ARML---Fire, Ice, and Lightning

The American Regions Math League (ARML) is a national math contest for teams of fifteen high school students. Existing for 31 years, it takes place the Saturday after Memorial Day simultaneously at Penn State, Iowa, and Las Vegas (previously San Jose).

Many states, such as Massachusetts, Georgia, Texas, Ohio, and Washington, have all star teams, usually an A team and a B team. Some major metropolitan areas, such as New York City, Chicago, and San Francisco Bay Area, do the same, often having as many as five teams, due to their tighter organization. Regional areas, such as Montgomery (Md.), Howard County (Md.), Bergen County (NJ), and Lehigh Valley (Pa.), are also represented. Finally, specialized schools, such as Thomas Jefferson (Va.), Phillips Exeter (NH), and AAST (NJ) are perennial powers. There are usually about 100 teams.

The contest consists of four parts. The fifteen team members work together to answer 10 Team Questions in 20 minutes, and to derive formulas and write proofs about a novel topic in a 60-minute Power Question. In the Relay portion, they are divided into five groups of three. Each group of three does the same thing. The second and third member have a question which says "Let x = the number which you will receive, and answer a certain question involving the number x." The first person has an ordinary question. The first person passes an answer to the second, and the second to the third. Only the third person's answer counts. You have 6 minutes to accomplish this, and get double credit for accomplishing it in 3 minutes. There are two relay rounds. Finally, there is an Individual portion. In each of four rounds, a student must answer two questions in 10 minutes.

A professor at Lehigh University, I founded the Lehigh Valley ARML team in 1993. Although I had been conducting a Lehigh University High School Math Contest since 1981, I had never heard of ARML until Johanna Miller, a sophomore who won my contest in 1993, told me about it. As a freshman, she had been on the Central Pa team, organized out of Penn State, but so dispersed that they had no practices. She suggested that we form a Lehigh Valley team and have practices. Moreover, Keystone Consulting Engineers, of which her father was a Vice President, would sponsor the team. They have continued to be one of the sponsors of the team, long after Johanna's graduation and now even after her father's retirement.

I select the team based on performance in my LU Contest, held in early March. We have practices almost weekly throughout the spring. Practices mainly consist of practicing old ARML contests. Rather than spending valuable practice time going over solutions of problems, I give a packet at the end of practice consisting of all the problems and solutions, and strongly suggest that the students study these.

We have one main instructional handout, a "Playbook" written by Assistant Coach Ken Monks, a professor at University of Scranton. Monks obtained his PhD at Lehigh in 1989 under my direction. We have been close friends since that time, as we share many interests such as marathon running and fractals. He became Assistant Coach in 2003, when his talented daughter Maria joined the team as a freshman. The drive from their home in Hazleton to Lehigh requires 60 minutes. It has become a family affair for them, as Ken's son Keenan joined the team as a sixth grader in 2005, and in 2006, when we expanded to three teams, Ken's wife Gina started coming to practices to help with logistics. The team members love her home-baked goodies. Monks' 28-page "Playbook" contains a wealth of useful formulas.

The Lehigh Valley team had varying success from 1993-2002, with our best performance 14th/85 in Johanna Miller's senior year and our worst 51st/90 in 2002 when we had a very young team. During that period virtually all the team came from the Lehigh Valley, which consists of Allentown, Bethlehem, Easton, and adjacent communities. We had an occasional member from 40 to 50 miles away.

One team that usually beat us was the inappropriately-named All Penn team, which comprised the greater Philadelphia region. Their star from 1997-2000 was Sasha Schwartz, from Radnor High School. Sasha finished 2-1-1-1 in my Lehigh contest, and led the All Penn team to ARML finishes as high as 9th. He was a gold medalist on the US team in the International Olympiad and later a Putnam Fellow (top 5) twice at Harvard. Interestingly, he now works for the hedge fund D. E. Shaw, which is the principal ARML sponsor. D. E. Shaw sponsors ARML in order to ultimately attract top ARML participants to work for them.

In 2002, I saw on the internet the list of the 200 students nationwide who were taking the USAMO exam, the third elimination exam for the US Olympiad team. I noticed the name of 8th grader Ameya Velingker from Orefield Middle School. This school is in the Lehigh Valley, 15 miles from Lehigh. I called the family and invited the boy to be on my ARML team. He was happy to do so, and told me about a student named Jason Trigg who was on the state MathCounts team with him and lived in suburban Philadelphia 75 miles away. He said that Jason's abilities were similar to his, and that he thought Jason might like to be on the team, despite living so far away.

Ameya was right on both counts. In my 2003 Lehigh contest, Jason was the first 9th grader ever to be the overall winner, and Ameya finished second. As 10th graders, they tied for first with 37 right out of 40, while the next highest person had 29. As 11th graders, Ameya had the first perfect score in the 25-year history of the contest, while Jason got 39/40. Finally as seniors, Jason was first and Ameya third.

