Question 146
A *section* of a finite set of points in the plane is a partition of that set into disjoint subsets $A$ and $B$, such that there is a line not passing through any of the points in the set so that all the points of the set $A$ are on one side of the line, and all the points of the set $B$ are on the other. Determine the maximum possible number of sections of a set of $n$ points in the plane. (Putnam 2006)