2004 Cayley Problem 18

In the diagram, ABCDEFGH is a cube with an edge length of 12 cm. An ant sits on the cube at vertex A. The ant can only walk along the edges of the cube, and cannot walk along any edge more than once. What is the greatest distance that the ant can walk before it cannot continue?

\textbf{(A)}\ 96 \text{ cm}\quad \textbf{(B)}\ 144 \text{ cm}\quad \textbf{(C)}\ 84 \text{ cm}\quad \textbf{(D)}\ 108 \text{ cm}\quad \textbf{(E)}\ 132 \text{ cm}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.