Naked Pair (Obvious Pair)

Used in Classic 9×9 Sudoku, 6×6 Sudoku, Difference Sudoku, Irregular 6×6 Sudoku, Relational 6×6 Sudoku, Odd/Even Sudoku, Windowed Sudoku, Killer Sudoku, Skyscraper Sudoku 5×5 and Triangle Sudoku.

A naked pair is two cells in the same row, column or box that have the same two candidates, and nothing else. You don't know yet which cell gets which digit, but you know the two digits are used up between them. So no other cell in that house can hold either one.

An example

A classic 9×9 board with candidates. In the rightmost column, two cells with only 7 and 9 as candidates are ringed, and 7 and 9 are struck out of the other empty cells in the column.

Look at the rightmost column. The cells in the fifth and seventh rows both have exactly two candidates: 7 and 9.

One of them will be 7 and the other 9. Either way, the column's 7 and its 9 are in those two cells. That means no other cell in the column can be 7 or 9, and they can be struck out:

  • The top cell goes from 4, 5, 7, 8, 9 to 4, 5, 8.
  • The second goes from 4, 5, 6, 7, 9 to 4, 5, 6.
  • The eighth goes from 6, 7, 8 to 6, 8.
  • The bottom cell goes from 6, 8, 9 to 6, 8.

Notice what that leaves at the bottom of the column: two cells with only 6 and 8. That is a new naked pair, and it frees up more of the column and the bottom-right box. Pairs often come in chains like this.

How to look for them

  • Scan for cells with two candidates. In a house that still has many empty cells, look for two cells showing the same two digits.
  • Check every house the pair shares. The two cells in the example are in the same column but different boxes, so the pair only works in the column. If both cells sit in one box and one row, the pair clears both.
  • The pair doesn't place anything by itself. Its value is in what it removes. Look at the cells that lost candidates for a new single.

Why it works

Each of the two cells must hold one of the two digits, and they can't hold the same one, because they share a house. So between them they use both. The rest of the house has to get its 7 and its 9 from somewhere, and there is nowhere left.

The same reasoning extends to three cells and three digits. That is a naked triple.

Where it fits

The app's hints call this an "Obvious pair". It is the first technique past the singles, and a puzzle that needs it is graded Medium. The mirror image, where two digits can only go in the same two cells, is a hidden pair, and it is harder to spot.

More techniques

  • Naked Single (Obvious Single): A cell with only one candidate left must hold it. The first thing to look for in any sudoku, and how to spot it quickly.
  • Hidden Single: When a digit fits in only one cell of a row, column or box, it goes there, even if that cell has other candidates.
  • Naked Triple (Obvious Triple): Three cells in a house whose candidates use only three digits take all three, even when no cell shows all of them.
  • Hidden Pair: Two digits that fit in only the same two cells of a house claim those cells, so every other candidate there can go.
  • Hidden Triple: Three digits confined to the same three cells of a house claim them, clearing out every other candidate in those cells.
  • Pointing Pairs and Triples: A digit confined to one line inside a box (or to one box along a line) can be removed from the rest of that line or box.