In this article, students build a prototype guitar. One way to get students to take creative risks is to allow playful approaches to their designs--let them come up with wild or silly ideas. By starting from such a wide-open place, many students will change their definitions and assumptions of what a guitar has to be. The result will be a wider…

How should men and women be seated around a dinner table to maximize conversation between members of the opposite sex? What can be said about the distribution of points around two concentric circles? How are the white and black keys on the piano keyboard organized? What spin configuration in the Ising model minimizes energy? These four problems…