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A Hidden Pair is a two-digit Hidden Subset.
Inside one row, column, or box, two digits are confined to the same set of two cells. Those cells may still contain several other candidates, which visually hide the reservation.
Once the two-for-two restriction is proved, every non-pair candidate can be removed from the two target cells.
Hidden Pair at a glance
Two digits.
Only two cells available for those digits inside one house.
→ The two cells are reserved for the two digits.
→ Keep the pair digits and remove the other candidates from those cells.
Schematic unit view — crossed candidates are the logical eliminations.
- Source candidates
- Eliminations
Why a Hidden Pair is logically forced
Suppose row 3 still needs digits 4 and 9.
Across the entire row:
- candidate 4 appears only in cells A and B;
- candidate 9 also appears only in cells A and B.
The row must place both 4 and 9 somewhere.
Because neither digit has any legal position outside A and B, those two cells must contain 4 and 9 in some order.
If A or B took an unrelated value, the row would no longer have enough cells available to place both required digits.
Therefore every candidate in A and B other than 4 or 9 is impossible.
A simple example
Suppose row 3 contains:
r3c2 {1,4,6,9};r3c7 {2,4,8,9}.
Now inspect candidate positions in the whole row.
If 4 appears only in r3c2 and r3c7, and 9 also appears only in those two cells, then the cells are reserved for {4,9}.
Clean the pair:
- remove 1 and 6 from
r3c2; - remove 2 and 8 from
r3c7.
After the elimination, both cells visibly show {4,9}.
Step-by-step row example
Verify a Hidden Pair digit-first:
- choose one house;
- identify two missing digits with very few remaining positions;
- confirm that both digits are confined to the same two cells;
- keep the two pair digits in those cells;
- remove every other candidate from the pair cells;
- re-scan all houses touching those cells.
Hidden Pairs work in rows, columns, and boxes
The source house can be any:
- row;
- column;
- 3×3 box.
The cells do not need to be adjacent.
The proof depends only on the positional fact:
the two target digits have no legal positions outside the same two-cell set in the source house.
What does “hidden” mean?
The pair is hidden because the important reservation is not obvious from the cell candidate counts.
The target cells may look busy:
A {1,2,4,6,8}
B {2,3,4,7,8}If digits 4 and 8 occur nowhere else in the house, A and B form a Hidden Pair {4,8}.
The extra notes are distractions. The useful information lives in the distribution of the digits across the house.
Hidden Pair vs Naked Pair
The two techniques are dual views of the same two-digits-for-two-cells reservation.
Naked Pair — cell-first
These two cells contain only X and Y.
Remove X and Y from other cells in the house.
Hidden Pair — digit-first
X and Y can appear only in these two cells.
Remove every other candidate from the two pair cells.
After the cleanup, a Hidden Pair often becomes visually identical to a Naked Pair.
The difference is how the reservation was discovered and where the elimination occurs.
Hidden Pair vs Hidden Single
Hidden subsets form a natural counting progression.
Hidden Single
1 digit → 1 possible cell.
→ Place the digit.
Hidden Pair
2 digits → 2 possible cells as a set.
→ Remove other candidates from those cells.
Hidden Triple
3 digits → 3 possible cells as a set.
→ Remove other candidates from those cells.
This is why Hidden Pair is not an isolated pattern name. It is the first non-trivial member of a general positional-reservation family.
What if one digit has only one position?
Suppose digit 4 can appear only in cell A, while digit 9 can appear in A or B.
The two digits are technically confined to the set {A,B}, but you already have a simpler deduction:
4 is a Hidden Single in A.
Solve the Single first.
In practical Hidden Pair searching, both target digits normally remain unresolved across the two-cell set. This follows the general principle of using the simplest available deduction before a larger subset description.
How to find Hidden Pairs
Hidden Pairs are naturally digit-first.
1. Choose one house
Rows, columns, or boxes with several unresolved cells are useful targets.
2. Count positions for each missing digit
Which digits have only two possible locations?
