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Sudoku Clan › Sudoku techniques › Naked pair

Naked pair in Sudoku

  • Advanced
  • Needed from Expert puzzles
  • 3 points in Duel

Also called a conjugate pair.

Two cells in the same row, column or box that can each hold only the same two digits form a naked pair. Those two digits are used up, so they leave every other cell of the unit.

How it works

Say two cells in a row can each be only 1 or 3. If one is 1 the other is 3, and the other way round. You cannot tell yet which is which, but you do know that both digits will be used by these two cells. No other cell of the row can be 1 or 3, so you can erase those notes.

If the two cells also share a box, the pair clears the rest of that box as well as the line.

  1. Fill in pencil marks for a unit.
  2. Look for two cells whose notes are the same two digits and nothing else.
  3. Remove both digits from every other cell of the unit.
  4. If the pair shares a second unit, clear that one too.

A real example

1122334455667788995214894731879636734671346892147579138937865171324287196435365369438278917841397385289628834734214765967925678134131465346927827
Naked pair. In column 7, cells R3C7 and R8C7 can only hold 1 and 3, so those digits leave the other cells of column 7. That leaves a simple move: in row 1, 1 fits in only one cell: row 1, column 3.Blue: the pattern. Red: candidates that are removed. R3C7 means row 3, column 7.

The two blue cells hold the same two candidates. Any red candidate in the same unit is one of those digits and is removed.

How to spot them

A naked pair is the easiest pattern to see once notes are on the board: look for cells with exactly two notes, then check whether another cell in the same row, column or box has the same two. In Sudoku Clan, turn on Notes and fill in the candidates, and matching cells are easy to compare.

Common mistakes

  • Treating cells with three notes as a pair. Both cells must have exactly the same two candidates. If two digits are confined to two cells that also have other notes, that is a hidden pair, and it works differently.
  • Pairing cells that do not share a unit. Two matching cells in different rows, columns and boxes tell you nothing.
  • Working from incomplete notes. A missed candidate makes a false pair.

Questions

What is a naked pair in Sudoku?

Two cells in the same row, column or box that both have the same two candidates and no others. Those two digits can be removed from all other cells in that unit.

Do naked pairs need pencil marks?

In practice, yes. Very experienced solvers see some pairs without notes, but writing candidates is the reliable way to find them.

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