A puzzle from James F. Fixx’s More Games for the Superintelligent, 1976:
A rope 150 feet long is strung between the tops of two flagpoles, each 100 feet high. At its lowest point the rope sags to within 25 feet of the ground.
*original question* What is the distance between the poles?
*my question* How long did it take you to get the correct answer?
3 points are drawn on a plane, and inside their triangular region, more points are added such that no 3 are collinear, such that there are n points in total. What is the maximum possible number of line segments one could draw connecting two of these points such that none intersect other than at their endpoints?