Latin Square
A mathematical structure where n symbols are arranged in an n x n grid such that each symbol appears exactly once in every row and column. The foundation of Sudoku.
A Latin Square is a combinatorial structure in which n symbols are arranged in an n x n grid so that each symbol appears exactly once in every row and column. It was studied by the 18th-century Swiss mathematician Euler. Sudoku can be viewed as a Latin Square with the additional constraint of 3x3 blocks.
Relationship to Sudoku
A 9x9 Latin Square satisfies only the row and column constraints of Sudoku. Adding the block constraint creates Sudoku. The total number of Latin Squares is far greater than the number of valid Sudoku grids, showing that the block constraint dramatically restricts the solution space.
Applications
Latin Squares are applied in many fields of mathematics and engineering, including experimental design, cryptography, and error-correcting codes. Sudoku can be considered the most successful popular application of Latin Squares.