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Sudoku techniques

Hidden pair

If two digits fit in only the same two cells of a unit, those cells hold them, and nothing else.

The idea

Take a unit and two digits it needs, say 4 and 9. If each of them can only go in the same two cells, those two cells must be 4 and 9 in some order.

So any other candidates in those two cells can be crossed out. The pair was there all along, hidden among the other notes.

How to spot it

  • Count, for each digit a unit needs, how many cells can hold it. Two digits with the same two cells make a hidden pair.
  • It often appears in a box where most digits are placed.

Worked example

Hidden pair on a real puzzle

From our hard puzzle #34 (30 clues), after 16 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out.

Before. Hidden pair: in column 6, 4 and 5 fit only in the marked cells. So those cells can't hold any other digit.
After. Remove 6 from row 5, column 6. Remove 7 from row 6, column 6.

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 hidden pair at least once:

  • 102 of our 1000 hard puzzles
  • 314 of our 1000 expert puzzles
  • 230 of our 1000 master puzzles

The easiest level that can need it is hard Sudoku.