We are given 100 points. N of these are vertices of a convex N-gon and the other 100āN of these are inside this N-gon. The labels of these points make it impossible to tell whether or not they are vertices of the N-gon. It is known that no three points are collinear and that no 4 points belong to two parallel lines. It has been decided to ask questions of the following type: What is the area of the triangle XYZ, where X,Y and Z are labels representing three of the 100 given points? Prove that 300 such questions are sufficient in order to clarify which points are vertices and to determine the area of the N-gon. (D. Fomin, Leningrad) combinatorial geometrycombinatoricsgeometryconvex polygonpolygon