Abstract: The core of this paper consists of a reflective account of the means a solution of a particular problem was obtained. The problem solving literature now includes a number of books that commend such reflective activity, and sest out particular frameworks encompassing heuristics for arriving at solutions. The account in this paper is largely descriptive in the sense that it does not claim to offer a heuristic menu for others to use. It does, however, contrast successful deductive and inductive approaches to solving the same problem, and is intended to encourage students and other problem solvers to maintain reflective awareness of the possibilities available to them as they work on a problem.