Question 6
Find all integers $n \ge 3$ such that among any $n$ positive real numbers $a_1, a_2, \ldots, a_n$ with
$$ \max(a_1, a_2, \ldots, a_n) \le n \cdot \min(a_1, a_2, \ldots, a_n), $$
there exist three that are the side lengths of an acute triangle.
Illustration only; the configuration/coloring may vary.
$$ \max(a_1, a_2, \ldots, a_n) \le n \cdot \min(a_1, a_2, \ldots, a_n), $$
there exist three that are the side lengths of an acute triangle.
Illustration only; the configuration/coloring may vary.