Question 1
Find all integers $n \ge 3$ such that among any $n$ positive real numbers
$a_1$, $a_2$, …, $a_n$ with
\[ \max(a_1,a_2,\dots,a_n)
\le n \cdot \min(a_1,a_2,\dots,a_n), \]
there exist three that are the side lengths of an acute triangle.
$a_1$, $a_2$, …, $a_n$ with
\[ \max(a_1,a_2,\dots,a_n)
\le n \cdot \min(a_1,a_2,\dots,a_n), \]
there exist three that are the side lengths of an acute triangle.