In 2008, the American Mathematics Competition AMC 12 asked a simple question about heavy-tailed permutations of size 5. A heavy tail permutation of odd size n means that the first (n-1)/2 elements are less than the last (n-1)/2 elements. The problem is trivial for small size but proved to be difficult for me when trying to expand it to large n, which is why I ask for help after this blog in improving what I know so far.
If interested, here is the problem link and YouTube video explaining the problem:
