You have mastered naked pairs and yet some grids still resist. There is a good chance the naked triple is the technique you are missing, and one single misconception is enough to make it invisible.
Here is that misconception: believing a naked triple requires three cells each holding the same three candidates. That is wrong, and it is in fact the rarest case.
The real definition of the naked triple, the three shapes it can take, how to apply it in a row, a column and a box, and the Domino33 method for spotting one without getting lost.
🎬 The Domino33 video on naked triples
Here is the full tutorial, with the technique worked through in all three units: row, column and box.
▶ English audio track and English subtitles: pick either from the ⚙️ icon.
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The real definition
Forget the idea of three identical cells. The actual rule is looser, and far more powerful:
Three cells of the same unit whose candidates, once pooled together, amount to only three different digits.
Each cell may hold 2 or 3 candidates, it does not matter. What counts is the union of the three. If it gives exactly three digits, those three digits will occupy those three cells, in one order or another. They are therefore forbidden everywhere else in the unit.
The three possible shapes
For a triple on the digits {2, 4, 7}, here is everything that qualifies:
- Full shape: {2,4,7} · {2,4,7} · {2,4,7}, the most visible, and the rarest
- Mixed shape: {2,4} · {2,4,7} · {4,7}, very common
- Split shape: {2,4} · {4,7} · {2,7}, three interlocking pairs, no cell carries all three digits
Looking only for the full shape means missing the vast majority of naked triples. The split shape is the most frequent one in real grids, and it is precisely the one nobody sees.
A worked example
Here is a row from a grid. Look at cells C3, C5 and C9:
C3 holds {2,4}, C5 holds {4,7} and C9 holds {2,7}. None of these cells carries all three digits, but their union gives exactly {2, 4, 7}. That is a naked triple in its split shape.
Consequence: the 2, the 4 and the 7 are eliminated from every other cell of the row.
C2 goes from {1,3,4,5} to {1,3,5} · C6 goes from {1,2,5,7} to {1,5} · C8 goes from {3,5,7} to {3,5}
The result is striking. C6 is left with {1, 5} and C8 with {3, 5}: two brand new two-candidate cells, where nothing was usable before. A single triple just knocked out six candidates.
Part 2
In a row, a column and a box
The reasoning is exactly the same in all three units. Only the elimination area changes:
- In a row: the 9 cells of one horizontal line
- In a column: the 9 cells of one vertical line
- In a box: the 9 cells of one 3×3 square
The box, prime hunting ground
Naked triples are especially common inside boxes, because candidates are naturally more concentrated there. And when the three cells of a triple also happen to be aligned in the same row or column, you eliminate in both units at once.
Part 3
The search method
Step 1, Spot the cells with 2 or 3 candidates
A cell with 4 candidates or more can never be part of a naked triple. You can dismiss it straight away, which shrinks the search space enormously.
Step 2, Start from a 3-candidate cell
That is the most efficient anchor point. Take a cell holding, say, {2,4,7}, then look in its unit for two other cells whose candidates are all drawn from those three digits. A {2,4} and a {4,7} will do.
Step 3, Or start from two neighbouring pairs
If you find two 2-candidate cells sharing one digit, such as {2,4} and {4,7}, you are one cell short: it must hold only digits taken from {2,4,7}. Look for {2,7}, {2,4}, {4,7} or {2,4,7}.
Step 4, Check, eliminate, read again
Count the distinct digits before eliminating. Three of them, apply. Four of them, it is not a triple. Then go through the unit again from the start, because one triple very often opens up another.
Write the candidates of the three cells side by side and count the distinct digits. Three digits: it is a triple. Four: it is not. That simple count prevents almost every mistake.
What comes next?
The naked triple has two direct extensions. The hidden triple, its exact mirror, where three digits hide among other candidates. And the naked quad, which applies the same logic to four cells and four digits.
🎬 See the method in action
In the video the technique is worked through on real grids, in all three units. It is the fastest way to build the reflex.
Exercise
Your turn
Here is another grid row, with a naked triple different from the one in the example.
Three cells whose pooled candidates amount to only three digits. None needs to carry all three.
Part 4
Practice quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
A naked triple is three cells of the same unit (row, column or box) whose pooled candidates amount to only three different digits. Those three digits will necessarily occupy those three cells, in one order or another. They can therefore be eliminated from every other cell of the unit.
No, and that is the most widespread mistake. Each cell may hold only 2 of the 3 digits. The three cells {2,4}, {4,7} and {2,7} form a perfectly valid naked triple even though none of them contains all three digits. Only the union of the candidates matters.
Write the candidates of the three cells side by side and count the distinct digits. If there are exactly three, it is a naked triple. If there are four, it is not, and no elimination is allowed.
The naked triple is visible: three cells hold only three digits in total, and you clean the other cells of the unit. The hidden triple is concealed: three digits appear in only three cells, but those cells also hold other candidates, and it is the inside of those three cells that you clean.
📋 Summary
Naked triple essentials
- Setup: 3 cells of the same unit whose pooled candidates amount to only 3 digits
- Action: eliminate those 3 digits from every other cell of the unit
- Remember: no cell needs to contain all 3 digits
- Starting point: cells with 2 or 3 candidates, never more
- The test: count the distinct digits, three and not four
- Related techniques: naked pairs, hidden triples, naked quads
The naked triple is the natural extension of the naked pair, and it opens the way to the hidden triple, which rests on the opposite reasoning.
📘 Go further with the Domino33 books
Naked triples and every other technique on this site are covered step by step in the Domino33 memento, available in English.
