The ARML Competition is an impressive sight. I
have been fortunate on several occasions to have been
invited to help out at an ARML "meet" at Penn State
University. To see almost 1,000 students competing and
enjoying mathematics under one roof is inspiring and
It is a tribute to the quality of the problems and the
efficiency of the organizing committee that these students
trek here from all over the country. Many get in buses early
in the morning and ride the whole day for the privilege and
excitement of participating in the ARML event, as well as
meeting old and new friends.
The problems in this book cover the ARML contests from 1989
to 1994 and the NYSML contests from 1989 to 1992. These are
the contests for which Larry Zimmerman and Gil Kessler were
the principal authors and which have not appeared previously
in book form. These authors are well-known for their
interesting and original problems. When they present a talk
at a mathematics conference, people flock to fill up the
room to see their lively presentation. This excitement
carries over to the problems that they create. There are
dozens, perhaps hundreds of smaller city and state math
leagues from all over the country; yet somehow the ARML and
NYSML contests seem to stand out as unique and distinct. I
am therefore pleased to be able to present these problems to
We have changed very little in the statements of the
problems. (They were correct and precise to begin with!) The
notation was changed in a few places to be consistent with
other books in this series and the solutions were somewhat
expanded. See the glossary at the end of the book if you are
uncertain about the terminology or notation used. In several
instances, the authors had underlined important phrases in
the problem statements that they did not want students to
overlook under the pressure of the time constraints imposed.
While helpful during the competition, such emphasis was
deemed unnecessary when presenting the problems in book
form. We have not modified the diagrams, but please note
that the figures are not necessarily to scale.
We hope you will enjoy the variety and originality of these
problems. The "power questions" are especially noteworthy.
These are almost mini-research problems. They guide the
students along and give them a feel for what mathematical
research is like. They inevitably spawn additional research
by students well after the contests are over. For example,
in a year when the power question involved lattice points,
you would find an unusually high number of Westinghouse
projects later that year investigating properties of lattice points.
The "relay races" are also fun to watch at one of these
meets. As soon as one student gets an answer to a problem,
he or she passes the solution back to the next student in
line. It is rare to find "power questions" or "relay races"
in other math league competitions. We hope that
these problems can be put to good use as practice problems
for future competitions and to enliven the learning of
mathematics in the classroom.
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