Last Possible Number

The Last Possible Number is one of the simplest and most reliable sudoku techniques. You use it when a row, column, or 3x3 box has exactly one digit missing or when a single cell can only take one remaining candidate. It is perfect for beginners and remains useful at all difficulty levels because it converts clear logic into certain placements with no guessing.

When To Look For It

• A row, column, or box has eight numbers placed and one gap left.
• A cell’s notes reduce to a single candidate after basic eliminations.
• You have just made a placement and want quick follow ups in affected regions.

How It Works

1. Scan a region: Pick a row, column, or 3x3 box and list the digits 1 through 9.
2. Cross off what you see: Remove digits that already appear in that region.
3. Identify the gap: If only one digit is missing, that digit must fill the empty cell.
4. Or check a single cell: If a cell’s candidates shrink to one value, place it.

Quick Example

Suppose a row already contains the digits 1, 2, 3, 4, 5, 6, 8, and 9. The only digit missing is 7. If there is one empty cell in that row, it must be 7.

Why It Works

Sudoku rules require each digit 1 to 9 to appear exactly once in every row, column, and box. If all but one digit are accounted for, the remaining digit has only one valid place.

Tips

• Cycle your scans: After any placement, quickly rescan its row, column, and box. Fresh Last Possible Numbers often appear immediately.
• Keep notes tidy: Clean candidate notes make single-candidate cells easier to spot.
• Pair with Last Remaining Cell: Use both together to unlock a cascade of safe placements.

Common Mistakes To Avoid

• Skipping an update: Forgetting to remove a candidate after a placement can hide easy singles.
• Mixing regions: Make sure your “missing digit” check applies to exactly one region at a time.

Where You’ll Use It

This technique appears everywhere: in easy puzzles it solves large portions of the grid; in harder ones it closes loops after advanced eliminations. Whenever a region or cell reduces to one option, place it with confidence.