There are 100 vertices in a prism with a 50-gon as its base. Those vertices are assigned integers 1 to 100 (inclusive) in a random order. Each number can only be assigned once. The objective is to prove that there are always two adjacent vertices (two vertices that are connected by an edge) whose number differ by 48 or less.

Can you help me?

Are you sure the problem isn't to show that at least two adjacent sides must differ by 49 or less? Also, what's with the "50-gon" base - to have 100 sides shouldn't it be a "100-gon" base?