MathDB
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 2n2n distinct points on a circle. The numbers 11 through 2n2n 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 aa and bb, so we assign the value ab |a - b| to the segment . Show that we can choose the routes such that the sum of these values ​​results n2n^2.