Hidden single
A digit that has only one place left in a row, column or box goes there, whatever else that cell could hold.
The idea
Every row, column and box needs each digit from 1 to 9 exactly once. Pick a digit and a unit (a row, column or box) that still lacks it. Look at the empty cells of that unit and cross out every cell that already sees that digit in its row, column or box.
If only one cell is left, the digit must go there. The cell may still have other candidates; it doesn't matter, because the unit has nowhere else for the digit. That is why it is called hidden: the cell doesn't look solved until you look at the digit.
How to spot it
- Scan one digit at a time across the board, starting with digits that are already placed many times.
- Boxes are the easiest units to check: three placed copies of a digit in the neighbouring boxes often leave a single cell.
- Then check rows and columns that are nearly full.
Worked example
Hidden single on a real puzzle
From our hard puzzle #146 (26 clues), after 5 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out, green is the digit it places.
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 single at least once:
- 1000 of our 1000 easy puzzles
- 1000 of our 1000 medium puzzles
- 1000 of our 1000 hard puzzles
- 1000 of our 1000 expert puzzles
- 1000 of our 1000 master puzzles
The easiest level that can need it is easy Sudoku.