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.
Readership
Undergraduate and graduate students and researchers
interested in problem solving.
