Given 100 points on the plane, construct the perpendicular bisector of each pair, and count all the points on the plane in which two or more (non-parallel) bisectors intersect. At most how many points could you have counted?
To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:
If x = 6, y = 5 and z = 4, what is x + y - z?