Question 38
There are $2^{2013}$ points on a circle, labeled arbitrarily $1,2,\dots,2^{2013}$, each number appearing once. Prove that one can draw 500 pairwise nonintersecting chords between these points so that the sums of the endpoint labels are all equal.
Schematic only: eight representative points, not the full number in the problem.
Schematic only: eight representative points, not the full number in the problem.