Hidden pair: two digits with only two homes

What is a hidden pair?

A hidden pair is two digits that, inside one unit (a row, a column or a 3×3 box), appear as candidates in exactly the same two cells and nowhere else in that unit. The two cells may also contain other candidates, which is why the pair is called hidden.

Once you find it, you can remove every other candidate from those two cells. They are left holding only the two digits of the pair, which often starts a chain of new singles around them.

Why it works

Every unit must contain each digit exactly once. Suppose that in a box the digits 1 and 3 can only go in two cells, A and B. The 1 must land in A or B, and so must the 3. Two digits need two cells, and only these two cells are available, so A and B are fully taken by 1 and 3. Neither cell has room left for any other digit, so their extra candidates are impossible.

How to find hidden pairs

Work digit by digit inside one unit. For each digit that is not yet placed, count how many cells can still hold it. You are looking for digits that have exactly two possible cells.

When you find two such digits, compare their positions. If both digits are limited to the same two cells, you have a hidden pair. If the positions differ, even by one cell, there is no pair. Boxes are a good place to start, because pencil marks in a box are easy to scan at a glance.

A useful shortcut: if a unit has a cell with many candidates and you suspect it is crowded with digits that belong elsewhere, count how often each of its candidates appears in the unit. Rare digits are pair material.

A worked example

In the example board, no singles are left. Look at box 4, the middle-left box. Its empty cells are R4C2 (row 4, column 2) with candidates {1,3,5}, R5C1 with {5,6,8}, R5C2 with {5,6}, R6C1 with {6,8} and R6C3 with {1,3}.

The digit 1 can only go in R4C2 or R6C3, and the digit 3 can only go in the same two cells. These two highlighted cells form a hidden pair {1,3}. R6C3 already has nothing else, but R4C2 also lists a 5, and that 5 can now be removed. R4C2 becomes {1,3}.

Now look at row 4. Before the pair, the 5 could go in R4C2 or R4C8. With R4C2 ruled out, R4C8 is the only cell in row 4 that can take a 5. That is a hidden single, shown in gold: R4C8 is 5.

Common mistakes

Counting positions across different units. The two digits must be limited to the same two cells inside one unit. A digit that has two spots in a row but more spots in the box is only a pair candidate in the row.

Accepting digits that share only one cell. If 1 fits in cells A and B while 3 fits in cells A and C, there is no hidden pair. The two digits need identical positions.

Removing the pair digits from other cells. A hidden pair removes the other candidates from its own two cells. It says nothing new about the rest of the unit, because the pair digits already appear nowhere else in it.

Hidden pairs and related techniques

Hidden and naked pairs are two views of the same situation. In a unit with some empty cells, a hidden pair of two digits always leaves a naked subset in the other empty cells, with the remaining digits. Some players find the naked version easier to see in a row with few empty cells, and the hidden version easier in a box full of candidates. The same idea extends to hidden triples and quads.

The hidden pair is also a close cousin of the hidden single: instead of one digit with one home, it is two digits with two homes. On Quietdoku, pairs are what separates Hard puzzles from Medium ones, and a hint will name the technique when it is the next logical step.