What is ARML?

The American Regions Mathematics League's annual competition brings together the nation's top math students for a weekend of friendly competition. In 2024 the contest involved 113 fifteen-member teams from almost every state. International teams from China, Korea, Philippines, Macao, Turkey, Colombia, and Indonesia have participated in the past. Check out the 2024 Competition for sample problems.

What is Colorado ARML?

Thirty to forty high school students will represent the state of Colorado at the ARML Competition in May 2025. We will meet throughout the year to prepare for the competition. Meetings will emphasize teamwork, collaborative problem solving, and student presentations of solutions.

How will the Colorado ARML teams be chosen?

Two fifteen-member teams will be selected to represent Colorado at the national ARML competition.

Team tryouts will take place in March. Selection will be based on the following criteria: tryout results, past contest performance, previous ARML experience, grade level, and math circle participation. Team members typically rank among the top in the state in the AIME and AMC contests. Minimum background: Algebra II/Trigonometry.

When and where will meetings take place?

Practice sessions will be held on the CU Boulder campus. See the meeting schedule for dates and times.

After team tryouts we will have at least five team practices to prepare for the ARML competition. We recommend that team members attend as many practices as possible, with a minimum requirement of three meetings. Students who live more than 2 hours from Boulder are excused from this requirement.

How has Colorado ARML placed in recent ARML competitions?

In 2023, 2021, and 2006, the Colorado Team placed 1st in the B Division. Colorado students have ranked among the top ten individuals in the competition in six different years. Other results are listed at the top of this page.

What is the ARML Power Contest?

The ARML Power Contest is a two-round team competition that takes place during the school year. It is similar to the Power Round of the ARML Competition. Any Colorado student is welcome to participate. See the meeting schedule for dates and times. The math circle ranked among the top seven teams for ten consecutive years and won first place in 2016.

How much will it cost?

There is no charge to attend math circle meetings or ARML practices. For Colorado ARML Team members, there are travel and registration costs (TBD) for the trip to the University of Nevada in Reno.

What if I can't make the trip to ARML? Can I come to the meetings anyway?

Yes. You're welcome to join us to work on challenging math problems.

Who will be leading the ARML practice sessions?

Directors Thomas Davids and Silva Chang will be coaching the Colorado ARML Team.

How do I join?

The best way is to fill out a registration form, then come to the next math circle meeting.

Team Round

The team will have 20 minutes to work together on 10 problems, each worth 5 points.

Power Question

This problem, broken into a sequence of mini-problems, is a theoretical exercise requiring the writing of mathematical proofs. The team will have 60 minutes to write complete solutions, worth up to 50 points.

Individual Questions

There will be 10 individual questions, administered in pairs, with a 10-minute time limit for each pair. Each individual question is worth one point, for a maximum of 150 points per team.

Relay Round

Each team of fifteen will be split into five three-person Relay teams. Each Relay team will compete in two Relay Rounds. On each Relay, 5 points will be awarded to each Relay team that correctly completes the Relay within 3 minutes, and 3 points will be awarded for a correct answer within 6 minutes. Only the last answer submitted by each Relay team will be counted. A total of 50 points is available to each team on the Relay Round.

Each Relay team member will receive a different problem. TNYWR stands for the number you will receive. When the first person solves his (or her) problem, he writes the answer on a piece of paper and passes it to the second person. The second person needs that number to solve his problem (the number is referred to as “the number you will receive,” or TNYWR). When the second person comes up with an answer, he passes that number to the third person. When the third person gets an answer, he writes it on an official answer slip, and that slip will get handed in. The third person of each group should take all the official slips and fill in the complete team information on each.

The second and third persons can usually do most of their work before getting a number from the person ahead of them. Nothing may be passed except a number—NO COMMENTS, NO OTHER INFORMATION. You should double underline the answer you pass in case it accidentally gets turned upside down and looks like a different number. You may continue to pass answers, even if they are the same as before. NOTHING MAY BE PASSED FORWARD. IF YOU RECEIVE AN ANSWER THAT IS IMPOSSIBLE FOR YOU TO USE, JUST WAIT AND HOPE THAT A DIFFERENT ANSWER WILL GET PASSED TO YOU!

The third person may hand in an answer only at the 3-minute mark and at the 6-minute mark. If the answer handed in at 3 minutes is correct, and no answer is handed in later, it gets maximum points. If any answer is handed in at 6 minutes, the previous answer is discarded by the proctor (even if the number is the same as before!), and you can get only the lower number of points, provided the answer is correct. OBVIOUSLY THE THIRD PERSON SHOULD NOT HAND IN THE SAME ANSWER A SECOND TIME! The announcer will give a 15 second warning before the 3-minute and 6-minute time limits. If you are handing in an answer then, put it on the appropriate answer slip, hold that slip up, and the proctor will collect it.

Additional ARML resources can be found in the Members section. for the password.