MagicSquare 2002-01-31 00:38:27 2005-03-03 18:17:41 Definition \usepackage{amsmath} A magic square of order $n$ is an $n\times n$ array using each one of the numbers $1,2,3,\ldots,n^2$ once and such that the sum of the numbers in each row, column or main diagonal is the same. Example: \begin{equation*} \begin{pmatrix} 8 & 1 & 6\\ 3 & 5 & 7\\ 4 & 9 & 2 \end{pmatrix} \end{equation*} It's easy to prove that the sum is always $\frac{1}{2}n(n^2+1)$. So in the example with $n=3$ the sum is always $\frac{1}{2}(3\times 10)=15$. One way to generalize this concept is to allow any numbers in the entries, instead of $1,2,\ldots,n$.