The numbers from $1$ to $8$ are placed at the vertices of a [cube](https://artofproblemsolving.com/wiki/index.php/Cube) in such a manner that the sum of the four numbers on each face is the same. What is this common sum?
$\text{(A)}\ 14 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ 24$
The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these $8$ numbers represent all of the vertices of the cube. Thus the answer is $\frac{1 + 2 + \cdots + 8}{2} = 18\ \mathrm{(C)}$.