Give $n$ black points on the plane such that no three are collinear and the distance between any two of them are pairs distinct. Starting with an arbitrary point and make it red. At each step, we draw the smallest segment such that one of its endpoints is red and the other is black—that has not yet been drawn—and doesn't cut any other yet drawn segments. Then, we make its black endpoint red. Is it true that for any $n$ and for any formation of these $n$ points, after finitely many steps, we can make all the points red?