Henry Ernest Dudeney/Modern Puzzles/172 - A Magic Square Delusion

by : $172$

 * A Magic Square Delusion
 * Here is a magic square of the fifth order.


 * $\begin{array}{|c|c|c|c|c|}

\hline 17 & 24 & 1 & 8 & 15 \\ \hline 23 & 5 & 7 & 14 & 16 \\ \hline 4 & 6 & 13 & 20 & 22 \\ \hline 10 & 12 & 19 & 21 & 3 \\ \hline 11 & 18 & 25 & 2 & 9 \\ \hline \end{array}$


 * I have found that a great many people who have not gone very profoundly into these things believe that the central number in all squares of this order must be $13$.
 * One correspondent who had devoted years to amusing himself with this particular square was astounded when I told him that any number from $1$ to $25$ might be in the centre.
 * I will show that this is so.
 * Try to form such a magic square with $1$ in the central cell.