A variation of the Newton–Pepys problem and its connections to size-estimation problems

This paper considers a variation of the 17th century problem commonly known as the Newton–Pepys problem, or the John Smith’s problem. We provide its solution and interpret the result in terms of maximum likelihood estimation. In addition, we illustrate the practical relevance of these findings for solving size-estimation problems, and in particular for determining the number of agents in a wireless sensor network.