Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries (Dolciani Mathematical Expositions)

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. This book provides a collection of 191 mathematical problems aimed at the advanced high school student level and above. Problems cover general mathematical areas including plane geometry, three-dimensional geometry, number theory, algebra, combinatorics and graph theory, and a number of miscellaneous questions that combine mathematical disciplines. The book is divided into two major sections: the first section contains the problems themselves; the second section contains the solutions, historical and other notes, and auxiliary problems without solutions. Problems range from determining the direction of travel of a bicycle leaving tracks in the mud, to determining if two equal amounts of pizza are cut using eight 45-degree wedges meeting at a point other than the center, to determining if a manufacturer's claim that a certain unusual combination lock allows for thousands of combinations. Contains 175 references. (AIM)