3. Compare the two-cell position sets
Do two digits depend on the same two cells?
4. Confirm the complete source house
Make sure neither digit has a legitimate candidate outside those cells.
5. Clean the target cells
Remove every candidate except the two reserved digits.
6. Re-scan the affected houses
The cleanup can simplify more than the source house because both cells also belong to other rows, columns, or boxes.
Candidate filters make Hidden Pairs easier to see
Hidden Pairs can be hard to recognize from full candidate notation because the target cells may contain many notes.
A digit filter changes the question from:
“What candidates are inside this cell?”
to:
“Where can this digit still go in this house?”
If two digits repeatedly highlight the same two cells, investigate a Hidden Pair.
This is the same digit-first search lens used for Hidden Singles, only extended from one digit/one position to two digits/two positions.
Complete candidates matter
A Hidden Pair proof depends on the target digits having no valid positions elsewhere in the source house.
If your displayed notes are incomplete, two digits may appear to be confined when they are not.
With selective notation, verify the missing positions from the actual row, column, and box constraints before deleting anything.
What does the cleanup unlock?
A Hidden Pair can remove several candidates at once from two busy cells.
That can:
- expose a Naked Pair;
- create a Naked Single later;
- simplify another house shared by one of the pair cells;
- expose another subset;
- create a Locked Candidates pattern.
Do not stop after cleaning the pair. Update and re-scan.
Hidden Pair as the foundation of Hidden Subsets
The same logic scales directly:
2 digits confined to 2 cells
→ Hidden Pair
3 digits confined to 3 cells
→ Hidden Triple
4 digits confined to 4 cells
→ Hidden QuadThe surface patterns become harder to notice as the sets grow, but the underlying proof remains the same: a group of required digits has only enough cells available to contain that group.
Productive pair vs already-clean pair
Sometimes two digits are confined to two cells, but those cells already contain only the pair digits.
The relationship is still true, but there are no extra candidates to remove from the target cells.
At that point the same structure is already visible as a Naked Pair in the source house.
For practical solving, prioritize Hidden Pairs that actually clean candidates.
Common mistakes
Finding two digits that each occur twice, but in different cells
The position sets must resolve to the same two-cell set.
Removing the pair digits
Keep the reserved digits. Remove the distracting candidates.
Assuming two crowded cells automatically form a Hidden Pair
The proof comes from candidate occurrence across the whole house, not from the appearance of the two cells.
Using incomplete notes as complete evidence
A missing legitimate candidate can create a false pair.
Ignoring a simpler Hidden Single
If one target digit has only one legal position, solve that Single before describing a larger subset.
Forgetting to re-scan after cleanup
The candidate removals can create immediate progress in several houses.
Recognition drill
Inside one row, column, or box, ask:
“Which digits are running out of places?”
When two digits each have very limited positions, compare their position sets.
If both depend on the same two cells, check whether those cells contain extra candidates that can be removed.
FAQ
Does a Hidden Pair become a Naked Pair?
After all extra candidates are removed, the two cells contain only the reserved pair digits, so the structure is visible as a Naked Pair within that house.
Must both target digits appear in both pair cells?
For the usual unresolved Hidden Pair, both digits have the same two possible cells. If one digit has only one legal position, that simpler Hidden Single should normally be solved first.
Must the pair cells be adjacent?
No. They only need to belong to the same source house.
Why are Hidden Pairs harder to notice than Naked Pairs?
Because the useful relationship lives in the positions of two digits across a house, while the individual target cells may contain many distracting candidates.
Is a Hidden Pair a type of subset?
Yes. It is the two-digit form of a Hidden Subset.
Do I need full pencil marks to find Hidden Pairs?
Not necessarily, but the proof must account for every legal position of both digits. Complete candidates or digit filters make that verification much easier.
What to learn next
Move to Naked Triples and Hidden Triples to extend the reservation principle from two cells/digits to three.
The same framework later extends to Quads during the Expansion phase.