Problem

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Tags: combinatorics, geometry, 3D geometry, dodecahedron



An ant craws along a closed route along the edges of a dodecahedron, never going backwards. Each edge of the route is passed exactly twice. Prove that one of the edges is passed both times in the same direction. (Dodecahedron has 12 faces in the shape of pentagon, 30 edges and 20 vertices; each vertex emitting 3 edges). (8)