Magic Square/Examples
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Examples of Magic Squares
Order $1$
The Order $1$ magic square is trivial:
- $\begin{array}{|c|} \hline 1 \\ \hline \end{array}$
Order $3$
- $\begin{array}{|c|c|c|} \hline 2 & 7 & 6 \\ \hline 9 & 5 & 1 \\ \hline 4 & 3 & 8 \\ \hline \end{array}$
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 $5$
- $\begin{array}{|c|c|c|c|c|} \hline 23 & 6 & 19 & 2 & 15 \\ \hline 10 & 18 & 1 & 14 & 22 \\ \hline 17 & 5 & 13 & 21 & 9 \\ \hline 4 & 12 & 25 & 8 & 16 \\ \hline 11 & 23 & 7 & 20 & 3 \\ \hline \end{array}$