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Putnam 2012 A1

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December 3, 2012
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Problem Statement

Let d1,d2,…,d12d_1,d_2,\dots,d_{12} be real numbers in the open interval (1,12).(1,12). Show that there exist distinct indices i,j,ki,j,k such that di,dj,dkd_i,d_j,d_k are the side lengths of an acute triangle.
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