Three rounds a year. Five problems a round. A full month to solve each one. Zero dollars to enter. And a score of 68 out of 75 opens a door to the AIME that has nothing to do with your AMC score.
That is the entire pitch of the USA Mathematical Talent Search, and if you have only ever sat a timed contest, it is worth reading twice before you decide it sounds easy.
Key Takeaways
- USAMTS runs 3 rounds a school year, 5 problems each, roughly a month per round, and costs nothing to enter.
- One puzzle problem plus four problems that require a written proof, not a bubbled answer.
- A total of 68 points out of 75 across the year qualifies you for the AIME, a separate route from the AMC.
- You may use books, the internet and software like WolframAlpha while working, but you must show your sources and cannot ask another person for help.
What USAMTS Is
USAMTS is a math competition built around research time instead of exam time. Each of its three yearly rounds gives you five problems and at least a month to work through them, alone, with your notes and the internet open the whole time. One problem is a short-answer puzzle.
The other four ask for a full written justification: a proof that convinces a grader you understand why the answer is correct. There is no proctor and no bubble sheet. Getting the right number on a proof problem earns you nothing by itself if the reasoning behind it never makes it onto the page.
Most students meet USAMTS after they are already deep in the AMC and AIME world, and it’s worth placing on the ladder before you decide whether it’s for you. If your student is aiming further up, at the full US pathway to the IMO, USAMTS is one of several legitimate on-ramps: a way to build proof-writing muscle long before USAMO makes that skill mandatory, at a pace no timed contest allows.
That pace is the whole point of the design. A timed contest measures how fast you can recognize a technique you already know.
USAMTS measures something else: can you sit with a problem you don’t immediately know how to solve? Can you try several approaches, throw most of them out and still land on a correct, well-argued answer a month later? Those are different muscles, and a student can be strong in one without being strong in the other yet.
Who Can Enter, and Who Can’t
USAMTS is open to any student who is a citizen or resident of the United States and has not yet finished high school, which means middle schoolers can enter alongside seniors.
If you live abroad but hold US citizenship, you can still compete, though you will need a US address on file to receive any prize. If you’re outside the US and don’t hold citizenship, this particular contest isn’t open to you, and your time is better spent on something like the IMO pathway or your own country’s national olympiad instead.
Registration itself has no separate application or interview. You sign up with an email address, and once you’ve registered in one year you don’t need to do it again for the next.
How a Round Works
Three Rounds, Five Problems, a Month Each
| Round Structure | Detail |
|---|---|
| Rounds per year | 3 |
| Problems per round | 5 (1 puzzle, 4 proof) |
| Time per round | At least one month |
| Cost | Free |
The exact opening and deadline dates shift from year to year, so check the current schedule directly on the official USAMTS rules page before you plan around it. What stays constant is the shape: three rounds spread across the school year, each one giving you far longer than any AMC or AIME problem set ever will. You don’t have to enter every round to take part. Plenty of students start at Round 2 or Round 3 in their first year and pick up the full three-round rhythm the following season.
The Puzzle and the Four Proofs
Problem one is usually the fastest to answer and the easiest on a student used to multiple choice: get a number, show a bit of work, move on. Problems two through five are a different exercise entirely. You have to write a proof that a grader can actually follow, in complete sentences, with every claim justified instead of asserted.
A correct final answer with no supporting argument scores close to nothing on these four; the number was never the point. Graders return personalized written feedback on your solutions, and they have discretion to take off a point for a solution that is mathematically correct but poorly written or hard to follow, on top of whatever the mathematics itself earns.
Getting the right answer is the easy half of a USAMTS problem. Writing it down so a stranger can follow your reasoning, without you standing there to explain the gaps, is the harder half, and the one most students have never practiced.
What You’re Allowed to Use
This is the rule set that surprises students most. You may use books, the internet, calculators and computer software to research and work through a problem. That includes Mathematica, Maple, Matlab, Desmos and WolframAlpha.
