Question 94
Given a positive integer $n$. There are $n$ boys and $n$ girls standing in a line. Give each person $X$ in the line a number of sweets which is exactly equal to the number of the pair $(a, b)$ such that $a$ and $b$ are of opposite sex of $X$ and $X$ is standing between $a$ and $b$. Prove that the total number of sweets of $n$ boys and $n$ girls does not exceed $\frac{1}{3}n(n^2 - 1)$.