Naked Pair

The first technique to reach for when singles run out. Some Hard puzzles need it, and Expert puzzles always need it or one of its cousins.

What is a naked pair?

A naked pair is two cells in the same row, column or box that each have exactly the same two candidates and nothing else.

Those two numbers must go into those two cells, in some order. You don't know which is which yet, but you know that no other cell in that row, column or box can hold either number.

the pair the column they share candidates you can remove blue numbers: already filled in with the basics

Example from a real puzuru puzzle. Rows and columns are numbered 1 to 9 from the top left. Candidates are shown only for the column we are working in.

The example

In column 7, the cells R1C7 and R5C7 can each only be 5 or 9.

So 5 and 9 are used up by those two cells. Remove 5 and 9 from every other cell in column 7. Here that clears the red candidates in R3C7.

After a naked pair, look again for singles. Removing candidates often leaves a cell with one option, or a number with one place.

How to spot naked pairs

Fill in all candidates first. Naked pairs are almost impossible to see without notes.

Scan for cells with exactly two candidates. When two of them match and share a row, column or box, you have a pair.

If the two cells share both a box and a row (or column), you can remove the two numbers from both units.

Related: naked triples and hidden pairs

The same idea works with three cells and three numbers (a naked triple). Each cell doesn't need all three numbers, but together they may only contain those three.

A hidden pair is the mirror image: two numbers that can only go in the same two cells of a unit. Then you can remove every other candidate from those two cells.

Practice on Expert puzzles →

← Hidden Single　Next: Hidden Pair →

FAQ

What level needs naked pairs?

On puzuru, some Hard puzzles need it. Expert puzzles are checked to be unsolvable with singles alone, and solvable once you add pairs, triples and pointing.

Can a naked pair be in a box?

Yes. Two cells in the same 3x3 box with the same two candidates also form a naked pair, and you remove those numbers from the rest of the box.

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