There is a fly on a cube's vertex. The fly is expected to walk over every side of the cube once and return to the starting vertex. Is that possible?
2026-04-06 10:40:25.1775472025
A fly on a cube's vertex
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At each vertex, there are odd number of edges connected to it. Hence it is not possible, you need even degree to return to the starting vertex.
Further explanation:
The very first time you you leave the starting vertex. you used one edge connected to the starting edge.
The next time, you revisit the starting vertex, you used another edge.
If you use the third edge connected to it, you run out of edge to come back to the starting vertex.