Editing Magic hypercube (section)

===Curiosities===

====all orders are either even or odd====
A fact that can be easily seen since the magic sums are:
:S<sub>k</sub> = m<sub>k</sub> (<sub>j=0</sub>Π<sup>n-1</sup>m<sub>j</sub> - 1) / 2

When any of the orders m<sub>k</sub> is even, the product is even and thus the only way S<sub>k</sub> turns out integer is when all m<sub>k</sub> are even. Thus suffices: all m<sub>k</sub> are either even or odd.

This is with the exception of m<sub>k</sub>=1 of course, which allows for general identities like:
* N<sub>m</sub><sup>t</sup> = N<sub>m,1</sub> * N<sub>1,m</sub>
* N<sub>m</sub> = N<sub>1,m</sub> * N<sub>m,1</sub>
Which goes beyond the scope of this introductory article

====Only one direction with order = 2====
since any number has but one complement only one of the directions can have m<sub>k</sub> = 2.