The American Regions Mathematics League (ARML) competition is an annual national event that attracts a wide audience from across the United States and Canada. The New York State Mathematics League (NYSML) competition is also an annual event, drawing teams primarily from New York State. Both contests are identical in format, each offering four basic rounds for the 15-member teams. The students compete both jointly and individually.

The **TEAM ROUND** consists of 10 short answer questions whose difficulty level varies from easy to quite formidable. Team members distribute the problems among themselves, using whatever strategy they deem best suited for swift and accurate completion under the imposed time limit.

The **POWER QUESTION** is a challenging, multi-section problem usually focused about a single mathematical theme. It requires in-depth analysis and original thinking on the part of the entire team. Within a one-hour time limit, the students must produce a well written, mathematically accurate solution, including all necessary proofs. Over the years, we have received numerous letters indicating that power questions have served as the basis of classroom enrichment, student research papers, and Westinghouse Science Talent Search projects.

The contestants then gather in a large auditorium for the **INDIVIDUAL ROUND**. Here each participant works independently on a set of 8 short answer questions. These are administered in pairs, with ten minutes allowed for each pair. The results of this round are used to determine individual awards, while the scores also contribute to the team total.

For the **RELAY ROUND**, each team splits into groups of three. Within each sub-team, the first person solves his or her problem and passes the answer back. This number is needed for the solution of the second person's problem. The second person then passes an answer back. How quickly the third person produces the final answer determines the number of points awarded the team.

**TIEBREAKERS** are used to break ties among the individual top scores. While the entire audience tries these problems (flashed on overheads), those top scorers race the clock to submit the correct answer.

This book includes the ARML contests from 1989 to 1994, the NYSML contests from 1989 to 1992, and the tiebreakers back to 1983. An answer key is provided separate from the section containing complete solutions to all problems. These solutions have often been selected on the basis of instructional value rather than simply being the shortest approach. Frequently, extensions and directions for further investigation are suggested. The problems are indexed by topic. A listing of team and individual winners is also included.

The contests themselves represent only a beginning. What takes place after the competition is of great importance. The problems and solutions are a source of challenging material for contest practice, for classroom discussion, and for further mathematical research leading to student projects. They are also a great source of enjoyment.