A magic square of order $n$ contains each integer from 1 to $n^2$, with each number appearing once. Every row and every column sum to the same number - the magic constant for that magic suqare.
For a magic square of order 3, any magic square you find will be the magic square found below, or one of its three roatations or a mirror image of one of the four rotational positions.
\begin{tabular}{ | *{3}{>{\collectcell\fwcell}c<{\endcollectcell} |} }
\hline
4 & 9 & 2
\hline
3 & 5 & 7
\hline
8 & 1 & 6
\hline
\end{tabular}
Show why for a magic square of order 3 the central cell is one third the magic constant and that the value is always 5. Use the labeling below.
\begin{tabular}{ | *{3}{>{\collectcell\fwcell}c<{\endcollectcell} |} }
\hline
a_1 & a_2 & a_3
\hline
a_4 & a_5 & a_6
\hline
a_7 & a_8 & a_9
\hline
\end{tabular}