Question 10
Let $n$ be a positive integer. A good word is a sequence of $3n$ letters, in which each of the letters $A$, $B$ and $C$ appears exactly $n$ times. Prove that for every good word $X$ there exists a good word $Y$ such that $Y$ cannot be obtained from $X$ by swapping neighbouring letters fewer than $\frac{3}{2}n^2$ times. (IMO Shortlist 2017)