The following problem is open in the sense that no solution is currently known to part (b). Let $n\geq 2$ be an integer, and $P_n$ be a regular polygon with $n^2-n+1$ vertices. We say that $n$ is $\emph{taut}$ if it is possible to choose $n$ of the vertices of $P_n$ such that the pairwise distances between the chosen vertices are all distinct. (a) show that if $n-1$ is prime then $n$ is taut. (b) Which integers $n\geq 2$ are taut?