naked triple.
  4. Eliminate those three digits from every other cell in the unit.
  5. Re-scan. The eliminations often expose a naked or hidden single straight away.
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Indigo: the triple {3, 8, 9} spread across three cells. The green cell used to hold {5, 8}; removing the 8 leaves a Naked Single - 5.

Naked triple vs hidden triple

Don't confuse the two. A naked triple is three cells that contain only the three digits. A hidden version works the other way round: three digits that appear in only three cells, buried among other candidates. Naked triples are usually easier to spot - the short candidate lists give them away.

Common mistakes

  • Counting four digits. If the three cells use four or more distinct candidates between them, it isn't a triple - keep looking.
  • Expecting all three digits in every cell. They rarely are. {3,8}, {3,9}, {8,9} is a perfect triple even though no cell shows all three.
  • Forgetting to re-scan. The point of the triple is the eliminations it triggers elsewhere - check the unit again straight after.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.

Great fit Classic Sudoku The natural next step after the naked pair - same idea, one cell wider. → Great fit Killer Sudoku Common in Killer, where cage sums frequently pin three cells to three digits. → Great fit Sudoku X The diagonals give the triple two more units to lock digits out of. → Great fit Samurai Sudoku Works per sub-grid, just as it does on a plain 9×9. →

Where to practise this

This technique starts paying off at Easy, which is where puzzles first stop yielding to anything simpler. Reading about a pattern and spotting it on a live grid are different skills - the second one only comes from playing.

Play Easy Sudoku About Easy Sudoku

Related techniques

Naked Pair - Sudoku Elimination Technique Two cells in a unit holding the same two candidates claim those digits, removing them elsewhere in the unit. Hidden Triple in Sudoku - How to Spot It Three digits that can go in only the same three cells of a unit - every other candidate can be cleared from those cells. Naked Quad - Sudoku Elimination Technique Four cells in a unit using only four candidates between them claim those digits, removing them elsewhere in the unit. Crosshatching - the First Sudoku Scanning Technique Scan a digit's existing rows and columns through a box to find the single cell in the box where it can still go.
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