Naked pair: two cells, two digits, fewer candidates

What is a naked pair?

A naked pair is two cells in the same unit (a row, a column or a 3×3 box) that each have exactly the same two candidates and nothing else. For example, two cells in a row that can each only be 2 or 4.

When you find one, you can remove those two digits from every other cell in that unit. The pair itself does not tell you which cell gets which digit. It only tells you that the two digits are used up by those two cells.

Why it works

Take two cells in a row that both hold only {2,4}. Whatever happens, one of them will be 2 and the other will be 4, because each cell needs a digit and neither has any other option. That means both the 2 and the 4 of this row are already spoken for. No third cell in the row can be 2 or 4, or the row would end up with a duplicate.

If both cells also share a box, the same reasoning applies to the box, and you can clear the two digits from the rest of the box as well. A pair in the same row and box is a double win.

How to find naked pairs

Naked pairs only show up when you keep pencil marks, so fill in candidates first and keep them up to date after every placement. Then scan each unit for cells that have exactly two candidates. These bi-value cells are the only possible members of a naked pair.

For each bi-value cell, look along its row, its column and its box for another cell with the identical two candidates. A match in the same unit is a naked pair. Then check whether any other cell in that unit still contains one of the two digits. If none does, the pair is real but useless for now, so move on.

A good habit is to look at crowded units first. A row with only four or five empty cells has fewer combinations to compare, and pairs stand out quickly.

A worked example

In the example board, singles have run out: no cell has a single candidate and no digit has only one place in any unit. Look at row 5. Its empty cells are R5C1 (row 5, column 1) with candidates {4,6}, R5C2 with {3,6,8}, R5C3 with {2,4}, R5C7 with {2,4} and R5C9 with {3,6,8}.

R5C3 and R5C7, highlighted on the board, both contain only 2 and 4. They are a naked pair in row 5, so no other cell of row 5 can be 2 or 4. The only other cell in the row that still lists one of them is R5C1, which loses its 4.

That leaves R5C1 with a single candidate, 6, shown in gold. A naked pair did not place the digit directly, but it turned R5C1 into a naked single, and the puzzle is moving again. Note that R5C3 and R5C7 are in different boxes, so this pair only works along the row.

Common mistakes

Using cells that are not in the same unit. Two {2,4} cells in different rows, columns and boxes tell you nothing, because each could be 2 at the same time.

Counting a cell with three candidates. A cell with {2,4,7} next to a {2,4} cell is not a pair. It may belong to a naked triple, but on its own it does not lock the digits.

Eliminating from the pair cells themselves, or from units the two cells do not share. The removals apply only to the other cells of the shared row, column or box. Also make sure your pencil marks are current: a stale candidate can create a pair that does not really exist.

Naked pairs and related techniques

The mirror image of a naked pair is the hidden pair: two digits that can only go in the same two cells of a unit. Hidden pairs remove the other candidates from those two cells, while naked pairs remove the two digits from everything else. The same idea grows into naked triples and quads, where three or four cells share three or four digits between them.

On Quietdoku, naked pairs belong to Hard puzzles. Easy puzzles need only singles and Medium adds pencil marks and locked candidates, so if you can already spot pointing pairs, pairs are the natural next step. When you are stuck, a hint will point to the next logical step and name the technique it uses.