Question 45
Mark 2014 points on a circle. Write a nonnegative real number on every segment joining two marked points. For every convex polygon whose vertices are among the marked points, the sum of the numbers on its sides is at most 1. Determine the largest possible sum of all the numbers.
Schematic circular order and a sample inscribed convex polygon; only 12 of the 2014 points are represented.
Schematic circular order and a sample inscribed convex polygon; only 12 of the 2014 points are represented.