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?

The question does not merely ask for the maximum number of crossings.  That is trivial.  Both of the solutions give the formula.  The question is for the full set of possible/impossible numbers.

With 4 lines can you actually draw each of the cases with 0 through 6 crossing points? 

Posted by Jer on 2014-10-08 14:29:43