Intersections

Two distinct lines L1 and L2 are parallel. One hundred distinct points P1, ..., P100 are selected on L1, and another one hundred distinct points Q1, ..., Q100 are selected on L2.

Then lines are drawn from each point on P to each point on Q. There will be 10,000 of these crossing lines, and in many cases one crossing line will intersect with another crossing line. What is the maximum number of points of intersection that can occur between L1 and L2?

Solution