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A Cube Made from Wire

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June 8, 2009
geometry3D geometrytopology

Problem Statement

A cube is made by soldering twelve 3 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: <spanclass=′latex−bold′>(A)</span> 24 in.<spanclass=′latex−bold′>(B)</span> 12 in.<spanclass=′latex−bold′>(C)</span> 30 in.<spanclass=′latex−bold′>(D)</span> 18 in.<spanclass=′latex−bold′>(E)</span> 36 in. <span class='latex-bold'>(A)</span>\ 24\text{ in.}\qquad <span class='latex-bold'>(B)</span>\ 12\text{ in.}\qquad <span class='latex-bold'>(C)</span>\ 30\text{ in.}\qquad <span class='latex-bold'>(D)</span>\ 18\text{ in.}\qquad <span class='latex-bold'>(E)</span>\ 36\text{ in.}
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