MathDB

We are given

100

points.

N

of these are vertices of a convex

N

-gon and the other

100 - N

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)

Problem Statement