International Mathematical Olympiad 1984 Problem 5

Let $d$ be the sum of the lengths of all the diagonals of a plane convex polygon with $n$ vertices $(n > 3)$, and let $p$ be its perimeter. Prove that

$$n - 3 < \frac{2d}{p} < \left\lfloor\frac{n}{2}\right\rfloor\left\lfloor\frac{n+1}{2}\right\rfloor - 2,$$

where $\lfloor x \rfloor$ denotes the greatest integer not exceeding $x$.