A Naked Triple is a set of three unsolved cells in one row, column, or box whose combined candidate set contains exactly three digits.
Those three digits must occupy the three cells in some order.
So those digits can be removed from every other cell in the shared unit.
The most important detail is this:
The three cells do not need identical candidate sets.
Quick rule
Three cells.
Three distinct candidates total across those cells.
One shared unit.
→ Remove those three digits from the rest of the unit.
A classic Naked Triple
Consider three cells in one row:
{2,5}{2,7}{5,7}
Across the three cells, the candidate union is:
{2,5,7}
Three cells.
Three possible digits.
Those cells must therefore receive 2, 5, and 7 in some order.
The rest of the row cannot use any of those three digits.
Why identical triples are only one special case
This is also a valid Naked Triple:
{1,4,9}{1,4,9}{1,4,9}
It is visually obvious.
But this is valid too:
{1,4}{1,9}{4,9}
And so is:
{1,4,9}{1,4}{4,9}
The rule is about the union of candidates, not visual matching.
This is the main conceptual jump from Naked Pairs.
Why Naked Triples work
The three cells need three values.
If the only values available anywhere inside that three-cell set are X, Y, and Z, then those three digits are completely consumed by those cells.
There is no room for a fourth digit inside the subset.
And there is no room for X/Y/Z elsewhere in the unit, because the unit may contain each digit only once.
The exact permutation remains unresolved.
The reservation is still certain.
Step-by-step board example
Naked Triples in a box or column
The unit can be any row, column, or box.
A Locked Triple can affect two units
If all three Triple cells share:
- one row and one box;
- or one column and one box;
the same three-digit reservation may create eliminations in both units.
This is often called a Locked Triple.
Like Locked Pair, it is not new logic.
It is a Naked Triple whose cells happen to share two units.
The union test
When testing three cells:
- collect every candidate appearing in those cells;
- remove duplicates;
- count the distinct digits.
If the union contains:
- 3 digits → possible Naked Triple;
- 4+ digits → not a Naked Triple.
Example:
{1,2} + {2,3} + {3,4}
Union:
{1,2,3,4}
Three cells, four digits.
Not a Naked Triple.
This union test is one of the most reusable concepts in subset solving.
Naked Triple vs Naked Pair
The rule scales directly.
Naked Pair
2 cells → 2 digits.
Naked Triple
3 cells → 3 digits.
Naked Quad
4 cells → 4 digits.
The larger the subset, the more combinations you must compare.
That increases recognition difficulty even though the logical idea barely changes.
Naked Triple vs Hidden Triple
Naked Triple
Start with cells.
These three cells contain only X/Y/Z.
Remove X/Y/Z elsewhere.
Hidden Triple
Start with digits.
X/Y/Z can appear only in these three cells.
Remove other candidates from the three cells.
Again, Naked and Hidden are dual viewpoints.
How to find Naked Triples without brute-force searching every combination
A manual solver should not test all cell triplets randomly.
Start with candidate-dense but constrained areas.
Good signals:
- several bivalue cells in one unit;
- a trivalue cell sharing candidates with nearby bivalue cells;
- repeated candidate digits across three small sets.
Try the smallest candidate sets first.
Example visual seed:
{1,4}{1,7}{4,7}
The cyclical overlap makes the three-digit union easy to notice.
What Triples usually unlock
A useful Triple can remove many candidates at once.
But even one elimination can matter if it:
- creates a Single;
- reduces another cell to a Pair;
- makes a Hidden subset visible;
- restricts one digit into an intersection.
That is why the follow-up re-scan remains part of the technique.
Common mistakes
Requiring all three cells to contain all three digits
Not required.
Using a three-cell set with four candidates total
Then the three cells are not restricted enough.
Removing subset digits from the Triple cells
Keep the subset candidates there.
Eliminate from other cells in the shared unit.
Selecting cells from different units
The reservation must exist inside at least one common unit.
Searching Triples before simpler subsets
Pairs are easier to recognize and may simplify the candidate state enough to make the Triple unnecessary.
Recognition drill
Select three small candidate sets and ask:
What is their candidate union?
Do not ask:
Do these cells look similar?
The first question tests the actual logic.
FAQ
Does every cell in a Naked Triple need three candidates?
No. Two- and three-candidate cells can combine into a valid Triple.
Can a Naked Triple contain three identical candidate sets?
Yes, but that is only one possible form.
Can a Naked Triple affect both a row and a box?
Yes, when all three subset cells share both units.
Why are Triples harder than Pairs?
There are more possible candidate-set combinations to compare, so recognition usually requires more attention.
What to learn next
Compare the same three-for-three reservation from the opposite direction in Hidden Triple.