2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160086Let $α:\mathbb{Z}_n\to\mathbb{Z}_n$ be a permutation and $Ψ(α)$ be the number of collinear triples modulo $n$ in the graph of $α$. Cooper and Solymosi had given by induction the bound $\min_αΨ(α)\geq\lceil(n-1)/4\rceil$ when $n$ is a prime number. The main purpose of this paper is to give a direct proof of that bound. Besides, the expected number of collinear triples a permutation can have is also been determined.4 pagesCombinatorics51E15;11T99text