Andy Clemens, Maria Jantz, and Daniel Fecher were three of the 4,277 contestants from 578 institutions in the 73rd William Lowell Putnam Mathematical Competition. Each spent six hours on Saturday, December 1, 2012, solving twelve mathematics problems.
Problem A1: Let d1, d2, …, d12 be real numbers in the open interval (1, 12). Show that there exist distinct indices i, j, k such that di, dj, dk are the side lengths of an acute triangle.
The problems are challenging and the scoring is tough: the median score this year was 1 out of 120 possible points! Andy Clemens scored 20 points for a rank of 713th. Congratulations!