I'm assuming this is homework of some sort, whether assigned for a class or for your own study, so I'll just give you a hint:
The key here is the counterclockwise order, or more accurately, the fact that vertices are in a consistent order.
Given three consecutive vertices p1, p2 and p3, consider the two vectors defined by:
V1 = (p1 - p2) and
V2 = (p3 - p2).
What do we know about the cross product V1 x V2? How will this value be different if p2 is on the boundary of the polygon versus in the center? The correct answer to this should divide our vertices into two classes. How will these classes be different for clockwise rather than counterclockwise orderings?