2012 USAMO Problems/Problem 1

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Find all integers $n \ge 3$ such that among any $n$ positive real numbers $a_1$, $a_2$, $\dots$, $a_n$ 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.


See also

2012 USAMO (ProblemsResources)
First Problem Followed by
Problem 2
1 2 3 4 5 6
All USAMO Problems and Solutions
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