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Problem of the Day #130: Minimizing acute angles July 27, 2011

Posted by Mitchell in : potd , trackback

If $A_1, A_2, \cdots, A_{100}$ are points in the plane, no three collinear, what is the minimum possible number of triples $(i, j, k)$ of distinct integers such that $1 \leq i, j, k \leq 100$, $i < k$, and $\angle A_i A_j A_k$ is acute?

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