American Regions Mathematics League

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American Regions Mathematics League

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

The contest is largely made possible by the monetary contribution of D. E. Shaw & Co. among other smaller contributors.[1]

Teams consist 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. Calculus is not required to successfully complete any problem, but may facilitate solving the problem more quickly or efficiently. 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 most high school mathematics competitions.

Competition format[edit]

The competition consists of four formal events:

  • A team round, where the entire team has 20 minutes to solve 10 problems. Each problem is worth 5 points, for a possible total of 50 points
  • 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. Each problem is weighted for a possible 50 points.
  • An individual round, where each team member answers five groups of two questions each, with ten minutes per pair. Starting in 2009, the individual round expanded from eight questions to ten. Each problem is worth 1 point, for a grand total of 150 points possible for the team.
  • 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. The allotted time is six minutes, but extra points are given for solving the problem in three minutes. Solving the relay in 3 minutes gives 5 points, solving it in 6 minutes gives 3 points. The whole process is done twice, making the maximum 50 points possible for the team.

At the end, the student(s) with the highest scores on the individual compete for first place. Each student tied for the highest score is given a single question, and the quickest to get the correct answer wins. In the event of a tie (no one is able to get the correct answer in the given ten minutes), another tiebreaker is given, generally easier than the previous. The tiebreaker results are shared between the four sites to determine the top overall scorer, based on time to get the correct answer. The teams are scored based on the number of points they attained. The maximum being 300 points.

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 substitutes 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. The 2008 super relay at UNLV ended when a team guessed the correct answer. Realizing the likelihood of the fifteenth person receiving two correct answers was small, and knowing their answer to be a small integer, the fifteenth person of some teams began to run answers up to the proctors before the other members of the team finished their problems. This continued until the correct answer was guessed. To fix this, the writers made the final answer for the 2009 super relay a four-digit number. However, the 2008 disaster reoccurred in 2010, when a San Diego team correctly guessed the answer, 24, immediately after the "go" signal.

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[by whom?] more difficult than the NYSML competition. This format also inspired the Great Plains Math League.


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:

Year Location
1976 C. W. Post College
1977 Brown University
1978 Rutgers University
1979 Brown University
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 1995. In 2008, ARML added a fourth site at the University of Georgia in Athens 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.

Past Team Winners[edit]

Year Team[2] Score
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 County, Maryland A
1986 New York City A
1987 New York City A
1988 Chicago A
1989 Chicago A
1990 Ontario A 197
1991 Ontario A
1992 Georgia A
1993 Thomas Jefferson A
1994 New York City A
1995 New York City A
1996 San Francisco Bay Area A
1997 Minnesota Gold
1998 Massachusetts A 171
1999 San Francisco Bay Area A 187
2000 Chicago A/San Francisco Bay Area A (tie) 172
2001 San Francisco Bay Area A 191
2002 Thomas Jefferson A 190
2003 Thomas Jefferson A 155
2004 Thomas Jefferson A 166
2005 Lehigh Valley Fire 172
2006 North Carolina A 186
2007 Phillips Exeter Red 171
2008 New York City A 170
2009 Lehigh Valley Fire 215
2010 Lehigh Valley Fire 204
2011 Lehigh Valley Fire 232
2012 North Carolina A 223
2013 San Francisco Bay Area A 234

Past Individual Winners[edit]

Year Team
1979 Irwin Jungreis (New York City A)
1980 Paul Feldman (New York City A)
1981 Benji Fisher (New York City A)
1982 Noam Elkies (New York City A)
1983 David Zuckerman (New York City A)
1984 Mike Reid (New York City A)
1985 Ken Fan (Montgomery County, Maryland A)
1986 John Overdeck (Howard County A)
1987 Danny Cory North Carolina
1988 Michael Zieve (Greater Richmond)
1989 Sam Vandervelde (Lynchburg/Harrisonburg)
1990 Akira Negi (North Carolina)
1991 Andrew Schultz (Chicago A)
1992 Robert Kleinberg (Upstate New York)
1993 Jeremy Bem (Upstate New York)
1994 Noam Shazeer (Massachusetts A)
1995 Daniel Stronger (New York City A)
1996 Nathan Curtis (Thomas Jefferson A)
1997 Davesh Maulik (Nassau A)
1998 Gabriel Carroll (San Francisco Bay Area A)
1999 Gabriel Carroll (San Francisco Bay Area A)
2000 Tiankai Liu (San Francisco Bay Area A)
2001 Gabriel Carroll (San Francisco Bay Area A)
2002 Ruozhou Jia (Chicago A)
2003 Anders Kaseorg (North Carolina A)
2004 Aaron Pixton (Upstate New York A)
2005 Ryan Ko (Phillips Exeter A)
2006 Samuel Dittmer (Indiana Gold)
2007 Tao Ran Chen (New York City A)
2008 Qin Xuan Pan (Montgomery A)
2009 Zhuo Qun (Alex) Song (Ontario West)
2010 Ben Gunby (Georgetown Day School)
2011 Zhuo Qun (Alex) Song (Ontario West)
2012 Allen Liu (Upstate New York)
2013 Allen Liu (Upstate New York)


  1. ^
  2. ^ Results from before 1992 are taken from "PAST WINNERS AT ARML". . This site may not be accurate; it is wrong in at least one year of Division B standings.

External links[edit]