## Description

This collection of problems is directed to students in high school, college and university. Some of the problems are easy. needing no more than common sense and clear reasoning to solve. Others may require some of the results and techniques which we have included in the fool Chest. None of the problems require calculus. so the collection could be described as “problems in pre-calculus mathematics”. How ever, they are definitely not the routine nor “drill” problems found in tex”tbooks. They could be described as challenging, interesting. thought-provoking, fascinating. Many have the “stuff’ of real mathematics; indeed quite a few are the simplest cases of research-level problems. Hence they should provide some insight into what mathematical research is about.

The collection is dedicated to students who find pleasure in wrestling with. and finally overcoming. a problem whose solution is not apparent at the outset. It is also dedicated to teachers who encourage their students to rise above the security offered by prefabricated exercises and thus experience the creative side of mathematics.

Teachers will find here problems to challenge mathematically oriented students. such as may be found in mathematics clubs or training sessions for mathematical competitions. Seeking solutions could be a collective experience, for collaboration in research often succeeds when a lonely effort might not.

Pay no attention to the solutions until your battle with a problem has resulted in a resounding victory or disappointing defeat. The solutions we have given are not to be regarded as definitive. although they may suggest possibilities for exploring similar situations. A particular problem may be resolved in several distinct ways, embodying different approaches and revealing various facets. Some solutions may be straightforward while others may be elegant and sophisticated. For this reason we have often included more than one solution. Perhaps you may discover others.

While many of these problems should be new to you. we make no claim for the originality of most of the problems. We acknowledge our debt to the unsung creators of the problems. recognizing how hard it is to create a problem which is interesting, challenging. instructive. and solvable without being impossible or tedious. With few exceptions. the problems appeared in a series of five booklets which were available from the Canadian Mathematical Society. Indeed, the first of these appeared in 1973. Since then they have received a steady distribution, and now we feel that an edited, revised version of all five together is desirable. The problems are arranged in no particular order of difficulty or subject matter. We welcome communications from the readers, comments. corrections. alternative solutions, and suggested problems.

Collecting and creating the problems. and editing them. has been a re\.\arding learning experience for us. We will feel fully rewarded if teachers and students find this collection useful and entertaining.