Around the Block

Mark every vertex of a cube and every midpoint of its six faces. An ant sets out to visit all of these points, walking only along face diagonals, never retracing a step.

1. The cube has 8 vertices and 6 face-center points — 14 stops in all.
2. Every face diagonal connects a vertex to a face center, never vertex to vertex or center to center.
3. The ant can't repeat a diagonal it's already walked.

Can the ant visit every vertex and every face center?

Reveal the answer

No. Face diagonals only ever connect a vertex to a face center, so any walk along them must alternate strictly between the two kinds of point. A cube has 8 vertices but only 6 face centers — an even alternation can never cover an unequal split, so the full tour is impossible.