Latin Square

A Latin square is an ‘n x n’ grid populated by n symbols and each of those symbols appears once in every column and once in every row.

Assume the set {1,2,3,4} and let the operation be “clock addition”:

\begin{bmatrix} + && 1 && 2 && 3 && 4 \\ 1 && 2 && 3 && 4 && 1 \\ 2 && 3 && 4 && 1 && 2 \\ 3 && 4 && 1 && 2 && 3 \\ 4 && 1 && 2 && 3 && 4 \end{bmatrix}

We can say that the results of the addition form a Latin Square, and we show them below:

\begin{bmatrix} 2 && 3 && 4 && 1 \\ 3 && 4 && 1 && 2 \\ 4 && 1 && 2 && 3 \\ 1 && 2 && 3 && 4 \end{bmatrix}