A Latin square of order$n$ is an $n\times n$ array such that each column and each row are made with the same $n$ symbols, using every one exactly once .

Examples. \begin{equation*} \left(\begin{array}{cccc} a & b & c & d\\ c & d & a &b\\ d & c & b & a\\ b & a & d & c \end{array}\right) \qquad \left(\begin{array}{cccc} 1 & 2& 3& 4\\ 4 & 3 & 2 & 1\\ 2 & 1 & 4 & 3\\ 3 & 4 & 1 & 2 \end{array}\right) \end{equation*}