The Green Book of Mathematical Problems

There is a famous set of fairy tale books, each volume of which is designated by the colour
of its cover: The Red Book, The Blue Book, The Yellow Book, etc. We are not presenting you
with The Green Book of fairy stories. but rather a book of mathematical problems. However,
the conceptual idea of all fairy stories, that of mystery, search, and discovery is also found in
our Green Book. It got its title simply because in its infancy it was contained and grew between
two ordinary green file covers.
The book contains lOO problems for undergraduate students training for mathematics
competitions, particularly the William Lowell Putnam Mathematical Competition. Along with
the problems come useful hints, and in the end Oust like in the fairy tales) the solutions to the
problems. Although the book is written especially for students training for competitions, it
will also be useful to anyone interested in the posing and solving of challenging mathematical
problems at the undergraduate level.
Many of the problems were suggested by ideas originating in articles and problems
in mathematical journals such as Crux Mathematicorum, Mathematics Magazine, and the
American Mathematical Monthly, as well as problems from the Putnam competition itself.
Where possible, acknowledgement to known sources is given at the end of the book.
We would, of course, be interested in your reaction to The Green Book, and invite
comments, alternate solutions, and even corrections. We make no claims that our solutions are
the "best possible" solutions, but we trust you will find them elegant enough, and that The Green
Book will be a practical tool in the training of young competitors. .
We wish to thank our publisher, Integer Press; our literary adviser; and our typist,
David Conibear, for their invaluable assistance in this project.

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