MathDB

3

Part of 2013 Philippine MO

Problems(1)

PMO Finals #3

Source:

2/3/2013
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 n2n^2 .
absolute value