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.
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, although this varies from year to year) 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.