The minimum number of clues required for a Sudoku puzzle to have a unique solution. The finding, announced in January, is considered a major breakthrough in mathematics.

77%: Maximum number of clues a Sudoku puzzle can have without having a unique solution.

6.67 sextillion: The number of all possible Sudoku puzzles.

SOURCES: “There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem,” by Gary McGuire et al.; January 1, 2012; Preprint online at arxiv.org/abs/1201.0749; “Taking Sudoku Seriously: The Math Behind the World’s Most Popular Pencil Puzzle,” by J. Rosenhouse and L. Taalman, Oxford University Press, 2012

FURTHER READINGS AND CITATIONS ScientificAmerican.com/mar2012/advances