Proven Sudoku
Full House
Also called Last Digit in a house, Last Cell, Single in a unit, Full Unit.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A row, column or box has just one empty square left. Only one digit is missing, so that digit goes there.
The exact rule, for stronger players
The rule, stated exactly: For a house H, if exactly one cell of H is unsolved, that cell takes the single digit of 1..9 not already placed in H.
What it removes: Place the missing digit in the single empty cell of the house.
Why it works: A house contains each of the nine digits exactly once. If eight are placed, the ninth digit has only one remaining cell, and that cell has only one remaining digit. No candidate bookkeeping is required.
Worked examples
These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.
Related singles
- Hidden SingleLook at one digit in one row, column or box.
- Naked SingleA square has only one digit left that fits.
How often does it come up?
Our rough estimate: appears in essentially every solved grid, most often near the end of a solve. It is the cheapest deduction available.