... Paul J. Francis . ... 3mm] Joint appointment with the Research School of Astronomy and Astrophysics . I present a way of adapting the techniques of Problem Based Learning (PBL) to undergraduate astronomy classes. A fictitious astronomical mystery is invented, and presented to the class. The students, working in small groups, propose observations to crack the mystery. ... Two case studies of this technique are presented and discussed. ... Student Briefing . Running the Exercise . ...