MathDB

Two ants are moving along the edges of a convex polyhedron. The route of every ant ends in its starting point, so that one ant does not pass through the same point twice along its way. On every face

F

of the polyhedron are written the number of edges of

F

belonging to the route of the first ant and the number of edges of

F

belonging to the route of the second ant. Is there a polyhedron and a pair of routes described as above, such that only one face contains a pair of distinct numbers?
Proposed by Nikolai Beluhov

Problem Statement