Problem orientation is gaining interest as a way of approaching the development of software intensive systems, and yet, a significant example that explores its use is missing from the literature. In this paper, we present the basic elements of Problem Oriented Software Engineering (POSE), which aims at bringing both nonformal and formal aspects of software development together in a single framework. We provide an example of a detailed and systematic POSE development of a software problem: that of designing the controller for a package router. The problem is drawn from the literature, but the analysis presented here is new. The aim of the example is twofold: to illustrate the main aspects of POSE and how it supports software engineering design and to demonstrate how a nontrivial problem can be dealt with by the approach.