suma cardinale multimi

[Antonie]

Fie $A_1, A_2, \ldots, A_{2n}$ submultimi distincte ale multimii $\{1, 2, \ldots, n\} (n\in\Bbb{N}, n\geq{3})$.
Se cere maximul sumei $\displaystyle\sum\limits_{i=1}^{2n}{\frac{|A_i \cap A_{i+1}|}{|A_i|\cdot|A_{i+1}|}} (A_{2n+1}=A_1).$