1989 IMO Problems/Problem 5
Problem
Let 
and consider a set 
of 2n−1 distinct points on a circle. Suppose that exactly 
of these points are to be colored black. Such a coloring is “good” if there is at least one pair of black points such that the interior of one of the arcs between them contains exactly 
points from set . Find the smallest value of such that every such coloring of points of is good.
