# 2017 USAJMO Problems/Problem 6

## Problem

Let be distinct points on the unit circle other than . Each point is colored either red or blue, with exactly of them red and exactly of them blue. Let be any ordering of the red points. Let be the nearest blue point to traveling counterclockwise around the circle starting from . Then let be the nearest of the remaining blue points to traveling counterclockwise around the circle from , and so on, until we have labeled all the blue points . Show that the number of counterclockwise arcs of the form that contain the point is independent of the way we chose the ordering of the red points.