Let $\Omega_n$ be the set of all permutations of the set
$N_n = \{1, 2, \dots, n\}$ and let us suppose that each permutation
$\omega = (a_1, \dots, a_n) \in \Omega_n$ has probability $1/n!$.
For $\omega = (a_1, \dots, a_n)$ let $X_{nj} = |a_j - a_{j+1}|$,
$j \in N_n$, $a_{n+1} = a_1$, $M_n = \max\{X_{n1}, \dots, X_{nn}\}$.
We prove herein that the random variable $M_n$ has asymptotically
the Weibull distribution, and give some remarks on the domains
of attraction of the Fréchet and Weibull extreme value
distributions.