1990 IMO Problems/Problem 2

2. Let $n\ge3$ and consider a set $E$ of $2n-1$ distinct points on a circle. Suppose that exactly $k$ 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 $n$ points from $E$ . Find the smallest value of $k$ so that every such coloring of $k$ points of $E$ is good.