Question 34
Let 13 real numbers $a_{1}, a_{2}, \ldots, a_{13}$ be given, all different from zero, of which at least three are positive, and let $n$ be the number of negative $a_{i}$. Knowing that, among all the possible $a_{i} a_{j}$ products, exactly 22 are negative, how much is $n$ worth? ($a_{i} a_{j}$ and $a_{j} a_{i}$ count as one product.)