Sudoku Clan › Sudoku techniques › Last empty cell
Last empty cell in Sudoku
- Beginner
- Needed from Gentle puzzles
- 1 point in Duel
Also called a full house or last digit.
When a row, column or box has eight of its nine cells filled, the ninth is decided. It is the first move every Sudoku player learns, and it never stops being useful.
How it works
Every row, column and 3×3 box must hold the digits 1 to 9 exactly once. So if eight cells of a unit are filled, only one digit is missing, and it has only one place to go. You do not need to look at anything outside that unit.
- Find a row, column or box with exactly one empty cell.
- Count through 1 to 9 and find the digit that is not there yet.
- Write it in the gap.
A real example
Read the digits already in the highlighted unit and you will find one is absent. The green cell is the only place left, so that digit goes there without any further checking.
When to look for it
Early in a puzzle there are few of these, because no unit is nearly full. They appear in waves: each digit you place brings some row, column or box one step closer to full. Good solvers glance at the three units of every cell they have just filled. If any of them is down to one gap, that is a free move.
Near the end of a puzzle almost every move is a last empty cell, which is why the finish of a Sudoku goes so much faster than the start. In Clash and Battle Royale, where speed decides the match, spotting these without thinking is worth real seconds.
A quick way to find the missing digit
Rather than counting from 1 to 9 each time, add the pairs you can see: 1 and 9, 2 and 8, 3 and 7, 4 and 6, with 5 on its own. A digit whose partner is on the board but which is missing itself is your answer. With practice you will simply see which digit is absent.
Questions
What is a full house in Sudoku?
A full house is a row, column or box with only one empty cell. The digit that is missing from that unit must go in the gap. It is also called the last empty cell or last digit.
Is the last empty cell the same as a naked single?
It is the simplest kind of naked single. In a naked single the other eight digits are ruled out by the row, column and box together. In a full house one unit alone rules them out.