Unique Solution
The property of a puzzle having exactly one solution. Sudoku puzzles are designed to have a unique solution.
Unique solution means that a puzzle has exactly one valid completion. Sudoku puzzles are designed to have a unique solution. Puzzles with multiple solutions are considered "flawed" because they cannot be solved purely by logic (guessing becomes necessary).
Why Uniqueness Matters
Without a guaranteed unique solution, players cannot confirm placements through logic alone. If a situation like "this cell is either 3 or 7" could have both as valid answers, that requires guessing, which undermines the puzzle's value as a logic exercise. One appeal commonly cited for Sudoku is that every placement can be logically derived.
Verification Methods
Whether a puzzle has a unique solution is verified by counting solutions with a solver. As soon as a second solution is found, the puzzle is deemed non-unique. In a common puzzle-generation procedure, this verification is performed each time a cell is removed, and any removal that breaks uniqueness is reverted.