3 lines in a plane can be easily be drawn such that there are 0, 1, 2 or 3 points where at least 2 of them cross.
What are the possible numbers of crossing points for 4, 5, or 6 lines?
Can any of these results be generalized?
It looks like 1/2*n*(n-1) is the maximal number of crossing points for n lines.
Proof: by induction, adding a line that is not parallel to any of the existing lines.