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Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles

Daniel J. Velleman Amherst College, Amherst, MA and University of Vermont, Burlington, VT
Stan Wagon Macalester College, St. Paul, MN
MAA Press: An Imprint of the American Mathematical Society
Available Formats:
Softcover ISBN: 978-1-4704-4759-5
Product Code: PRB/36
List Price: $55.00 MAA Member Price:$41.25
AMS Member Price: $41.25 Electronic ISBN: 978-1-4704-5702-0 Product Code: PRB/36.E List Price:$55.00
MAA Member Price: $41.25 AMS Member Price:$41.25
Bundle Print and Electronic Formats and Save!
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List Price: $82.50 MAA Member Price:$61.88
AMS Member Price: $61.88 Click above image for expanded view Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles Daniel J. Velleman Amherst College, Amherst, MA and University of Vermont, Burlington, VT Stan Wagon Macalester College, St. Paul, MN MAA Press: An Imprint of the American Mathematical Society Available Formats:  Softcover ISBN: 978-1-4704-4759-5 Product Code: PRB/36  List Price:$55.00 MAA Member Price: $41.25 AMS Member Price:$41.25
 Electronic ISBN: 978-1-4704-5702-0 Product Code: PRB/36.E
 List Price: $55.00 MAA Member Price:$41.25 AMS Member Price: $41.25 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$82.50 MAA Member Price: $61.88 AMS Member Price:$61.88
• Book Details

Problem Books
Volume: 362020; 286 pp
MSC: Primary 00;

Bicycle or Unicycle? is a collection of 105 mathematical puzzles whose defining characteristic is the surprise encountered in their solutions. Solvers will be surprised, even occasionally shocked, at those solutions. The problems unfold into levels of depth and generality very unusual in the types of problems seen in contests. In contrast to contest problems, these are problems meant to be savored; many solutions, all beautifully explained, lead to unanswered research questions. At the same time, the mathematics necessary to understand the problems and their solutions is all at the undergraduate level. The puzzles will, nonetheless, appeal to professionals as well as to students and, in fact, to anyone who finds delight in an unexpected discovery.

These problems were selected from the Macalester College Problem of the Week archive. The Macalester tradition of a weekly problem was started by Joseph Konhauser in 1968. In 1993 Stan Wagon assumed problem-generating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twenty-five years of the archive. The title problem in that collection was inspired by an error in logic made by Sherlock Holmes, who attempted to determine the direction of a bicycle from the tracks of its wheels. Here the title problem asks whether a bicycle track can always be distinguished from a unicycle track. You'll be surprised by the answer.

• Problems
• Can a bicycle simulate a unicycle?
• Geometry
• Number theory
• Combinatorics
• Probability
• Calculus
• Algorithms and strategy
• Miscellaneous
• Solutions
• Can a bicycle simulate a unicycle?
• Geometry
• Number theory
• Combinatorics
• Probability
• Calculus
• Algorithms and strategy
• Miscellaneous

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 362020; 286 pp
MSC: Primary 00;

Bicycle or Unicycle? is a collection of 105 mathematical puzzles whose defining characteristic is the surprise encountered in their solutions. Solvers will be surprised, even occasionally shocked, at those solutions. The problems unfold into levels of depth and generality very unusual in the types of problems seen in contests. In contrast to contest problems, these are problems meant to be savored; many solutions, all beautifully explained, lead to unanswered research questions. At the same time, the mathematics necessary to understand the problems and their solutions is all at the undergraduate level. The puzzles will, nonetheless, appeal to professionals as well as to students and, in fact, to anyone who finds delight in an unexpected discovery.

These problems were selected from the Macalester College Problem of the Week archive. The Macalester tradition of a weekly problem was started by Joseph Konhauser in 1968. In 1993 Stan Wagon assumed problem-generating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twenty-five years of the archive. The title problem in that collection was inspired by an error in logic made by Sherlock Holmes, who attempted to determine the direction of a bicycle from the tracks of its wheels. Here the title problem asks whether a bicycle track can always be distinguished from a unicycle track. You'll be surprised by the answer.

• Problems
• Can a bicycle simulate a unicycle?
• Geometry
• Number theory
• Combinatorics
• Probability
• Calculus
• Algorithms and strategy
• Miscellaneous
• Solutions
• Can a bicycle simulate a unicycle?
• Geometry
• Number theory
• Combinatorics
• Probability
• Calculus
• Algorithms and strategy
• Miscellaneous
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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