Question 3
A convex polyhedron has at least 5 vertices, and exactly three edges meet at each vertex. Prove that rational numbers can be assigned to its vertices so that:
(i) at least one assigned number is 2020;
(ii) for every face, the product of the numbers at all its vertices is 1.
(i) at least one assigned number is 2020;
(ii) for every face, the product of the numbers at all its vertices is 1.