This is the authoritative version of the rules for the 2021 LMT Spring Online competition. The entire rules section has recently been updated to reflect the current status of the competition. Please note that LMT is not typically an online competition and that our archive reflects the usual format of the competition, which involves multiple rounds, rather than this fall's LMT Spring Online competition, which only has two rounds.


The competition is targeted towards 6th, 7th and 8th grade students, although younger students may also compete.

Teams may contain up to six members, and must have at least one member. Registering teams across different schools is allowed, and encouraged. With the exception of team members from the same household, teams are expected to collaborate remotely. Please respect local social distancing guidelines and do not meet in person to work on LMT!

Teams must designate one member as captain. The captain is in charge of registering their team.


Each team will have the opportunity to register in either Division A or Division B. Division A will consist of a more challenging Team Round and is designed for teams with more experience in math competitions, while Division B is designed for teams that are less experiences or new to math competitions. The Guts Round will be the same for both divisions. Awards for the two divisions will be determined separately.

Teams consisting of students from multiple schools or organizations must participate in Division A.

Test Information

The competition consists of two rounds: the Team Round and the Guts Round.

The Team Round consists of 30 short answer problems to which all answers are nonnegative integers. The problems are arranged in order of increasing difficulty, and the problems will be worth 20-40 points, for a maximum of 600 points for each team on this round. The problems will be made available on the homepage of the LMT website on Friday, April 30th, at 12:00 pm ET. Teams will have until Friday, May 7th, at 11:59 pm ET to submit their answers using the link provided by email.

The Guts Round consists of 36 short answer problems given in twelve sets of three. Teams are given 75 minutes to solve as many problems as they can. The guts round is an exciting, fast-paced round in which teams solve problems as quickly as possible, then submit answers for real-time grading. When a team is ready to submit answers to a set of three problems, the team captain will enter their answers online and the next set of problems will be distributed. Real-time scores of all teams will be displayed on a livestream. The problems are arranged in order of increasing difficulty, and the number of points per problem increases from 5 to 15 for later sets of problems, for a maximum of 600 points for each team on this round, which results from two times the raw score. The round will begin promptly on Sunday, May 9th, at 3:00 pm ET with the release of the first set of problems. The round will end at 4:15 pm ET.

You may have noticed that past years' competitions have included individual and theme rounds, whereas this fall's competition only has a team and guts round. As stated previously, the LMT has, in going online this fall, temporarily adopted the more streamlined competition format described above.

For instructions on submitting answers, see the Submitting Answers and Editing Team Information section below.

With the exception of standard four-function calculators only allowed on the Team Round, computational aids including but not limited to scientific and graphing calculators, computer programs, protractors, rulers, compasses, slide rules, and software such as Geogebra, Mathematica, and WolframAlpha, are not allowed. Communication of any form between students on different teams is similarly prohibited, and any team caught either giving or receiving an unfair advantage over other competitors will be disqualified. What constitutes cheating will be up to the final discretion of the competition organizers, who reserve the right to disqualify any team suspected of violating these rules.

Submitting Answers and Editing Team Information

During registration, your captain will be emailed a link to your team’s homepage. This is where you will be able to update team information and answer submissions. We recommend that your captain distribute this link to the rest of the team so that the entire team has access.

Once on your team’s homepage, to enter or edit team answers, click the link next to “Submission Link: “. Team name, team member names, and grades may be edited through the homepage as well. Remember, team member names must be the real names of the people on your team, and the team name must be appropriate.


If you believe that there is an error in one of the questions, email us at Clarifications for problems will be posted on the LMT homepage should they be necessary.

Scoring and Prizes

Point values of problems are noted in the previous section. The top five teams in the team and guts rounds will be recognized from each division. In addition, the top ten overall teams from each division will be recognized and the top five teams from each division will receive prizes. Prizes have been provided on behalf of our generous sponsors and include AoPS gift certificates, RSM classes, Wolfram products, XYZ Press books, and gift cards. Note that prize distribution is subject to change and will be finalized closer to the day of the competition.


In general, ties will not be broken. In the case of a tie that affects the distribution of prizes, both teams will receive equivalent prizes.