How to Tell Whether a Sudoku Has a Unique Solution

You should not need to choose between two equally valid completed grids. A well-formed classic Sudoku has one solution, even if the route to it is difficult.

Checking uniqueness formally is a construction task, but solvers can recognise several warning signs when a puzzle feels ambiguous.

A stalled grid is not proof

Difficulty, stale notes or a missed technique can make a unique puzzle look ambiguous. First verify the givens and rebuild the affected candidates before concluding that the puzzle is flawed.

Two completions are a red flag

If you can complete the grid in two ways while respecting every row, column and box, the givens do not determine a unique solution. Record both completions and check that no assumption slipped into either.

Transcription causes false ambiguity

A copied digit in the wrong cell or an omitted given changes the puzzle. Compare the source box by box, especially around the first contradiction, before blaming the generator.

Generators test uniqueness

Reliable puzzle software solves the candidate grid, searches for a second solution and rejects the puzzle if one exists. It may then rate the accepted puzzle by the techniques needed to solve it.

Choose trustworthy sources

Use publishers or apps that explain their generation and validation standards. If a printed puzzle is impossible or ambiguous, report the exact givens rather than spending an evening trying to rescue it.