Full House

A Full House (also called the Last Free Cell or Last Digit) is the simplest move in all of Sudoku: a unit — a row, column or box — with just one empty cell left. Whatever digit is missing has to go there. It sounds too obvious to name, but spotting full houses quickly keeps you moving and often triggers a cascade of them.

How it works

Every unit holds the digits 1–9 exactly once. So if eight cells of a unit are filled, the ninth is forced — it's simply the one number not yet present. No candidates, no reasoning: just read off what's missing.

1 2 3 4 5 6 7 8 9

Eight cells hold 1–8, so the last (amber) can only be the 9. That's a full house.

When to look for it

Full houses appear constantly in the late stages of a solve, and every placement you make brings more units close to complete. The habit worth building: after filling any cell, glance along its row, column and box to see if you've just left one of them with a single gap.

Full house vs naked single

They're cousins. A full house looks at a whole unit that's nearly full; a naked single looks at a single cell whose candidates have narrowed to one. Both place a digit for free — the full house is just the fastest of all to spot.


Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.