Naked pairs

When two cells in a row, column or box share the same two candidates and nothing else, those two digits are spoken for. Everything else in the house can drop them.

What is a naked pair?

Say two cells in the same house can each only be 3 or 8. One of them will be 3 and the other 8; we just do not know which way round yet. Either way, no other cell in that house can be 3 or 8. Erasing those two candidates from the rest of the house often leaves a single behind.

Example

R1C1 and R1C2 hold 3 and 8, so the rest of row 1 cannot.

Row 1 is missing 3, 6, 8 and 9. R1C1 and R1C2 both see the 6 in R2C1 and the 9 in R3C2, so each can only be 3 or 8: a naked pair.

That means 3 and 8 can be erased from the other empty cells of row 1. R1C5 drops from {3, 6, 8} to just 6, a naked single. R1C7 drops from {3, 6, 8, 9} to {6, 9}, and once R1C5 is filled it becomes 9.

How to find naked pairs

  1. Fill in pencil marks for a house that has four or five empty cells.
  2. Look for two cells with exactly two candidates each, the same two.
  3. Erase those two digits from every other cell in the house.
  4. If the pair also sits in one box, erase them from the rest of the box too.

Naked triples

The same idea works with three cells and three digits. If three cells in a house only hold candidates from {2, 5, 7}, those digits belong to those cells, even if each cell has only two of them, like {2, 5}, {5, 7} and {2, 7}.

Tip: naked pairs only show up when your pencil marks are complete and up to date. A missing candidate can make a fake pair, so check before you erase.

Where it fits

Naked pairs come after singles and are the first technique that needs pencil marks. Next, learn pointing pairs, which also clears candidates but across houses.

Practise on your phone

Our free Sudoku app has hints that point out the technique you can use next, with the cells highlighted. It plays offline.

Get it on Google Play