Manasataramgini has a problem from plane geometry embedded in a short story, which I extract here:
Given a unit square, if a point lies on the same plane as the square at not more than a unit distance simultaneously from each of the four vertices of the square then what will be: 1) the minimum distance it can reach from any side of the square; 2) what fraction of the area of the square can the point be located in.Since the short story includes the requirement of solving it in 7 minutes, I was asked to try my hand at it.
