Question 4
In the plane are given $\nu$ different points such that any three of them are not collinear. We color these points red, green and black. In the sequel we consider all line segments with ends these $\nu$ points and we correspond to each of them an “algebraic value” according to the following rules:
1) If at least one of the ends of the line segment is black, then it has algebraic value 0.
2) If both ends of the line segment have the same colour, red or green then it has the algebraic value 1.
3) If ends of the line segment have different colour red or green, then it has the algebraic value -1.
Determine the least possible value of the sum of algebraic values of the all line segments.
1) If at least one of the ends of the line segment is black, then it has algebraic value 0.
2) If both ends of the line segment have the same colour, red or green then it has the algebraic value 1.
3) If ends of the line segment have different colour red or green, then it has the algebraic value -1.
Determine the least possible value of the sum of algebraic values of the all line segments.