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.