Magic Square/Examples

Examples of Magic Squares

Order $1$

The Order $1$ magic square is trivial:

$\begin{array}{|c|}

\hline 1 \\ \hline \end{array}$

Order $3$

Order $3$ magic square:

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

\hline 2 & 7 & 6 \\ \hline 9 & 5 & 1 \\ \hline 4 & 3 & 8 \\ \hline \end{array}$

Order $4$

There are many order $4$ magic squares.

Dürer's Order $4$ Magic Square

This is one of the more famous ones, due to Albrecht Dürer:

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

\hline 16 & 3 & 2 & 13 \\ \hline 5 & 10 & 11 & 8 \\ \hline 9 & 6 & 7 & 12 \\ \hline 4 & 15 & 14 & 1 \\ \hline \end{array}$

Moessner's Order $4$ Magic Square

This one, created by Alfred Moessner, has extra interesting properties:

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

\hline 12 & 13 & 1 & 8 \\ \hline 6 & 3 & 15 & 10 \\ \hline 7 & 2 & 14 & 11 \\ \hline 9 & 16 & 4 & 5 \\ \hline \end{array}$

Order $5$

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

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