Question 95
Let $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ be real numbers whose sum is $20$. Determine with proof the smallest possible value of
$$
\sum_{1 \leq i\lt j \leq 5}\left\lfloor a_{i}+a_{j}\right\rfloor.
$$
$$
\sum_{1 \leq i\lt j \leq 5}\left\lfloor a_{i}+a_{j}\right\rfloor.
$$