1989 IMO Problems/Problem 5
Problem
Let and consider a set
of $2n − 1$ (Error compiling LaTeX. Unknown error_msg) 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.