The hidden triple is the most feared of the six basic techniques, and that reputation is largely undeserved. It scares people because it is usually approached from the wrong end.
The right way to see it: it is exactly the same reasoning as the hidden pair, with three digits instead of two. If you have one, the other is already within reach.
Why the hidden triple is the exact opposite of the naked triple, how to apply it in a row, a column and a box, and the Domino33 counting method that makes it appear without guesswork.
🎬 The Domino33 video on hidden 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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Naked or hidden, a matter of direction
Both techniques describe the same reality, but you look at it from opposite sides.
- Naked triple: three cells whose pooled candidates amount to only 3 digits. You eliminate those 3 digits from the other cells of the unit.
- Hidden triple: three digits appearing in only 3 cells, but those cells also hold other candidates. You eliminate all the other candidates from those 3 cells.
The naked one cleans the outside, the hidden one cleans the inside. The same sentence works for pairs and for triples, and it is enough to never mix them up again.
Why "hidden"?
Because the three digits are buried among other candidates. In a cell containing {1,4,6,9}, the fact that the 1 and the 4 belong to a triple is anything but obvious. Only by counting where each digit can go across the whole unit does the configuration surface.
A worked example
Here is a row from a grid. Look at where the 1, the 4 and the 7 can go:
The 1 appears only in C2 and C8. The 4 appears only in C2 and C4. The 7 appears only in C4 and C8. Those three digits therefore spread across C2, C4 and C8 only, and all three of them have to be placed.
Consequence: those three cells are reserved for the 1, the 4 and the 7. All their other candidates are impossible.
C2 goes from {1,4,6,9} to {1,4} · C4 goes from {3,4,7} to {4,7} · C8 goes from {1,7,9} to {1,7}
Look at the result: {1,4}, {4,7} and {1,7}. You have just created a naked triple in its split shape, where nothing was visible before. And the 3, the 6 and the 9 are now freed up for the rest of the grid.
Each digit of the triple does not need to appear in all three cells. Here each one appears in only two of them. The single requirement is that none of the three escapes the group of three cells.
Part 2
In a row, a column and a box
The reasoning is exactly the same in all three units. Only the place where you count 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
Hidden triples are most frequent in well-filled units, the ones with only 4 or 5 empty cells left. With few digits still to place, the odds of three of them concentrating on three cells become high.
Part 3
The search method
Step 1, Pick one unit and finish it
A row, a column or a box. Jumping from one unit to another is the surest way to find nothing. Favour the ones with 4 or 5 empty cells left.
Step 2, Map out the possible locations
For each digit still to be placed in the unit, write down the list of cells where it is still a candidate. That is the heart of the method, and it is what most solvers never do.
Step 3, Keep only the rare digits
Discard any digit present in 4 cells or more: it cannot be part of a hidden triple. You are normally left with a handful of digits to examine, the ones with only 2 or 3 possible locations.
Step 4, Look for three digits fitting in three cells
Among the remaining digits, look for three whose combined locations do not exceed three cells. If you find three, eliminate all the other candidates from those three cells.
Always start from the rarest digit of the unit, the one with only two possible locations. If a hidden triple exists, it is almost always part of it. All that is left is to find its two companions.
🎬 See the method in action
In the video the counting is worked through on real grids, in all three units. It is by far the clearest way to grasp the mechanism.
Exercise
Your turn
Here is another grid row. It contains a hidden triple, elsewhere than in the example.
List each digit's locations, then look for three that fit into three cells.
Part 4
Practice quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
A hidden triple is three digits that appear in only three cells of the same unit (row, column or box), while those cells also hold other candidates. Since those three digits must be placed in those three cells, all the other candidates can be eliminated from them.
No. Each digit of the triple may appear in only two of the three cells. The single requirement is that none of the three digits is a candidate outside the group of three cells.
The naked triple is visible: three cells hold only three digits in total, and you eliminate those digits from the other cells of the unit. The hidden triple is concealed: three digits appear in only three cells, and you eliminate all the other candidates from those three cells. The naked one cleans the outside, the hidden one cleans the inside.
For each digit still to be placed in the unit, list the cells where it is still a candidate. Discard every digit present in 4 cells or more. Among those left, look for three digits whose combined locations do not exceed three cells. Starting from the rarest digit speeds the search up considerably.
📋 Summary
Hidden triple essentials
- Setup: 3 digits appearing in only 3 cells of the same unit
- Action: eliminate all the other candidates from those 3 cells
- Remember: each digit need not be present in all 3 cells
- Starting point: list the possible locations of every digit
- The right reflex: start from the rarest digit of the unit
- Related techniques: hidden pairs, naked triples, Box Reduction
The hidden triple takes more effort than the other basic techniques, which is exactly why it is still available when everything else is blocked. The counting work it demands is also what every advanced technique rests upon.
📘 Go further with the Domino33 books
Hidden triples and every other technique on this site are covered step by step in the Domino33 memento, available in English.
