Softcover ISBN:  9781470447595 
Product Code:  PRB/36 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Electronic ISBN:  9781470457020 
Product Code:  PRB/36.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 

Book DetailsProblem BooksVolume: 36; 2020; 286 ppMSC: 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 problemgenerating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twentyfive 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.ReadershipUndergraduate and graduate students and researchers interested in problem solving.

Table of Contents

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


Additional Material

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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 problemgenerating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twentyfive 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.
Undergraduate and graduate students and researchers interested in problem solving.

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