MathDB

We have

n

points in the plane, no three on a line. We call

k

of them good if they form a convex polygon and there is no other point in the convex polygon. Suppose that for a fixed

k

the number of

k

good points is

c_k

. Show that the following sum is independent of the structure of points and only depends on

n

\sum_{i=3}^n (-1)^i c_i

Problem Statement