Question 36
Let $k, n$ be positive integers. Given $A_0, A_1, \dots, A_n$ points and edges that connect them are colored with $k$ colors. $S(n, k)$ is the maximum number of angles, whose sides are colored with different colors. Prove that
$$
S(n, k) \gt \binom{k}{2} \cdot \left[\frac{n}{k}\right]^2 \cdot n.
$$
$$
S(n, k) \gt \binom{k}{2} \cdot \left[\frac{n}{k}\right]^2 \cdot n.
$$