IMO 1979 - Shortlisted problems Question 5

(CZS 2) Let $n\ge2$ be an integer. Find the maximal cardinality of a set $M$ of pairs $(j,k)$ of integers, $1\le j\lt k\le n$, with the following property: If $(j,k)\in M$, then $(k,m)\notin M$ for any $m$.