This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser's claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation.

• Full solutions are included • Problems selected to be appealing and challenging, but not intimidating • Particularly useful for teachers looking for ways to stimulate interest in mathematics

### Contents

Preface; 1. Plane geometry; 2. Number theory; 3. Algebra; 4. Combinatorics and graph theory; 5. Three-dimensional geometry; 6. Miscellaneous; Solutions.