This is not homework, and I don't even know if this is possible, but I'm curious:
Given a list of points in Euclidean space, is it possible to find the center of a sphere that encompasses all of the points? These points would either lie inside the sphere or on the surface. Ideally one wouldn't have to compare the distances of each endpoint from all the other endpoints, but if that's the only way then that's the only way.
Looking for the smallest radius sphere that encompasses a finite number of points.