American Regions Mathematics League

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The American Regions Mathematics League (ARML), is an annual high school mathematics team competition held simultaneously at three locations in the United States: the University of Iowa, Penn State, and UNLV. Past sites have included San Jose and at Duke University.

Teams are comprised of 15 members, which usually represent a large geographic region (such as a state) or a large population center (such as a major city). Some math and science magnet schools, such as Thomas Jefferson High School for Science and Technology, VA, and the Academy for the Advancement of Science and Technology (AAST), NJ, also field teams. The competition is held on the first Saturday after Memorial Day.

As of 2006, over 100 teams competed with around 1800 students.

ARML problems cover a wide variety of mathematical topics including algebra, geometry, number theory, combinatorics, probability, and inequalities. While part of the competition is short-answer based, there is a cooperative team round, and a proof-based power question (also completed as a team). ARML problems are harder than at most high school mathematics competitions.

1 Competition Format
2 History
3 Past Team Winners
4 Past Individual Winners
5 External links

[edit] Competition Format

The competition consists of four formal events:

A team round, where the entire team has 20 minutes to solve 10 problems.
A power question, where the entire team has one hour to solve a multiple-part (usually ten) question requiring explanations and proofs. This is usually an unusual, unique, or invented topic so students are forced to deal with complex new mathematical ideas.
A relay, where the team is broken into five groups of three. Within each group, the first team member solves a problem and passes the solution to the next team member, who plugs that answer into their question, and so on. Extra points are given for solving the problem in half the allotted time.
An individual round, where each team member answers four groups of two questions each, with ten minutes per pair.

At the end, the student(s) with the highest scores on the individual compete for first place. Each student tied for the highest score (typically eight correct out of eight, though some years fail to see a perfect score) is given a single question, and the quickest to get the correct answer wins. The tiebreaker results are shared between the three sites to determine the top overall scorer, based on time to get the correct answer.

In recent years, there has been a super relay, where two groups of seven team members (fourteen in all) both work to give a correct answer to the fifteenth team member. That last team member plugs two answers into his problem. For logistical reasons, the Super Relay has never counted towards the team score. It was instituted as a "filler" while scores are tabulated. Candies and other goodies are sometimes rewards for the super relay round.

Also in recent years, a song contest has become an informal event at ARML. Each school is allowed to have any number of their students perform a song related to mathematics, usually a parody of a popular song, with its lyrics replaced.

The format of the ARML competition is based on the NYSML competition, but is generally considered more difficult than the NYSML competition. This format also inspired the Great Plains Math League.

[edit] History

The New York State Mathematics League held its first competition in 1973, a competition intended for New York state teams. A team from Massachusetts asked to participate in the 1974 NYSML competition, and it took first place. This led to the creation of the Atlantic Regions Mathematics League in 1976, which became the American Regions Mathematics League in 1984.

When the Atlantic Regions Mathematics League was founded, the competition was held at a single eastern site that changed from year to year:

1976: C. W. Post College
1977: Brown University
1978: Rutgers University
1979: University of Hartford
1980: Rutgers University
1981: University of Maryland College Park
1982: University of Maryland College Park
1983: Pennsylvania State University

After 1983, the coordinators decided to keep the competition at Penn State University. ARML expanded to two sites in the late 1980s and to three sites in the 1990s. A fourth site might be added in the near future to better accommodate students in the Southeast.

The 2006 competition saw significant expansion. Around 120 teams and a total of around 1800 students competed, which was around 25% larger than during any other year. The Western site at UNLV nearly doubled.

[edit] Past Team Winners

1976: New York City A
1977: Massachusetts A
1978: Fairfax-Montgomery
1979: New York City A
1980: New York City A
1981: New York City A
1982: New York City A
1983: New York City A
1984: New York City A
1985: Montgomery A
1986: New York City A
1987: New York City A
1988: Chicago A
1989: Chicago A
1990: Ontario A
1991: Ontario A
1992: Georgia A
1993: Thomas Jefferson High School for Science and Technology A
1994: New York City A
1995: New York City A
1996: San Francisco Bay Area A
1997: Minnesota Gold
1998: Massachusetts A
1999: San Francisco Bay Area A
2000: Chicago A/San Francisco Bay Area A (tie)
2001: San Francisco Bay Area A
2002: Thomas Jefferson A
2003: Thomas Jefferson A
2004: Thomas Jefferson A
2005: Lehigh Valley Fire
2006: North Carolina A

Note: Results from before 1992 are taken from http://www.rose-hulman.edu/~rickert/ARML/armlwins.html. This site may not be accurate; it is wrong in at least one year of Division B standings.