This is problem 3 in [2]. The problem originally appeared in 1978 in [4] for four birds, and asked what the probability is that a bird picked at random is looking at another bird that is looking at it. Also, what is the probability if there are more than four birds? The solution appeared the next year in [1]. In one dimension, the probability is

, irrespective of the number of birds! (However, for two birds the probability is, of course, one.) In two dimensions, the probability that a randomly picked point is a part of a mutual neighbor pair is

. In three dimensions, the probability is

. As dimensions grow, the probability approaches the value

[3]. The problem is considered as a Poisson process in a Demonstration cited in the Related Links.