Hidden pairs

A hidden pair is two digits that can only go in the same two cells of a row, column or box. Those two cells may show other candidates too, which is why the pair is “hidden”. But since the two digits must go somewhere in the unit, and only these two cells can take them, the two cells must hold those two digits. Every other candidate in those two cells can be removed.

Hidden pairs are rarer and harder to see than naked pairs. In our medium bank only a small share of puzzles needs one, but when a puzzle does, nothing else from the medium toolbox will break it.

Why it works

Each digit must appear once in every unit. If the 3 and the 8 in a box can each go only in cells A and B, then one of A and B is 3 and the other is 8. There is no room left in A or B for any other digit, so their extra candidates are impossible. Removing them often turns one of the two cells, or a neighbour, into a single.

The hidden pair is the mirror image of the naked pair. A naked pair restricts cells to digits; a hidden pair restricts digits to cells. In fact, in any unit a hidden pair always sits alongside a naked group in the remaining cells, but in a nine-cell unit the hidden pair is usually much easier to state.

How to spot it

• Work digit by digit. In one unit, list where each missing digit can go. You are looking for two digits with the same two possible cells.
• Pay attention to digits that appear in only two cells of a unit: only they can form a hidden pair.
• Boxes are the best place to look, because their cells are close together and easy to compare.
• Once found, cross out every other candidate in the two cells, then look for singles that follow.

Common mistakes

• Choosing digits that also appear elsewhere in the unit. Both digits must be confined to the same two cells and nowhere else in that unit.
• Removing the pair digits from other cells instead of removing the other candidates from the pair cells. A hidden pair cleans up its own two cells.
• Mixing units: the two digits must be confined to the two cells within one specific row, column or box.

Related techniques

With three digits confined to three cells you have a hidden triple, which our grader counts as a hard technique. Hidden singles are the one-digit version: a digit confined to one cell. If you can find hidden singles quickly by scanning digit by digit, you already have the habit that finds hidden pairs.

Stuck on a real puzzle? The sudoku solver names every technique it uses, step by step, and the hint button in the game teaches the same way.

How to practise

Play the three practice puzzles below in order. Each one reaches a point where hidden pairs are the only way forward with the medium-level toolbox, so if you get stuck, that is the moment to look for the pattern. Try first without help. If you still cannot see a move, press Hint once: the first level names the technique, the second shows where to look, and only the third makes the move for you. After you finish, play a few medium puzzles without hints to make the habit stick.