Multiplicative Magic Square/Examples/Order 3/Smallest

Example of Order $3$ Multiplicative Magic Square

The order $3$ multiplicative magic square with the smallest magic constant is:

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

\hline 18 & 1 & 12 \\ \hline 4 & 6 & 9 \\ \hline 3 & 36 & 2 \\ \hline \end{array}$

Its magic constant is $216$.

Also see

• Smallest Multiplicative Magic Square is of Order 3
• Smallest Magic Constant of Order 3 Multiplicative Magic Square

Historical Note

The order $3$ multiplicative magic square with the smallest magic constant is believed to have been discovered by Georges Pfeffermann in $1893$.

Some sources erroneously ascribe it to Harry A. Sayles in $1913$, as work by Georges Pfeffermann has only recently come to light.

It is also sometimes erroneously ascribed to Henry Ernest Dudeney, who in $1917$ also rediscovered it.

Sources

• Weisstein, Eric W. "Multiplication Magic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MultiplicationMagicSquare.html