I have this problem in my homework but it doesn't seem quite right to me:
Every face of a convex polyhedron has at least $5$ vertices, and every vertex has degree $3$. Prove that if the number of vertices is $n$, then the number of edges is at most $5(n-2)/3$.
I was thinking that If the number of vertices of the polyhedron is $n$, and every vertex has degree $3$, then the number of edges should be $3n/2$. Am I interpreting the question wrongly or is there an error in my reasoning? Thanks so much!