This page contains the rules of the USAMTS in their entirety. To see a guide on how to participate, see our Getting Started page.
- Participants must be citizens or residents of the United States. US citizens living abroad are also eligible to participate, but they must provide a US address to receive prizes.
- Participants must not have completed high school. Middle school students are allowed to participate.
Solving the Problems
- Participants may not discuss the problems with others before the deadline for solution submission.
- Participants may use resources such as books or the internet to do mathematical research to try to solve the problems, but they may not use “live” help. For example, they may not ask for help on online forums or tutorial services.
- Participants are expected to show all work in their solutions. Students may cite (without proof) results from a reputable source, such as a widely accepted book or peer-reviewed journal, or from a professionally maintained reference website such as Wolfram MathWorld. For the purposes of the USAMTS, websites without expert oversight of content, such as the Art of Problem Solving forums or Wikipedia, are not citable sources. Furthermore, students may use “well known” theorems without citation, though the names of such theorems should be given. The USAMTS graders will decide, in their sole judgment, whether a citation is legitimate or not or if a theorem is “well known.” If in doubt, participants should prove all necessary results.
- Except where otherwise noted in problems, participants may use calculators and computers to solve problems. In this case, the participant must explain the program that was used to solve the problem. Symbolic manipulation calculators and mathematical programs such as Mathematica, Maple, Matlab, Desmos, and WolframAlpha are considered programs for this purpose. Therefore, if a key step of a participant’s solution uses these tools, the participant must include their inputs and outputs so the graders can verify that the software was used correctly. If a participant writes their own computer program to solve a problem, the source code should be included in the solution along with sufficient supplementary explanation so the grading team can understand what the program is doing.
- The use of AI tools such as ChatGPT is permitted, but participants should be aware that such tools often produce incorrect information and can’t be relied upon without additional verification. Again, if a key step of a participant’s solution uses these tools, they must include the inputs and outputs in their submission. If an AI tool leads a participant to results from a reputable source, the participant may use those results without proof, given that they cite the reputable source.
- In most cases, the USAMTS staff will not answer a question about a problem while a round is in progress. If a student believes that a problem is unclear or otherwise has a concern about a problem, they may contact the USAMTS staff at firstname.lastname@example.org. If a clarification is deemed necessary, the staff will provide a clarification to all participants. Students should refrain from asking clarification questions elsewhere, as this may inadvertently give some participants hints about how to solve the problems.
- Students who wish to participate must register on the USAMTS website and provide an email address to which USAMTS correspondence may be sent. Students who have registered in a past year do not need to register again. There is no fee for participating in the contest.
- Solutions can be submitted by web upload (preferred) or mail. Solutions submitted by any other method will not be accepted.
- For the 2023–2024 year, students are permitted a 24-hour extension for one of the three rounds. While this policy is intended to account for extenuating circumstances, a student may use the one-time extension for any reason. Students using the extension must submit online using our Submit page.
- Solutions must contain the participant‘s name, username, and USAMTS ID number on every page. The round and problem numbers must also appear on every page.
- Do not use color (except decoratively), and use a white background. The solutions may be printed and photocopied in black-and-white for grading.
- Solutions must be on Letter paper (8½ × 11 inches).
- Any handwriting must be clear and legible. The graders will not try to decipher sloppy handwriting.
- While a participant may choose not to solve every problem, the problems that are solved must appear in order in the participant’s submission.
- No page should contain work for more than one problem. In other words, each problem must start on a new page.
- Participants may only submit one set of solutions for each round. Participants submitting online have the option of resubmitting, in which case their previous submission will be deleted.
- Students are encouraged but not required to use LaTeX to typeset their submissions. More information, along with LaTeX templates and resources, can be found on our Getting Started with LaTeX page.
- All online submissions must be done through our Submit page. Online submissions must be a single PDF file at most 20 MB in size.
- Solutions submitted after the deadline will not be accepted. The deadline is for online submissions is 10 p.m. Eastern / 7 p.m. Pacific of the deadline day.
Mail submissions should be addressed to:
USAMTSWe recommended that participants keep a copy of their submissions for themselves.
55 Exchange Place
New York, NY 10005
- Solutions submitted after the deadline will not be accepted. Mail solutions must be postmarked on or before the deadline day. It is OK if a mail submission arrives after the deadline.
- All solutions must be stapled together.
Grading, Scoring, and Prizes
- Solutions will be graded by a group of mathematicians and university mathematics students. Participants can view their scores and feedback by logging on the USAMTS website and visiting the My Scores page.
Each solution will be given a score of 0, 1, 2, 3, 4, or 5.
Solutions will be graded on mathematical correctness, writing
style, and the clarity of the explanations. In particular, points
may be deducted if the following guidelines are not met:
- Solutions should not contain scratch work or conjectures.
- With the exception of the puzzle, solutions should be written in complete sentences.
- With the exception of the puzzle, every result or claim in a solution should be justified, either by a citation or a rigorous proof.
- The grading criteria for each problem will be published on the USAMTS website at the conclusion of the grading. Students who believe that a clear error has been made in the grading of one of their solutions may file a protest with the USAMTS Director on the Protest page. Disagreement with the grading criteria is not a valid reason to protest. Late protests will be disregarded.
- Prizes will be awarded at the end of the contest year.
- The USAMTS Director reserves the right to make clarifications or modifications to these rules in the best interest of the contest.
- The USAMTS Director may expel any participant from the contest for a gross failure to abide by these rules.