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A Naked Triple is a three-cell Naked Subset.
Inside one row, column, or box, choose three unsolved cells. If the union of every candidate in those cells contains exactly three distinct digits, then those three digits are reserved for those three cells.
They must occupy the cells in some order.
So the same three digits can be removed from every other cell in the shared unit.
The key idea is not that the cells look alike.
It is:
3 cells are restricted to 3 digits.
That is the same reservation principle used by Naked Pairs, extended from two cells to three.
Quick rule
A Naked Triple requires:
- three unsolved cells in one shared row, column, or box;
- no more than three distinct candidates across those cells;
- exactly three distinct digits in the combined candidate set;
- at least one other cell in the unit containing one of those digits if you want the Triple to produce an immediate elimination.
Then:
remove the three Triple digits from every other cell in that unit.
Schematic unit view — crossed candidates are the logical eliminations.
- Source candidates
- Eliminations
The candidate-union test
The most reliable way to understand a Naked Triple is to ignore how many notes are written in each individual cell and count the union.
Suppose three cells contain:
{2,5}{2,7}{5,7}
Merge the candidates and remove duplicates:
{2,5,7}
There are:
- 3 cells;
- 3 distinct candidate digits.
That is a valid Naked Triple.
Those cells must receive 2, 5, and 7 in some order.
Every other 2, 5, or 7 in the same unit can be eliminated.
A Naked Triple does not require identical candidate sets
This is a common recognition mistake.
The visually obvious case:
{1,4,9}{1,4,9}{1,4,9}
is valid.
But so are:
{1,4}{1,9}{4,9}
and:
{1,4,9}{1,4}{4,9}
and:
{1,4}{1,4}{1,4,9}
In every case, the three cells collectively contain only {1,4,9}.
A cell in a Naked Triple can contain:
- two of the Triple digits;
- all three Triple digits.
What it cannot contain is a fourth candidate outside the Triple set.
Why Naked Triples work
The proof is a simple capacity argument.
Three cells must eventually contain three solved digits.
If those cells can use only X, Y, and Z, then all three of X/Y/Z are consumed by the three-cell set.
There is no room inside the subset for another value.
And because a row, column, or box cannot repeat a digit, X/Y/Z cannot also appear elsewhere in the same unit.
We do not need to know the final order.
For example, these three cells may eventually become:
- X, Y, Z;
- X, Z, Y;
- Y, X, Z;
- or another valid permutation.
The unresolved order does not weaken the reservation.
Step-by-step board example
Naked Triples can appear in rows, columns, or boxes
The logic is identical in every house.
A Naked Triple may occupy three cells in:
- one row;
- one column;
- one 3×3 box.
The cells do not need to be adjacent.
They only need to share at least one complete unit in which the reservation is being used.
What is a Locked Triple?
Sometimes the three Triple cells share two houses at once.
For example, all three cells may sit:
- in one row and the same box;
- or in one column and the same box.
The subset then reserves the same three digits in both houses.
This is commonly called a Locked Triple.
It is not a different proof.
It is a Naked Triple whose geometry allows eliminations in two overlapping units.
If three Triple cells lie inside one row segment of a box, for example, the Triple digits may be removable:
- from other cells in the row;
- and from other cells in the box.
Always verify each target cell belongs to a house shared by the full Triple.
Naked Triple vs Naked Pair
The Naked Subset rule scales directly.
Naked Pair
2 cells → 2 digits.
Naked Triple
3 cells → 3 digits.
Naked Quad
4 cells → 4 digits.
The proof does not become fundamentally different.
Recognition becomes harder because there are more cell combinations and more possible candidate distributions.
This is why learning the union test matters more than memorizing Triple shapes.
Naked Triple vs Hidden Triple
The two techniques describe the same subset relationship from opposite search directions.
Naked Triple
Start with cells:
Which digits can these three cells contain?
