There must be at least one good point
Source:
August 29, 2010
combinatoricspoint setcombinatorial geometryRamsey TheoryIMO Shortlist
Problem Statement
A set of points is distributed around the circumference of a circle and each of the points is marked with or . A point is called “good” if the partial sums that can be formed by starting at that point and proceeding around the circle for any distance in either direction are all strictly positive. Show that if the number of points marked with is less than , there must be at least one good point.