2012 Putnam A1

Let $d_1, d_2, \dots, d_{12}$ be real numbers in the open

interval $(1, 12)$. Show that there exist distinct indices $i, j, k$

such that $d_i, d_j, d_k$ are the side lengths of an acute triangle.

设 $d_1, d_2, \dots, d_{12}$ 为开实数

区间 $(1, 12)$。表明存在不同的索引 $i, j, k$

这样 $d_i, d_j, d_k$ 是锐角三角形的边长。