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.

Posted by Ady TZIDON on 2014-10-08 13:02:14