RO-TST 1987 Problem 5

Let $A$ be the set $\{1,2,\ldots,n\}$ , $n\geq 2$ . Find the least number $n$ for which there exist permutations $\alpha$ , $\beta$ , $\gamma$ , $\delta$ of the set $A$ with the property: $$\sum_{i=1}^n \alpha(i) \beta (i) = \dfrac {19}{10} \sum^n_{i=1} \gamma(i)\delta(i) .$$ Marcel Chirita