Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries

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.

Joseph D. E. Konhauser was an avid problemist throughout his years at Macalester College (1968-1991). He studied at Penn State University, and obtained his doctorate there in 1963. He held teaching positions at Penn State and the University of Montana before coming to Macalester. He was a very active problemist and served on many contest committees such as those governing the USA Mathematical Olympiad and the William Lowell Putnam Mathematics Competitions. He served as editor of the "Pi Mu Epsilon Journal," and as book review editor for the "American Mathematical Monthly."

Dan Velleman received his PhD from the University of Wisconsin. He has taught at the University of Texas and the University of Toronto, and since 1983 he has taught at Amherst College. Currently, he is Chair of the Editorial Board for the Dolciani Mathematical Expositions Series (for the Mathematical Association of America). He is the author of "How to Prove it" (Cambridge University Press.)

Stan Wagon received his PhD from Dartmouth College. He taught at Smith College until coming to Macalester in 1990. Throughout his career has enjoyed the special beauty of succinctly stated and surprising mathematical facts. this led to his book on the Banach-Tarski paradox (Cambridge University Press), and with Victor Klee a book on unsolved problems in mathematics (MAA). Recently he has been intrigued with how "Mathematica" can help us see mathematical constructions in new ways, and he has written several books illustrating the power of this software: "Mathematica in Action" (Freeman), "The Power of Visualization" (Front Range Press), "Animating Calculus" (Springer) to name a few.