The 2002 team included three 8th graders and four 9th graders. This group grew together. Their finishing position during the four years for those 9th graders was 51, 22, 10, and 1. That's called improvement! Winning the national championship in 2005 was a peak experience for all concerned. Maria Monks was the same age as Jason and Ameya, and joined the team in 2003. She told her dad that joining the LV ARML team was, at the time, "the best thing that ever happened to me." These eight formed a very tight-knit group, becoming best friends, and developing the great teamwork that enabled them to win the national championship in 2005, despite scoring lowest of the top ten teams in the Individual portion. Next year, three will be at Harvard, three at MIT, and two at Penn State's Schreyer Honors College.

Another contributor to our success was the disintegration of the All Penn team. In 2004, when we finished 10th, we took 20 people to the contest, our regular team plus five alternates, while the All Penn team only had 10. It was natural for our five alternates to fill out the remainder of their roster. In the March 2005 Lehigh contest, some Radnor students, who had done very well in the contest, asked if they could be on the Lehigh Valley ARML team. They had gotten to know Jason, Ameya, Maria, and other LV ARML mainstays at other contests, and witnessed the camaraderie and talent of our team. I said Yes, if they came to practices. Without Radnor, the All Penn team ceased to exist, and other students from the Philly suburbs joined our team. With a little additional recruiting, I was able to have two teams for the 2005 season.

Having two teams seems to be almost a necessity for a top-5 finish. It gives the coach more to choose from in order to field an excellent A team. Most areas which send two teams call them A and B. There had been a few variations such as Texas Gold and Texas Silver. We chose the names Lehigh Valley Fire and Ice. This came about in the following way:

In one practice, I wanted to divide the students into two groups of equal ability. Most of the surnames of the top people were in the second half of the alphabet, and so to get equal teams, I said that one group would be Ho-T; i.e. their surnames begin with Ho through T, while the other team would be from the rest of the alphabet. I said we could call these the HoT and Cold teams. It was a short step from there to Fire and Ice for the names of our A and B teams.

The glory of winning the national championship in 2005 made it easy to recruit for 2006. We decided to make an effort to recruit middle school students who had finished near the top of the state in MathCounts. This would help us to build for the future. Thus we naturally expanded to three teams. Lightning was a fairly obvious choice for the third name. The Fire, Ice, and Lightning combination occurs in Pokemon and in video games, I am told. It also led to a very nice T-shirt design, as you can see in the accompanying photo. We wondered whether other teams would follow our lead in choosing more interesting team names, and were pleased to see that in 2006 the South Carolina A and B teams had changed to the Grits and the Shrimp.

Finishing third (out of 113 teams) in 2006 was a slight comedown after being first in 2005, but was still something to be proud of. The two teams that beat us, North Carolina A and Montgomery A, each had two of the 12 finalists for the Olympiad team, and Montgomery's Brian Lawrence had the only perfect score on the USAMO exam. Our team had none of the top 12, and only Jason Trigg in the top 25. But we won the Song Contest!

One activity to occupy students during the final stages of scoring is a Song Contest. Students are encouraged to write and perform a song about math or ARML. There is a preliminary round on Friday night in which three finalists are selected. The final round was held in the same place as the final part of the ARML contest, the 16,000-seat Bryce-Jordan Center, where Penn State plays its basketball games. Our entry in the finals was a mathematicized version of "Every time we touch" by Cascada. Our lead singer, Yale-bound senior Kurt Schneider, arranged to have the background music played from his I-Pod through the sound system of this huge arena. His mic'd voice blended well with the music and was nicely accompanied by a dance routine performed by eight male LV ARML members. The winner was decided by loudest applause, for which it was worthwhile that we had three teams.

This illustrates that an ARML team involves more than just math. These students form bonds and have great times together. Their favorite activity is a game called Mafia, which involves mostly role-playing and deduction, as far as I can tell. Some of them arrive early at practices to play it, and many of them play it on the school bus that we ride to Penn State, and in the dorm the night before the contest, until lights out at midnight. Ken Monks' home in Hazleton is 1/3 of the way from Lehigh to Penn State. During Maria's first three years on the team he did the reasonable thing of driving her directly from home to Penn State. But this year she and younger brother Keenan were so desirous to join in the bus activities that they prevailed on Dad to drive them to Lehigh, in the opposite direction from Penn State, so that they could join the Mafia game on the bus with their friends.

Much more information about the Lehigh Valley ARML team can be found at I would encourage teachers in eastern Pa to prepare a group of students for the Lehigh contest March 3, 2007, by having them practice from previous contests, available from the above website. Then these students, too, may possibly join the Lehigh Valley Fire, Ice, or Lightning.