# 2017 USAMO Problems/Problem 4

## Problem

Let , , , be distinct points on the unit circle , other than . Each point is colored either red or blue, with exactly red points and blue points. 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 travelling counterclockwise around the circle from , and so on, until we have labeled all of 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.