Another discrete geometric problem
Source: Romanian TST 1978, Day 4, P4
October 1, 2018
geometry
Problem Statement
Let be some points on a plane, no three collinear. We associate a positive or a negative value to every segment formed by these. Prove that the number of points, the number of segments with negative associated value, and the number of triangles that has a negative product of the values of its sides, share the same parity.