Puzzle Stories
Why Every Good Sudoku Has Exactly One Solution
When you solve a Sudoku, you trust that there is one right answer waiting for you. That promise is not an accident. It is designed into every good puzzle.
A puzzle, not a guessing game
If a grid allowed two different solutions, you would eventually reach a point where logic cannot decide between them. You would have to guess. Puzzle makers consider that a broken puzzle. A proper Sudoku has exactly one solution, so every step can be reached by reasoning.
How makers check it
Most puzzles today are built with the help of a computer. A common method is to start from a complete, valid grid and remove numbers one by one. After each removal, a solver program checks that the puzzle still has only one solution. If removing a number would allow a second solution, that number stays.
How many grids are there?
In 2005, mathematicians Bertram Felgenhauer and Frazer Jarvis calculated how many complete 9×9 Sudoku grids exist: about 6.67 sextillion, a number with 22 digits. Many of those grids are just rotations, reflections or relabelings of one another. Counting only truly different grids leaves about 5.47 billion.
The magic number 17
How few clues can a puzzle have and still have one solution? Puzzles with 17 clues were found long ago, but nobody had ever found one with 16. In 2012, Gary McGuire, Bastian Tugemann and Gilles Civario announced the answer after a huge computer search: there is no 16-clue Sudoku. Seventeen is the minimum. Their paper, “There Is No 16-Clue Sudoku,” was published in 2014.
Why it matters to you
Because every good Sudoku has one answer, you never need luck. When you feel stuck, the puzzle is telling you there is a pattern you have not found yet. That is what makes finishing so satisfying.
Sources
- Felgenhauer & Jarvis, “Enumerating possible Sudoku grids” (2005)
- McGuire, Tugemann & Civario, “There Is No 16-Clue Sudoku,” Experimental Mathematics (2014)
- Mathematics of Sudoku – Wikipedia