Putnam 2005 A6

Session A

Let $n$ be given, $n \geq 4$ , and suppose that $P_1, P_2, \dots, P_n$ are $n$ randomly, independently and uniformly, chosen points on a circle. Consider the convex $n$ -gon whose vertices are the $P_i$ . What is the probability that at least one of the vertex angles of this polygon is acute?

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

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