2012 USAMO Problems/Problem 1

Problem

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.

2012 USAMO (Problems • Resources)
First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6
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2012 USAMO Problems/Problem 1

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