A hidden pair occurs when two numbers can go in exactly the same two cells within one Sudoku unit: a row, column, or 3×3 box. The cells may contain other candidates, but once the pair is confirmed, remove every candidate except those two numbers from both cells.
The quickest way to find hidden pairs is to track where each number can go within a unit. Rather than comparing every pair of cells, look for two numbers that are each restricted to the same two positions.
What makes a hidden pair?
A valid hidden pair has four parts:
- Two numbers: for example, 4 and 8.
- Two cells: both numbers can go in the same two cells.
- One unit: the cells share a row, column, or 3×3 box.
- No other locations: each number appears as a candidate in exactly those two cells within the unit.
For example, suppose 4 can go only in r3c2 and r3c7 of a row, and 8 can go only in those same two cells. Even if the cells currently contain 2, 4, 6, 8 and 1, 4, 7, 8, the other candidates can be removed. Those two cells must contain 4 and 8 in some order.
The pair is “hidden” because the two numbers are mixed in with other candidates. You see the pattern only after checking candidate positions across the whole unit.
Scan candidate positions instead of comparing every cell
Use this position-first scan when a row, column, or box looks promising:
- Choose one unit. Start with a unit that has several unsolved cells or recently updated notes.
- Map one number. Mark every cell in the unit where that number can still go.
- Note numbers with two positions. These are the candidates worth checking first.
- Compare the positions. If another number appears in exactly the same two cells, you have a hidden pair.
- Remove the extras. Keep only the two pair numbers in those two cells.
This is more efficient than selecting two cells and comparing all their candidates. It also helps prevent false patterns because you check each number’s complete distribution in the unit.
Prioritize units where several candidates are limited to two or three locations, especially after a placement changes the notes. Accurate Sudoku pencil marks are essential. A missing or incorrect note can create a hidden pair that is not logically valid.
A worked hidden-pair example
Consider these candidate lists in one row:
| Cell | Candidates |
|---|---|
| r5c1 | 1, 3 |
| r5c2 | 2, 4, 7, 8 |
| r5c3 | 1, 5 |
| r5c4 | 3, 6 |
| r5c5 | 4, 8, 9 |
| r5c6 | 2, 5 |
| r5c7 | 6, 9 |
| r5c8 | 1, 7 |
| r5c9 | 2, 7 |
Now map the positions of 4 and 8:
- 4 appears only in r5c2 and r5c5.
- 8 appears only in r5c2 and r5c5.
Because both numbers are confined to exactly the same two cells, 4 and 8 form a hidden pair. Remove the other candidates from those cells:
- r5c2 changes from 2, 4, 7, 8 to 4, 8.
- r5c5 changes from 4, 8, 9 to 4, 8.
The two cells do not need to be next to each other. They only need to belong to the same unit. After the cleanup, they form a naked pair, so rescan the row and the columns and boxes that intersect these cells.
How to confirm the pattern
Matching positions are necessary, but you still need to check the entire unit before eliminating anything. If either number appears in a third cell, it is not a hidden pair. Likewise, if the two numbers use different pairs of cells, the pattern does not qualify.
For example, if 4 appears in r5c2, r5c5, and r5c7 while 8 appears only in r5c2 and r5c5, 4 and 8 do not form a hidden pair. The first number is not restricted to the same two cells.
Another false pattern occurs when several numbers share the same two positions. If 4, 7, and 8 all appear only in r5c2 and r5c5, the notes alone do not identify a particular two-number hidden pair. More information is needed before removing any of those candidates.
What to remove after finding the pair
Once the pattern is confirmed, remove every other candidate from the two identified cells. Do not remove the pair numbers from other cells in the unit. Hidden-pair elimination affects only the two cells that contain the pair.
For example, if two cells contain 2, 5, 7 and 1, 5, 8, they cannot form a hidden pair of 5 and 8: 8 is not a candidate in the first cell. If your notes do not show both pair numbers in both cells, recheck the candidate map before making the deduction.
After the cleanup, the two cells contain exactly the same two candidates and therefore form a naked pair. Rescan their unit and the intersecting units. The elimination may reveal a single or another useful deduction.
Hidden pairs versus naked pairs
| Technique | What you notice first | What you eliminate |
|---|---|---|
| Hidden pair | Two numbers are restricted to the same two cells. | Other candidates from those two cells. |
| Naked pair | Two cells contain only the same two candidates. | Those two numbers from the rest of the unit. |
A hidden pair can be hard to see because its cells may contain three or more candidates before the cleanup. A naked pair is visible directly in the cell notes. The terms describe how you discover the pattern: hidden pairs are found by scanning numbers, while naked pairs are found by scanning cells.
Hidden pairs apply independently within rows, columns, and 3×3 boxes. The cells do not have to be adjacent.
Using notes and checking tools without losing the logic
In an online Sudoku game, select one unit and use notes to map where a chosen number can go. Compare that position set with other candidates restricted to two cells. Apply only the eliminations supported by the complete unit.
Hints or mistake checking can serve as optional safeguards, but they should not replace the candidate-position check. If a hidden-pair deduction creates an impossible cell or duplicate number, pause and inspect the notes in the relevant row, column, and box. Common causes include a missed candidate, an outdated note, or a number that actually appears in a third cell.
For practice, choose one unit, map the possible locations of each number, and look for matching two-cell patterns. Repeat the scan after a placement changes several notes.
A compact hidden-pair checklist
- Choose one row, column, or 3×3 box.
- Map the candidate positions for each number.
- Find two numbers that each appear in exactly two cells.
- Confirm that both numbers use the same two cells and nowhere else in the unit.
- Check that your notes are complete and accurate.
- Remove every other candidate from those two cells only.
- Rescan the affected unit and the intersecting units.
Frequently Asked Questions
How many cells and numbers are involved in a hidden pair?
Exactly two numbers and two cells within one row, column, or 3×3 box. Each number must appear as a candidate in exactly those same two cells.
Can the two cells contain other candidates first?
Yes. That is what makes the pair hidden. After confirming it, remove every candidate other than the two pair numbers from both cells.
What if the two numbers appear in three cells?
They do not form a hidden pair. Each number must be limited to the same two cells within the unit.
Does a hidden pair have to use neighboring cells?
No. The cells can be separated. They only need to share the same row, column, or 3×3 box.
Find hidden pairs by tracking numbers, not by comparing every cell. When two candidates share exactly the same two positions in one unit, verify the full candidate map, restrict those cells to the pair, and then rescan the surrounding units.
Accurate notes are what make the technique reliable. Recheck them whenever a placement changes the grid or a supposed hidden pair produces a contradiction.
