Definition:Latin Square

Definition
A Latin square of order $n$ is a square array of size $n \times n$ containing $n$ different symbols, such that every row and column contains exactly one of each symbol.

That is, each row and column is a permutation of the same $n$ symbols.

This is an example of a Latin square of order $4$:


 * $\begin{array}

{|cccc|} \hline a & b & c & d \\ c & d & a & b \\ d & c & b & a \\ b & a & d & c \\ \hline \end{array}$

Also see

 * Existence of Latin Squares: Latin squares exist for all $n$.

Historical Note
The name Latin square originates from Leonhard Euler, who used Latin characters as symbols.