Hidden Pairs in Sudoku

What Is a Hidden Pair?

A hidden pair occurs when two candidate numbers appear in only two cells within a row, column, or 3×3 box — and nowhere else in that group. Even though those two cells may have other candidates as well, you know the pair must occupy them. Therefore you can remove all other candidates from those two cells.

The pair is "hidden" because the cells do not look special at first glance — they may have three, four, or five candidates each. The key insight is that the two paired numbers are exclusive to those two positions in the group.

Hidden Pairs vs. Naked Pairs

A naked pair is easy to see: two cells each contain exactly the same two candidates and nothing else. The pair is "naked" — fully visible.

A hidden pair is the reverse perspective. Instead of looking at cells and seeing matching candidates, you look at numbers and see that two of them can only go in two cells. The cells themselves may have additional candidates that disguise the pattern.

When you find a hidden pair and strip the extra candidates, you often reveal a naked pair — or even a naked single if one cell was reduced to one candidate.

How to Find Hidden Pairs

Step 1: Choose a row, column, or box. List the missing numbers and note which cells contain each number as a candidate.

Step 2: Look for two numbers that appear in exactly the same two cells and in no other cells in that group. Those two numbers form a hidden pair.

Step 3: Remove all other candidates from those two cells. The cells should now contain only the pair.

Step 4: Re-scan. The elimination often creates new singles or enables other techniques.

Worked Example

Consider Box 3 (rows 1–3, columns 7–9). After filling in pencil marks, the candidates in the empty cells are:

R1C7: {1, 3, 6, 9} — R1C8: {1, 6} — R2C7: {3, 4, 9} — R2C9: {4, 6, 9} — R3C8: {1, 3, 4} — R3C9: {3, 4}

Now check each missing number's distribution across these six cells. The number 6 appears in R1C7, R1C8, and R2C9. The number 9 appears in R1C7, R2C7, and R2C9. Not helpful yet — both appear in three cells.

But look at 1: it appears only in R1C7, R1C8, and R3C8. And look at... actually, let us check a cleaner pattern. Look at 6 and 9 together. Wait — let me recheck. Where does 6 appear? R1C7, R1C8, R2C9. Where does 9 appear? R1C7, R2C7, R2C9.

A better example: suppose in Row 5, the number 2 appears only in R5C3 and R5C7, and the number 8 also appears only in R5C3 and R5C7. That is a hidden pair for {2, 8}. Whatever other candidates R5C3 and R5C7 have, you can erase them — these cells will hold 2 and 8.

If R5C3 was {2, 5, 8} it becomes {2, 8}. If R5C7 was {2, 3, 8, 9} it becomes {2, 8}. Those are now a naked pair, and you can eliminate 2 and 8 from other cells in Row 5 if they appear elsewhere. (Though they should not, since we already established that 2 and 8 only appeared in these two cells in this row.)

Spotting Tips

Count candidate occurrences. For each group, tally how many cells contain each number. Numbers that appear in exactly two cells are your best candidates for a hidden pair. If two such numbers share the same two cells, you have found one.

Focus on rare numbers first. Numbers that appear as candidates in only 2 or 3 cells within a group are more likely to be part of a hidden pair than numbers appearing in 5 or 6 cells.

Check all three group types. A hidden pair in a box eliminates from the box. A hidden pair in a row eliminates from the row. Check both perspectives for the same cells.

Common Mistakes

The numbers appear in more than two cells. If number A appears in three cells within the group, it cannot form a hidden pair (though it might form a hidden triple with two other numbers).

The cells do not match. Both numbers must appear in exactly the same two cells. If number A is in cells 3 and 7, but number B is in cells 3 and 5, they are not a hidden pair.

Stripping from the wrong cells. You remove other candidates from the pair cells only. Other cells in the group keep their candidates unchanged.

Stale pencil marks. If your candidates have not been updated after recent placements, you may see false patterns. Always update first.

Confusing with hidden singles. A hidden single is one number in one cell. A hidden pair is two numbers in two cells. Related concepts but different scales.

Frequently Asked Questions