If two digits can only be placed in the same two cells of a box, row or column, those two cells hold them — so every other candidate in those cells can be crossed out.
How to spot it
A hidden pair is found by counting, not by looking. Pick a house and ask, digit by digit, where can this digit still go? You are hunting for two digits whose answer is the same two cells.
Choose a house and read its empty cells
Boxes are the easiest place to start — nine cells, all in view. This box has four empty cells and is missing the digits 1, 2, 4 and 7.
Count the homes of each missing digit
1 and 2 can go in three cells each. But 4 and 7 are each pencilled into only two cells — and they are the same two cells.
That is the whole pattern. Two digits, two cells, no other homes in the house.
Claim the cells, then clear them out
One of those cells takes the 4 and the other takes the 7 — you do not yet know which way round, and it does not matter. What matters is that nothing else fits.
The 2 pencilled into both cells is dead and can be struck out.
Take the win, then look again
Both cells are now reduced to 47. No digit was placed — but the box has one fewer place for a 2, which is often enough to make a single appear somewhere else.
If a hidden pair fires and nothing else moves, re-scan the same house before looking elsewhere. A house tight enough to hide a pair is usually hiding a second deduction too.
Why it works
Every house holds each of the nine digits exactly once. Suppose you tried to put the 2 into the first of our two cells. The 4 and the 7 would then both need the second cell — and one cell cannot hold two digits.
This is why a hidden pair is safe to apply the moment you see it: the deduction does not depend on how the rest of the grid resolves.
Naked or hidden?
The two techniques are the same fact read from opposite ends. A naked pair starts from cells that hold only two candidates. A hidden pair starts from digits that have only two homes. In our box, both are present — and both remove exactly the same candidates.
Found by counting digits. The pair is buried under a 2 in both cells — that is what makes it hidden.
Found by reading cells. Two cells show nothing but 1 and 2, so the 2 elsewhere in the box has to go.
Common mistakes
- Missing a third home. Check every empty cell in the house, including ones you have already narrowed down to two or three candidates.
- Only scanning boxes. Hidden pairs in rows and columns fire just as often and are far easier to overlook, because the cells sit far apart.
- Eliminating in the wrong place. The eliminations happen inside the pair's own two cells, not in the rest of the house. That is the opposite of a naked pair.
- Expecting a placement. Nothing gets written in. If you were hoping to fill a cell, look for a hidden single instead.
The pattern scales. n digits confined to n cells always own those cells, for any n from 2 to 4. The counting gets harder because the digits no longer need to appear in every cell of the set.
Two digits, two cells. Both digits usually appear in both cells.
Three digits, three cells. Each digit needs only two of the three cells.
Rare, and easier to find as a naked pair among the five remaining cells.
Which two digits form a hidden pair in this box?
Count the homes of each digit before you answer.
Итог
- Ищите
- Two digits whose only remaining homes in a house are the same two cells.
- Область
- Any box, row or column.
- Результат
- Every other candidate in those two cells is eliminated. Nothing is placed.
- Признак
- A house with few empty cells where one digit keeps showing up in only two of them.
- Если не сработало
- Try the naked pair, or size up to a hidden triple.