Full House
The last empty cell in a unit can only be one digit.
A Full House is the most basic move in Sudoku: whenever a single row, column or box has eight of its nine cells already filled, the last empty cell is forced to hold whichever digit that unit is still missing. Because only one number can possibly go there, the full house sudoku technique lets you place a digit instantly, with no candidate marking and no logic beyond simple counting. It is often called the 'last digit' or 'last in a unit', and it is the very first thing experienced solvers scan for on a fresh grid.
Worked example
Look at row 1 on this grid. Eight of its nine cells are already given: reading R1C1 to R1C9 they are 5, 3, 1, 9, _, 8, 7, 4, 2, leaving only R1C5 blank. Running through the placed digits — 1, 2, 3, 4, 5, 7, 8 and 9 — the single number the row has not yet used is 6. Since every unit must contain 1 through 9 exactly once, R1C5 can only be 6. You place the 6 straight away, with no pencil marks required.
When to use it
Check for a Full House first, before reaching for any harder technique, and re-check after every digit you write in — completing one cell often leaves a neighbouring row, column or box with just a single gap. To spot it, sweep your eyes for any unit that is almost full: a row, column or box showing exactly one empty cell. That lone square is always an instant, risk-free placement.
How to use it
- Find an almost-full unit. Look for a row, column, or 3×3 box with exactly eight digits already placed and a single empty cell.
- Find the missing digit. List the digits 1–9 and cross off the eight already present. Exactly one remains.
- Place it. Write the missing digit in the empty cell — it is the only value that keeps the unit valid.
Frequently asked questions
What is a Full House in Sudoku?
A Full House is the simplest solving move: a row, column or box that already has eight of its nine cells filled, so the one remaining cell must be the single digit the unit is still missing. In the example on this page, row 1 holds 5, 3, 1, 9, 8, 7, 4 and 2 with only R1C5 empty, so that cell can only be 6. No candidates or advanced logic are needed — you just place the missing number and move on.
How do I spot a Full House on the grid?
Scan every row, column and box for one that has exactly one empty cell. When you find such a near-complete unit, note the eight digits already present and the one that is absent is your answer. Re-check after each placement, because filling a cell can complete a neighbouring unit — that is how one Full House often cascades into several in a row.
What is the difference between a Full House and a Naked Single?
A Full House is spotted from a UNIT that is one cell short — you notice the near-complete row, column or box first, as with row 1 above. A Naked Single is spotted from a CELL whose own row, column and box together already use eight different digits, leaving just one candidate. They frequently coincide, but the Full House is the easier catch because the almost-full unit jumps out visually. It is the tier-1 free win, the easiest technique there is.