PMO Finals #3
Source:
February 3, 2013
absolute value
Problem Statement
3. Let n be a positive integer. The numbers 1, 2, 3,....., 2n are randomly assigned to 2n distinct points on a circle. To each chord joining two of these points, a value is assigned equal to the absolute value of the difference between the assigned numbers at its endpoints.
Show that one can choose n pairwise non-intersecting chords such that the sum of the values assigned to them is .