Question 56
Consider two integers $n \ge m \ge 4$ and $A = \{a_1, a_2, \dots, a_m\}$ a subset of the set $\{1, 2, \dots, n\}$ such that:
for all $a, b \in A$, $a \ne b$, if $a + b \le n$, then $a + b \in A$.
Prove that:
$$
\frac{a_1 + a_2 + \dots + a_m}{m} \ge \frac{n+1}{2}.
$$
for all $a, b \in A$, $a \ne b$, if $a + b \le n$, then $a + b \in A$.
Prove that:
$$
\frac{a_1 + a_2 + \dots + a_m}{m} \ge \frac{n+1}{2}.
$$