Variations on a Putnam Problem

Abstract

The following problem appeared in the afternoon session of the Fiftieth William Lowell Putnam Mathematical Competition in 1989. A dart, thrown at random, hits a square target. Assuming that any two parts of the target of equal area are equally likely to be hit, find the probability that the point hit is nearer to the center than to any edge. Express your answer in the form a√b + c/d, where a, b, c, d are positive integers. We will consider similar problems in both two and three dimensions using a variety of metrics.