There are few celebrations of mathematics anywhere in the world that can compare with an ARML meet. This annual event brings together not only the best high school students of mathematics from most of the country, but also some of the most enthusiastic organizers of competitions. Many great teachers are among them. Others come from the ranks of former contestants who are presently coaching the younger generation, while still others are the "elders" who originally conceived and developed this wonderful competition. Unfortunately, fewer and fewer of the latter group are present, and we can pay tribute only to their memories.
My first ARML meet dates back to 1979, when at the invitation of Al Kalfus, I was privileged to present some awards to the winners. Subsequently, Al challenged me to bring a team from Texas. The idea greatly appealed to me; it was only much later that I discovered how much work it would take to gather the students, to make the necessary arrangements, and to finance the trip. Looking back, I can still hardly believe that I managed to pull it off in 1980, '81, and '82, and that Sam Baethge has managed to keep Texas in ARML ever since. I am certain that Sam, as well as the many other organizers of ARML teams, will agree with me: However much work it takes, there is nothing more satisfying than bringing a team of enthusiastic students to an ARML meet!
Prior to the meet itself, there is always a meeting of the coaches, organizers, and other interested parties. In the early years, they often lasted late into the night. In addition to providing a forum for discussing the details of the program and electing the officers of ARML, this meeting used to provide an opportunity for lively discussions about future plans. I still remember clearly the uproar caused by my suggestion (following a 24-hour bus ride from Texas) to move the meet more to the interior of the country; for a moment, I thought I would be lynched by the 80-100 other coaches! Fortunately, by the time I returned with the Indiana teams some years later, my outrageous idea was forgiven---and put into practice. With the addition of the Iowa site and the plans for having one in Las Vegas, we can be certain that ARML will truly become nationwide in the near-future. That was Al's dream, and we are all happy to see it come true.
It is often said that mathematics is not a spectator sport, but the ARML meets should be declared exceptions to that rule---at least, on occasions. There is nothing more spectacular than to observe nearly 1,000 students in a large gymnasium, intent on getting the correct answer to the next problem posed. The silence is truly deafening as they wait for the signal to start working; one can almost hear the racing of their thoughts as they busily formulate their answers. The variety of reactions following the announcement of the correct answers is most interesting. Everyone wants to know who got the correct answer and how the other members of his or her team are doing. The ongoing rivalry among the teams is most healthy. The partial scores posted several times during the meet make the competition even more exciting.
For most participants, an ARML meet represents not only an exciting day of superb competitions, but a wonderful opportunity for fellowship in mathematics. Many lasting friendships are formed among the students and coaches in attendance, and much excellent mathematics is done during the few hours of these meets. And many of the problems continue to challenge everyone for years to come.
While the spirit of the ARML meets can not be preserved in book form, the mathematical experiences of the last few ARML meets and the closely related NYSML contests are faithfully represented in this volume. These contests should provide many hours of pleasure and instruction, and inspire further investigations by all enthusiasts of this superb competition, as well as by others interested in creative problem solving.
In closing, I want to extend my sincere congratulations to Larry Zimmerman and Gil Kessler for the beautiful problems and solutions of this volume. Thanks also to Mark Saul and Steve Adrian for their excellent leadership in furthering and realizing Al Kalfus's dreams, and to Stan Rabinowitz for adding yet one more masterpiece to the literature of mathematical competitions.
George Berzsenyi
Rose-Hulman Institute of Technology
Terre Haute, Indiana
October, 1994