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

Joseph D. E. Konhauser (Author), Dan Velleman (Author), Stan Wagon (Author)

Book Description

ISBN-10: 0883853256 | ISBN-13: 978-0883853252 | Publication Date: October 1, 1996

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.

Editorial Reviews

Review

The problems are not brain-teaser types that have a "trick" to their solution: They all involve insightful mathematics. This text devotes 60 pages to the problems and 160 pages to their annotated solutions. The solutions are well written, make historical references, and contain extensions to the original problems...The problems are suitable for college-level and might be within reach of superior high school students....a nice addition to the library of any problem solver since it contains a collection of thought-provoking , demanding problems that are unlikely to be duplicated in any other single book. The Mathematics Teacher -- The Mathematics Teacher

This stimulating little book is a collection of the 191 of the best "Problem of the Week" mathematical problems and puzzles that appeared over the last 25 y ears at Macalester College. This tradition was started by Joe Konhauser, a "great believer in the value of problem solving activity," and later continued by Stan Wagon., The problems appear to follow Joe's dictum that "they had to involve almost no prerequisites and be succinctly stated and inherently attractive."...there is sufficient variety included to appeal to most mathematically oriented people. -- AAAS Science Books and Films

This work...is exceptionally well written and well prepared technically...The carefully stated problems are grouped into categories...Following the problem statements are well-written solutions to each problem. Besides being appropriate for teachers, the book might also interest advanced high school and college mathematics students who would independently engage in the challenge of mathematical puzzles and be entertained by the surprising twists required to solve them. -- Choice

Book Description

This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. Complete solutions to the 191 problems are included along with problem variations and topics for investigation.

See all Editorial Reviews

Product Details

• Paperback: 256 pages
• Publisher: The Mathematical Association of America (October 1, 1996)
• Language: English
• ISBN-10: 0883853256
• ISBN-13: 978-0883853252
• Product Dimensions: 9.1 x 6.1 x 0.7 inches
• Shipping Weight: 8 ounces
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #983,037 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars Excellent Book for anyone with time, August 25, 2001

By 

Recent Convert (Nashville, TN) - See all my reviews

This review is from: Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries (Dolciani Mathematical Expositions) (Paperback)

The book has many intriguing problems that are sure to capture the minds of any mathematician. It also contains a very nice answer section. The only throwback is that most of the problems take significant thought and require some time to solve completely. However, the nice answer section takes care of the problem should you become obsessed with a problem you can't quickly solve, and the overall quality of the problems warrant a 5-star rating.

3 of 4 people found the following review helpful:

4.0 out of 5 stars A collection of shiny pearls for your solving pleasure, March 27, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries (Dolciani Mathematical Expositions) (Paperback)

Starting with tire tracks in the mud, this book engages the reader with many adventures in mathematical explorations. Selected from the Problem of the Week collection at Macalester College that spans over twenty-five years, these 191 pearls are truly special. With an undergraduate population as the target, all problems can be understood by the sophisticated mathematics student. Most are within the proof set of undergraduates, although everyone from student to professor will find them challenging.
The subject matter is generally restricted to topics that are encountered in high school. For example, calculus is essentially unused. The main categories are: plane geometry, number theory, algebra, combinatorics, and graph theory, and three-dimensional geometry. A chapter of miscellaneous problems rounds out the collection. Solutions to all problems are included and the authors took great care to choose the proof that was most elegant or unusual.
If you are looking for that special problem to challenge your students or have an urge to be intrigued, then you should find what you want in this book.

Published in Journal of Recreational Mathematics, reprinted with permission.