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Sudoku techniques

Pointing pairs

If a digit inside a box can only go on one row or column, it can't go anywhere else on that line.

The idea

Look at one box and one digit it still needs. If every cell in the box that can hold the digit lies on the same row (or the same column), the digit will end up on that line inside the box.

The line can hold the digit only once, so every other cell of that line, outside the box, can't be that digit. You cross it out of their notes. With two cells it is called a pointing pair, with three a pointing triple.

How to spot it

  • Keep notes, then look box by box for a digit whose notes sit on one row or one column.
  • Follow that line out of the box and remove the digit from it.
  • This often unlocks a hidden single elsewhere on the line.

Worked example

Pointing pairs on a real puzzle

From our hard puzzle #18 (26 clues), after 22 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out.

Before. In the top-middle box, the 4 can only go on row 2 (the marked cells). So no other cell on row 2 can be 4.
After. Remove 4 from row 2, column 2; row 2, column 9.

Play this puzzle

How often our puzzles need it

Our solver works like a careful player: it always uses the easiest technique that still makes progress. Counting the puzzles where it had to use pointing pairs at least once:

  • 936 of our 1000 hard puzzles
  • 846 of our 1000 expert puzzles
  • 729 of our 1000 master puzzles

The easiest level that can need it is hard Sudoku.