The American Regions Mathematics League (ARML), is an annual, national high school mathematics team competition held simultaneously at five locations in the United States: the University of Iowa, Penn State, University of Nevada, Reno, Western Carolina University, and Saint Anselm College. Past sites have included San Jose State University, Rutgers University, UNLV, Duke University, and University of Georgia.
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 schools also field teams. The competition is held in June, on the first Saturday after Memorial Day.
In 2022, 120 teams competed with about 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 it 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.
The contest is sponsored by D. E. Shaw & Co. Contest supporters are the American Mathematical Society, Mu Alpha Theta (the National Mathematics Honor Society for High School and Two-Year College students), Star League, Penguin Books, and Princeton University Press.
Competition format 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. Only 12 students nationwide received a perfect score in 2014. This round's format is similar to that of the Target Round in MATHCOUNTS. 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.
The teams are scored based on the number of points they attained with the maximum being 300 points. Team score ties are broken by first considering the sum of the Team and Power Rounds, then the Relay Round total.
At the end, there is a set of tiebreaker questions to determine the top 20 participants, who receive cash prizes from D. E. Shaw & Co. Each student tied for the highest score (or the highest two scores if there are fewer than 20 tied with the top score) is given up to three tiebreaker questions, one at a time, with the goal of answering correctly as quickly as possible. As soon as a student answers a tiebreaker question correctly, they have finished the tiebreaker. Students are then ranked by individual round score, followed by the time to answer the first tiebreaker question correctly, then the time to answer the second tiebreaker (if applicable), then the third. Students are given 10 minutes to answer the first tiebreaker question, and 6 minutes to answer each of the second and third tiebreaker questions.
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.
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.
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:
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, which moved to the University of Alabama in Huntsville in 2020.
The 2006 competition saw significant expansion of about 25% more participants than ever before. Attendance at the western site, UNLV, nearly doubled.
Due to the COVID-19 pandemic, the ARML competition was not held in 2020, and it was only held virtually in 2021.
In 2025, as a result of printing and procedural errors at one of the ARML sites, the last individual problem pair (problems 9 and 10) was discarded. Thus, the maximum individual score in 2025 was 8, and all competitors who achieved this score were invited to participate in the tiebreaker round.
Past team winners
Year TeamResults from before 1992 are taken from . This site may not be accurate; it is wrong in at least one year of Division B standings. Score 1976 New York City A 117 1977 Massachusetts A 148 1978 Fairfax-Montgomery 135 1979 New York City A 129 1980 New York City A 113 1981 New York City A 166 1982 New York City A 132 1983 New York City A 132 1984 New York City A 162 1985 Montgomery County, Maryland A 157 1986 New York City A 183 1987 New York City A 170 1988 Chicago A 197 1989 Chicago A 187 1990 Ontario A 197 1991 Ontario A 200 1992 Georgia A 172 1993 Thomas Jefferson A 190 1994 New York City A 183 1995 New York City A 126 1996 San Francisco Bay Area A 179 1997 Minnesota Gold 125 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 2014 PEARL (Phillips Exeter Academy Red Lions) A 260 2015 San Francisco Bay Area A 2112016San Francisco Bay Area A2102017San Francisco Bay Area A2452018Thomas Jefferson High School for Science and Technology A12342019Thomas Jefferson High School for Science and Technology A12452021SFBA / NorCal Pink2592022SFBA / NorCal A12492023SFBA / NorCal A12232024Lehigh Valley A12292025Lehigh Valley A12342026Texas Gold236
Past individual winners
Year Team 1977 Randal Dougherty (Fairfax County/Montgomery County) 1978 Fred Helenius (New York City A) 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) 2014 Darryl Wu (Washington A) 2015 Brice Huang (West-Windsor Plainsboro A) 2016 Daniel Kim (Bergen County Academies) 2017 Brian Reinhart (Florida A - Oxbridge Academy) 2018 Luke Robitaille (Texas A1) 2019 David Chen (Thomas Jefferson A1) 2021 Luke Robitaille (Texas A1 Gold) 2022 Luke Robitaille (Texas A1 Gold) and Christopher Qiu (Lehigh Valley A1) 2023 Sargam Mondal (Central Jersey A1) 2024 Alexander Wang (Lehigh Valley A1) 2025 Christopher Qiu (Central Jersey A1) 2026 Channing Yang (Texas Gold)
References
External links ARML homepage ARML Forum