A Hidden Triple occurs when three digits are confined to the same three cells inside one row, column, or box.
Those cells may contain many extra candidates.
Because the three target digits have nowhere else to go in the unit, the three cells are reserved for them.
Every other candidate can be removed from those cells.
Quick rule
Three digits.
No candidate positions outside the same three cells in one unit.
→ Keep the three target digits and remove the other candidates from those cells.
A simple example
Suppose one box contains three important cells:
- A
{1,2,5,7} - B
{2,3,5,8} - C
{4,5,6,8}
Now inspect candidate positions throughout the entire box.
Suppose:
- digit 2 appears only in A/B;
- digit 5 appears only in A/B/C;
- digit 8 appears only in B/C;
- none of 2/5/8 appears anywhere else in the box.
Those three digits are collectively confined to A/B/C.
So A/B/C must contain 2, 5, and 8 in some order.
Every other candidate in those cells can be removed.
The cleaned cells may become:
- A
{2,5} - B
{2,5,8} - C
{5,8}
The Hidden Triple has become visible.
Why the digits do not need to appear in all three cells
This is important.
A Hidden Triple does not mean:
Each of the three target digits appears in each of the three cells.
It means:
Across the source unit, those three digits have no positions outside the three-cell set.
One target digit might appear in:
- two cells;
- all three cells.
That is fine.
The reservation still works as long as the three-digit set is confined to the three-cell set.
Why Hidden Triples work
The source unit still needs all three target digits.
Those digits have only three cells available between them.
If one of those cells took some unrelated candidate, three required digits would be forced into only two remaining cells.
That is impossible.
So the unrelated candidates cannot be true.
The proof is the same N-digits-for-N-cells subset logic used by Hidden Pairs, just one size larger.
Step-by-step board example
Hidden Triple vs Hidden Pair
The same positional idea scales.
Hidden Pair
2 target digits → confined to 2 cells.
Hidden Triple
3 target digits → confined to 3 cells.
Hidden Quad
4 target digits → confined to 4 cells.
The logic barely changes.
The visual search becomes harder.
Hidden Triple vs Naked Triple
Hidden Triple
Digit-first:
Where can X/Y/Z go?
If the answer is “only these three cells,” clean the cells.
Naked Triple
Cell-first:
What can these three cells contain?
If the answer is “only X/Y/Z,” clean the rest of the unit.
A Hidden Triple may reveal a Naked Triple after the extra candidates are removed.
How to search for Hidden Triples
Hidden Triples are not usually found by staring at large candidate sets.
Search the occurrence counts of digits.
1. Pick one unit
Choose a row, column, or box with several unsolved cells.
2. Notice restricted digits
Which missing digits have only two or three candidate positions?
3. Compare three such digits
Do their combined positions fit entirely inside three cells?
4. Clean those cells
If yes, remove candidates that are not part of the target digit set.
Candidate highlighting can make this dramatically easier because it externalizes the position comparison.
A useful mental model
For Naked Triples, count candidate digits across cells.
For Hidden Triples, count candidate positions across digits.
That symmetrical wording helps keep the two techniques separate.
Why Hidden Triples feel difficult
Several reasons:
- the target cells can look messy;
- the relevant digits may not all appear in all three cells;
- you must compare candidate positions across a whole unit;
- the pattern is usually less visually obvious than a Naked Triple.
The proof is not especially advanced.
Recognition is.
That distinction matters for Learn and Practice design.
What the cleanup can unlock
A Hidden Triple can:
- turn three messy cells into a Naked Triple;
- create a bivalue cell;
- expose a Naked Single later;
- simplify overlapping row/column units;
- make another Hidden subset easier to spot.
Always inspect the cleaned cells in every unit they belong to.
Common mistakes
Looking for three identical cells
The cells do not need identical candidate sets.
Requiring each target digit in all three cells
Not necessary.
Removing X/Y/Z
Those are the reserved digits. Remove the other candidates.
Missing one candidate position elsewhere in the unit
That breaks the three-digit confinement.
Searching Hidden Triples before Hidden Pairs
Pairs are easier and often simplify the same area.
Recognition drill
Inside one unit, pick three digits with low occurrence counts and ask:
Are all their possible positions contained in only three cells?
This is the Hidden Triple question in its most compact form.
FAQ
Can a Hidden Triple cell contain extra candidates?
Yes. Removing those candidates is the point of the technique.
Does each target digit need exactly three positions?
No. A target digit may occupy two or three positions inside the three-cell set.
Can a Hidden Triple become a Naked Triple?
After cleanup, the same three cells contain only the three reserved digits, so the subset can also be described from the Naked viewpoint.
Are Hidden Triples common?
Their usefulness varies by puzzle. They are generally harder to recognize manually than Pairs because more candidate-position relationships must be compared.
What to learn next
After Pairs and Triples are comfortable, complete Intermediate Practice before moving to X-Wing and the Advanced pattern layer.