1957 AHSME Problem 17

A cube is made by soldering twelve 3-inch lengths of wire properly at the vertices of the cube. If a fly alights at one of the vertices and then walks along the edges, the greatest distance it could travel before coming to any vertex a second time, without retracing any distance, is:

\textbf{(A)}\ 24\text{ in.}\qquad \textbf{(B)}\ 12\text{ in.}\qquad \textbf{(C)}\ 30\text{ in.}\qquad \textbf{(D)}\ 18\text{ in.}\qquad\textbf{(E)}\ 36\text{ in.}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.