Diagrams play an important role in human problem solving. In response to a challenging assignment, three students produced diagrams and subsequent verbal protocols that offer insight into human cognition. The diversity and richness of their response, and their ability to address the task via diagrams, provide an incisive look at the role diagrams play in the development of expertise. This paper recounts how their diagrams led and misled them, and how the diagrams both explained and drove explanation. It also considers how this process might be adapted for a computer program.