Naked pairs

A naked pair is two cells in the same row, column or box that have exactly the same two candidates, and no others. If two cells can only be 2 or 7, then one of them is 2 and the other is 7. You do not know which is which yet, but you do know that no other cell in that unit can be 2 or 7, so those candidates can be removed from the rest of the unit.

Naked pairs are one of the first pencil-mark techniques most solvers learn. They are one of the four techniques that define our medium level, and they keep turning up in hard and expert puzzles too.

Why it works

Think of the two cells as a closed system. Each must hold one of the two digits, and they cannot hold the same digit because they share a unit. So between them they use up both digits. Every other cell in that unit is then left with one fewer or two fewer possibilities. Often the elimination leaves another cell with a single candidate, or creates a hidden single for a third digit.

If the two cells share more than one unit (for example, the same row and the same box), the pair works in both units at once. Those are the most productive naked pairs to find.

How to spot it

• You need pencil marks. Fill in the candidates for a whole row, column or box, then look for two cells with identical two-digit notes.
• Start with cells that have only two candidates: they are the only ones that can form a naked pair.
• Check each unit the two cells share. Two cells in the same row and box clear candidates from both.
• After removing the candidates, look again for singles in that unit before moving on.

Common mistakes

• Using cells with different pairs. {2,7} and {2,8} are not a naked pair; both cells must have exactly the same two candidates.
• Applying the pair to the wrong unit. The eliminations only apply to cells in a unit that contains both cells of the pair.
• Removing the digits from the pair itself. The two cells keep their candidates; only the other cells in the unit lose them.
• Working from incomplete notes. A cell that seems to have two candidates may have a third you forgot to note, which breaks the pair.

Related techniques

The same logic extends to three cells: a naked triple is three cells in a unit whose candidates, together, are only three digits, such as {1,4}, {4,9} and {1,9}. Each cell need not have all three. Naked triples appear in our hard puzzles. The mirror-image technique is the hidden pair, where two digits are confined to two cells.

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 naked 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.