CEMC Cayley, 2004

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

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?

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

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