2n distinct points on a circle, assign |a - b| to a segmentm sum n^2
Source: Switzerland - 2016 Swiss MO Final Round p7
January 14, 2023
combinatoricsSum
Problem Statement
There are distinct points on a circle. The numbers through are randomly assigned to this one points distributed. Each point is connected to exactly one other point, so that no of the resulting connecting routes intersect. If a segment connects the numbers and , so we assign the value to the segment . Show that we can choose the routes such that the sum of these values results .