Let's put up a new challenge: This is called the Fano plane: This is a geometric figure consisting of 7 points and 7 lines. However, it is a so-called projective plane. This means that it satisfies the following axioms: 1) Through any two points, there is exactly one line 2) Any two lines meet in exactly one point 3) There are four point such that no line goes to more than two of them The study of projective planes and spaces goes deep and far. But for now, I'm asking something simpler. When you look at the figure, you see that one of the "lines" is actually a circle and not a straight line. Prove that you can't draw the above configuration on a plane such that all the lines are actually straight lines. If you find this too easy, then there is this generalization: Given ##n## points on a plane. If they do not all lie on a straight line, then there is a straight line in the plane that contains exactly two of the points.