Hidden Pair
Two digits fit only the same two cells in a unit.
A hidden pair in Sudoku is a set of two candidate digits that can legally go in only two cells of a single row, column or box, even though those two cells still show other candidates alongside them. Because the pair is buried behind those extra digits, you have to hunt for it by tracking where each digit can go rather than by reading the cells directly. Once you catch a hidden pair sudoku situation, you can strip every other candidate from the two cells, because those two digits are now locked to that pair of cells.
Worked example
Box 1 already holds the givens 1, 2, 3, 4 and 5, and its top-row empties R1C1, R1C2 and R1C3 each read 6 or 7. But column 3 carries an 8 at R4C3 and a 9 at R5C3, which bar both 8 and 9 from R1C3 — so within box 1 the digits 8 and 9 can only land in R1C1 and R1C2, making {8,9} a hidden pair disguised behind the 6/7 candidates. Since a cell that must hold 8 or 9 cannot also be 6 or 7, you delete 6 and 7 from R1C1 and R1C2, leaving them as {8,9} and pushing the 6 and 7 onto R1C3.
When to use it
Reach for a hidden pair once simple scanning and naked singles have stalled and a unit still has cells crowded with three or more candidates each. Spot it by counting where each unsolved digit can go inside one row, column or box: if two digits are each restricted to the very same two cells — as 8 and 9 are pinned to R1C1 and R1C2 here — that is a hidden pair, even when those cells also list other candidates. It is the inward mirror of a naked pair, so if reading the cells shows nothing, try reading the digits instead.
How to use it
- Track two digits. In one unit, find two digits that can each go in only the same two cells.
- Confirm the hidden pair. Those two digits must fill those two cells, even if the cells currently list extra candidates.
- Clean the cells. Delete every other candidate from the two cells, leaving just the hidden pair.
Frequently asked questions
What is a hidden pair in Sudoku?
A hidden pair is two candidate digits that can legally appear in only two cells of one unit, yet those two cells also carry other candidates that hide the pair from view. In the board above, 8 and 9 can go nowhere in box 1 except R1C1 and R1C2, so {8,9} is a hidden pair even though both cells still list 6 and 7. Once you have found it, you delete every other candidate from the two cells, here removing 6 and 7.
How do I spot a hidden pair?
Instead of scanning cells for their candidates, scan digits: for each unsolved value in a unit, note which cells could still hold it. When two different digits map to exactly the same two cells, that is a hidden pair. In box 1, 8 is possible only in R1C1/R1C2 because R4C3 already uses an 8 in column 3, and 9 is possible only in R1C1/R1C2 because the 9 at R5C3 blocks R1C3 — the two lists coincide, so the pair is exposed.
What is the difference between a hidden pair and a naked pair?
A naked pair is two cells that show only those two candidates between them; you read it straight off the grid and remove those digits from the rest of the unit. A hidden pair works the other way: the two cells still display extra candidates (6 and 7 in R1C1 and R1C2), and the elimination strips those extras from the pair itself, not from other cells. Both lock the same two digits to the same two cells — the hidden version is just harder to see.