Magic Cube/Examples/Order 3

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Example of Magic Cube

Order $3$ magic cube:

$\begin{array}{|c|c|c|} \hline 2 & 13 & 27 \\ \hline 22 & 9 & 11 \\ \hline 18 & 20 & 4 \\ \hline \end{array} \qquad \begin{array}{|c|c|c|} \hline 16 & 21 & 5 \\ \hline 3 & 14 & 25 \\ \hline 23 & 7 & 12 \\ \hline \end{array} \qquad \begin{array}{|c|c|c|} \hline 24 & 8 & 16 \\ \hline 17 & 19 & 6 \\ \hline 1 & 15 & 26 \\ \hline \end{array}$


Its magic constant is $42$.


Proof

From Magic Constant of Magic Cube, we have that:

$M_3 = \dfrac {3 \paren {3^3 + 1} } 2$

which (after arithmetic) gives $42$.


Sources