  Let $\alpha:\mathbb{Z}_n\to\mathbb{Z}_n$ be a permutation and $\Psi(\alpha)$
be the number of collinear triples modulo $n$ in the graph of $\alpha$. Cooper
and Solymosi had given by induction the bound
$\min_{\alpha}\Psi(\alpha)\geq\lceil(n-1)/4\rceil$ 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.