If their combined candidate set is exactly three digits, remove those digits from other cells in the unit.
Hidden Triple
Start with digits:
Where can these three digits go in this unit?
If all their possible positions are confined to the same three cells, remove unrelated candidates from those cells.
After a Hidden Triple is cleaned up, the same cells may visibly look like a Naked Triple.
The logical relationship is dual, but the recognition process is different.
How to find Naked Triples efficiently
Randomly testing every group of three cells is possible in theory and miserable in practice.
Use constrained candidate sets.
1. Choose one unit
Look at one row, column, or box at a time.
2. Start with bivalue and trivalue cells
Cells containing only two or three candidates are the natural building blocks.
3. Compare overlapping candidate sets
Useful shapes include:
{1,4}+{1,7}+{4,7};{2,5,8}+{2,5}+{5,8};{3,6}+{3,6}+{3,6,9}.
4. Count the union
Do not count candidate marks visually.
List the distinct digits mentally or with highlighting.
If the union contains exactly three digits, continue.
If it contains four or more, the chosen cells do not form a Naked Triple.
5. Check for eliminations
Look only at other cells in the shared unit.
If none contain the Triple digits, the pattern may be logically true but is not currently productive.
A useful validity checklist
Before eliminating anything, verify all four questions:
- Do the three cells share one complete house?
- Does their candidate union contain exactly three digits?
- Have you accidentally included a fourth digit in one of the cells?
- Are your elimination targets outside the Triple but inside the same house?
If all four answers are correct, the elimination follows directly.
What a Naked Triple usually unlocks
A Triple is often a setup move rather than a placement.
Its eliminations can create:
- a Naked Single;
- a Hidden Single;
- a Naked Pair;
- a Hidden Pair;
- a Locked Candidate;
- a more constrained cell or unit.
A single elimination can be enough if it creates a forced follow-up.
After applying a Triple, re-scan the affected row, column, box, and peers before searching for another Triple.
Common mistakes
Requiring all three cells to contain all three digits
Not required.
The rule uses the candidate union.
Accepting three cells with four distinct candidates
For example:
{1,2} + {2,3} + {3,4}
has union {1,2,3,4}.
That is not a Naked Triple.
Removing the Triple digits from the Triple cells
The subset cells keep their reserved candidates.
Remove those digits only from other cells in the relevant house.
Mixing cells that do not share a unit
A reservation is meaningful only inside a row, column, or box shared by all three cells.
Forgetting that candidates must be accurate
An omitted legal candidate can make a false Triple appear valid.
Searching Triples before simpler subsets
Pairs and Singles are easier to recognize and may simplify the candidate state enough to remove the need for a Triple.
Recognition drill
Take three small candidate sets and ask:
How many distinct digits appear across all three cells?
If the answer is exactly three, ask:
Do these cells share a row, column, or box, and can those digits be eliminated elsewhere in it?
That two-question process is the core Naked Triple skill.
FAQ
Does every cell in a Naked Triple need three candidates?
No. Cells with two candidates are extremely common inside Naked Triples.
Can all three cells contain the same three candidates?
Yes. Three identical {X,Y,Z} cells are a valid and visually obvious Naked Triple.
Can a Naked Triple contain a cell with only one candidate?
If a cell has only one legal candidate, solve that Naked Single first. The Triple may disappear or simplify afterwards.
Can a Naked Triple affect both a row and a box?
Yes, when all three subset cells belong to both houses. This is often called a Locked Triple.
Does a valid Naked Triple always eliminate something?
No. A subset can be structurally valid but currently nonproductive if no other cell in the house contains its digits.
Why are Naked Triples harder than Naked Pairs?
Mostly because recognition requires comparing more cells and more candidate distributions. The underlying proof is the same N-cells/N-digits reservation rule.
What to learn next
Compare this cell-first subset with Hidden Triple, then continue into the Fish family with X-Wing once Pairs and Triples feel natural.