Naked pairs in Sudoku

A naked pair is one of the first techniques to learn once simple scanning stops working. It lets you remove candidates without placing a single number.

The idea

Look at one row, column or box. If exactly two empty squares in it have the same two candidates and nothing else, say both can only be 3 or 8, then those squares must contain a 3 and an 8 between them. Which is which does not matter yet. What matters is that 3 and 8 are used up, so no other square in that row, column or box can be a 3 or an 8.

A worked example

Suppose a row has these candidates in its empty squares: A = {3, 8}, B = {3, 8}, C = {3, 5, 8}, D = {2, 3, 8, 9}. Squares A and B are a naked pair. Remove 3 and 8 from C and D, leaving C = {5} and D = {2, 9}. C is now solved as a 5, and you have made progress without guessing.

How to find them

• Turn on Notes and fill in the candidates for a crowded row, column or box.
• Scan for two squares showing the identical pair of numbers.
• Check that the pair sits in the same unit. A pair that shares a row also removes candidates only along that row, unless the two squares are also in the same box, in which case the box benefits too.

Common mistakes

• Treating two squares with similar candidates as a pair. Both must contain exactly the same two numbers.
• Removing the pair’s numbers from the pair itself.
• Starting from notes that contain a mistake. If a result looks impossible, recheck your notes.

Going further

The same logic extends to naked triples and quads, and to “hidden” pairs, where two numbers appear in only two squares of a unit. Our next technique, pointing pairs, works across boxes and lines.