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Omni-MATH / Two ants are moving along the edges of a convex polyhedron. The route of every…

Problem

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problem

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 FF of the polyhedron are written the number of edges of FF belonging to the route of the first ant and the number of edges of FF 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?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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?

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Source and history

task_id
cccff63e-f01b-5975-b009-5a17a5a68948
task_key
test--cccff63e-f01b-5975-b009-5a17a5a68948
task_revision_id
1
config / split
/ test

Official source

initial import