[Math Lair] Latin Squares

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Latin squares are an n × n matrix of n elements, with no element occurring more than once within any row or column of the matrix. The number n is referred to as the order of the Latin square. For example, the following is a Latin square of order 3:

The properties of Latin squares were first systematically investigated by Swiss mathematician Leonhard Euler in 1779. They are called Latin squares because Euler used Latin letters as labels in his work on magic squares.

Sudoku is a type of Latin square, being a 9×9 Latin square where each 3×3 sub-square also contains no element more than once.

Not that this is highly relevant to Latin squares, but mathematicians have proven that any Sudoku puzzle must have at least 17 numbers. You can read about it at Mathematicians Solve Minimum Sudoku Problem.

See also magic squares, Eulerian squares.

Sources used (see bibliography page for titles corresponding to numbers): 45.