Naked pairs

What it is

A naked pair is two cells, in the same row, column or box, that both have exactly the same two candidates and nothing else. For example, two cells in a row that each have only 2 and 7 in their notes.

Between them, those two cells must hold the 2 and the 7. One gets the 2 and the other gets the 7. You may not know which way round yet, but you do know that no other cell in that row can be 2 or 7. So you can remove 2 and 7 from the notes of every other cell in the row.

It is called “naked” because the pair is out in the open: two cells showing the same two notes.

How to spot it

You need full pencil marks for this. Look for cells with exactly two candidates. When you find one, scan its row, column and box for another cell with the very same two candidates.

Cells with only two candidates are worth noticing in general. Some players lightly highlight them so pairs stand out.

A worked example

Look at row 8. After filling in your notes, you see:

• Row 8, column 2 has candidates 2 and 7.
• Row 8, column 6 has candidates 2 and 7.

These two cells form a naked pair in row 8. Whichever way round it turns out, the 2 and the 7 for row 8 are both used up by these two cells.

Now look at the other empty cells in row 8:

• Row 8, column 4 has candidates 2, 5 and 7. Remove 2 and 7, leaving only 5.
• Row 8, column 9 has candidates 1, 2 and 9. Remove 2, leaving 1 and 9.

Row 8, column 4 is now a naked single, so you can place the 5.

Pairs in boxes, and pairs that do double duty

Pairs work in boxes too. If two cells in box 7 both have only 3 and 8, every other cell in box 7 loses 3 and 8.

Sometimes a pair is in the same row (or column) and the same box at once. In that case you can remove the two digits from the rest of the row and from the rest of the box. That is a powerful move, so whenever you find a pair, check whether its two cells share a box as well as a line.

A common mistake

The pair must be exactly two candidates in each cell, and the same two. A cell with 2, 7 and a cell with 2, 7, 9 do not form a naked pair. The second cell might be the 9, which would leave the first cell free to be either 2 or 7.

Also, the two cells must share a row, column or box. Two cells with 2 and 7 at opposite ends of the grid tell you nothing about each other.

Finally, make sure your notes are accurate before trusting a pair. A stale candidate can make a pair look real when it is not, or hide one that is there.

When you will need it

Naked pairs are part of the Medium toolkit on sudoku.ie, along with pointing, claiming and hidden pairs. You will meet them on Tuesday, Wednesday and Sunday. Once pairs feel natural, the jump to naked triples is a small one.