Problem

Source: Turkey TST 2017 P9

Tags: Turkey, TST, combinatorics



Let $S$ be a set of finite number of points in the plane any 3 of which are not linear and any 4 of which are not concyclic. A coloring of all the points in $S$ to red and white is called discrete coloring if there exists a circle which encloses all red points and excludes all white points. Determine the number of discrete colorings for each set $S$.