Hidden Pairs in Sudoku
A hidden pair is two digits that can only appear in the same two cells of a unit — even though those cells also carry other candidates. When you find one, every other candidate can be wiped from those two cells, leaving just the pair. It's the trickiest of the pair techniques to spot, and one of the most satisfying.
Where a naked pair announces itself (two cells, two candidates, identical), a hidden pair is camouflaged. The two cells might show three, four, or five candidates each. The pair is "hidden" inside that clutter, and you only find it by tracking where two specific digits are allowed to go.
A worked example
- the unit in focus
- the pattern
- a placement
- an elimination
Scan this column for the digits 1 and 3. Both of them can only go in the same two cells (amber) — nowhere else in the column accepts a 1 or a 3. That's the hidden pair. Now reason it through: those two cells must hold the 1 and the 3 between them, so they can't hold anything else. Every other candidate in them — here an 8 in each — is removed (red). The two cells collapse to a clean {1, 3}, which is now a naked pair as well.
Notice the direction of the elimination. A naked pair clears candidates from the rest of the unit. A hidden pair clears candidates from the pair cells themselves. Same family of logic, opposite target.
How to find a hidden pair
Go through a unit two digits at a time, or watch for digits that are scarce. For each pair of digits, count the cells in the unit where each one can go. If two different digits are both restricted to the same two cells, you've found a hidden pair — regardless of what other candidates those cells contain.
In practice the shortcut is to look for digits that appear as candidates only twice in a unit. If two such digits share the same two cells, the pattern is there. It takes more searching than a naked pair, which is exactly why beginners miss it.
Why it's worth the effort
Hidden pairs often appear on hard boards precisely where no other move is available. Because the elimination cleans up the pair cells, it frequently turns one of them into a bivalue cell that feeds a naked pair, an pointing pair, or a chain elsewhere. One hidden pair can unstick an entire region.
The same idea scales: a hidden triple is three digits confined to three cells. It's rarer and harder to see, but the logic is identical — find the digits that have nowhere else to go.
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