Last Possible Number

When the grid leaves you no alternative.

Last Possible Number is the manual, ground-up way to solve a cell before you start keeping notes. For any empty cell, look at the digits already placed in its row, its column, and its 3×3 box — the three regions that constrain it.

Any digit appearing in at least one of those three regions is forbidden in that cell, since Sudoku never repeats a digit within a row, column, or box. Cross off every forbidden digit from the full set of 1 through 9, and whatever remains is what the cell must hold. When exactly one digit survives that elimination, you've found your answer with certainty, not a guess. This is the technique every solver starts with before candidate notes make the same logic faster: it reads directly off the board instead of pre-computed notes, which makes it slow on a crowded grid but useful for a quick first pass over a fresh, sparse puzzle.

How It Works

Focus on a single empty cell. Collect all digits already present in:

  • Its row (9 cells across)
  • Its column (9 cells down)
  • Its 3×3 box (9 cells surrounding)

Any digit appearing in at least one of these three regions cannot go in your cell. After eliminating all forbidden digits, if exactly one remains — place it.

  1. Choose an empty cell.
  2. Note which digits appear in its row, column, and box.
  3. The digit missing from all three is the answer.

Example

Below board presents an example of the last possible number for the center cell.

already in the row
already in the column
already in the box
must be 9

Look at the center cell. Its row already holds 1, 2, and 3. Its column holds 4, 5, and 6. Its box holds 7 and 8. Between the three regions, every digit from 1 to 8 is accounted for. Only 9 remains.

On Evil Boards

Typically, solvers start a puzzle by filling every empty cell with candidate notes, which makes the last possible number technique unusable on evil boards. Once notes are in play, obvious singles and hidden singles techniques take over. They read the same information straight off the notes instead of manually scanning a cell's row, column, and box from scratch.

Before scanning three regions by hand, check whether the cell's region is already down to a last free cell, or whether the digit itself has narrowed to a last remaining cell — both are cheaper to spot.