The Last Remaining Cell (Full House)
The last remaining cell — sometimes called a "full house" — is the simplest move in Sudoku. When a row, column, or 3×3 box already contains eight of its nine digits, the empty cell can only be the one that's missing. It's the first technique every solver learns, and it's worth doing deliberately rather than by accident.
Sudoku's one rule is that every row, every column, and every 3×3 box must contain the digits 1 through 9 exactly once. The last remaining cell is that rule at its most direct: count what's there, name what's missing, write it in.
How it works
- the unit in focus
- the pattern
- a placement
- an elimination
In the row above, eight cells are already filled. Reading along, the digits present are 5, 3, 4, 6, 7, 8, 9, and 1 — every digit except 2. Since the row must contain a 2 somewhere and there is only one empty cell left, the 2 goes there. No candidates, no notes, no doubt.
The same logic applies to columns and boxes. Whenever a unit is down to its last empty cell, you can fill it instantly. These moments cascade: filling one last cell often completes a neighbouring unit, which completes another, and a corner of the board falls in seconds.
Where to look for them
Last remaining cells appear most often near the end of a solve, but they also show up early in any unit that started with lots of clues. Scan the board for the rows, columns, and boxes that look most crowded — the ones with seven or eight digits already placed. Those are where a single missing number is easiest to spot.
A practical habit: every time you place a digit anywhere, glance at the three units that cell belongs to (its row, its column, its box). If placing your digit left any of them with exactly one empty cell, fill that cell immediately before moving on. This keeps the cascade going and stops you from re-scanning the same regions.
Last remaining cell vs. naked single
These two sound alike but come from opposite directions. A last remaining cell looks at a whole unit and asks "which digit is missing?" A naked single looks at one cell and asks "which digits are still allowed here?" — checking its row, column, and box together. Both leave exactly one answer, but they're found by scanning differently. The last remaining cell is usually the faster of the two to spot because you only have to read one line.
Why it matters
It's tempting to dismiss the last remaining cell as too obvious to name. But solvers who treat it as a deliberate step — actively hunting for almost-full units — finish easy and medium boards far faster than those who only notice these cells by luck. It costs nothing and it's the foundation every harder technique is built on.
Ready for the next step up? Hidden singles find a forced digit even when the cell still has several candidates — the technique that unlocks most medium boards.
Play Sudoku Zen — six difficulties