If a key step of your solution leans on one of those tools, you have to include the exact query or code you ran along with its output, so a grader can check that you used it correctly. Write your own program to search for a pattern and the same rule applies: the source code and enough explanation for a grader to follow it belong in your solution.
What you cannot do is get live help: no forum posts, no tutors, no discussing the problems with a classmate or a parent before the deadline. General background research with an AI tool is fine; asking one to solve a specific step for you is not. It runs on the honor system, and every solution has to be your own.
Scoring, and the 68-Point Door to the AIME
Each problem is worth 5 points, so a full year across three rounds is scored out of 75. Score 68 or higher and you qualify for the AIME, the same invitational exam that AMC 10 and AMC 12 high scorers earn a spot in. Do the arithmetic and the door looks less intimidating: 68 out of 75 means you can afford to give up roughly seven points across all fifteen problems in a year, the equivalent of missing something close to one and a half problems outright. That is a real margin for a student who thinks carefully but slowly, compared to a 75-minute AMC clock that punishes exactly that kind of thinker. Top scorers also earn something beyond the AIME door. The top 45% of participants each year, capped at 500 recipients, receive prize books, software subscriptions and a T-shirt, according to the official prizes page. The AIME door is still the number worth planning around.
If you want a sense of what a good AMC score even looks like for comparison, our AMC scoring guide walks through the cutoffs on the timed side of this same ladder, so you can see how the two routes compare.
Should Your Student Do USAMTS?
Here is the honest split. Gonit’s practice is built around multiple-choice and interactive-input questions, with a hint available before you answer and a step-by-step explanation waiting after a wrong one. That format is exactly what trains the skill the AMC and AIME score: get to the correct value, fast, under pressure.
It does not train proof writing, and four of USAMTS’s five problems every round are proof writing. A student who has only ever practiced multiple choice will find the jump to “justify this rigorously in paragraphs” genuinely uncomfortable at first, and no amount of speed drilling prepares you for a grader marking down a correct answer because the argument around it doesn’t hold together.
So the recommendation splits in two. Use Gonit for the AMC and AIME computational lane, where fast and correct is the whole game. For the USAMTS lane, you need separate practice at writing an argument. Get it from a proof-writing book, a teacher willing to mark up your drafts, or a coach who reads full solutions rather than final answers.
USAMTS fits a student who thinks well but doesn’t always finish first, or one who has come close to the AIME cutoff before and wants a second route in. It’s a poor fit for a student who isn’t yet comfortable putting a mathematical argument into full sentences, or for anyone outside the US, who isn’t eligible to enter at all.
If you’re starting this week, pick one of the four current proof problems, write a full solution in complete sentences, and have someone who didn’t help you solve it try to follow your writing without asking you a single clarifying question.
How to Enter
Registration is free on the official USAMTS site: you sign up with an email address, and if you registered in a past year you don’t need to do it again.
Once you’ve written your solutions, submit them as a single PDF of no more than 20 MB through the site’s submission process, or by mail if you prefer paper. Online submissions are due by 10 p.m. Eastern, 7 p.m. Pacific, on the deadline day, and work that arrives after that is not accepted.
A phone photo or scan of handwritten pages is completely acceptable, so you don’t need special software to type up a proof.
Make Preparing for Math Olympiad Simple!
FAQ
When does USAMTS start?
USAMTS runs three rounds across the school year, each with at least a month to work. Exact opening and deadline dates change year to year, so check the current schedule on the official USAMTS rules page rather than assuming last year’s dates.
What is USAMTS, in one line?
A free, proof-based math contest with three rounds a year, five problems per round, and a month to solve each one at your own pace.
Are you allowed to get help on the USAMTS?
You can use books, the internet and approved software like WolframAlpha. What you can’t do is get "live" help from a tutor, a forum or a classmate. Every solution has to be your own work.
Does a USAMTS score qualify you for the AIME?
Yes. A total score of 68 or higher out of 75 across the year qualifies you to take the AIME, separately from qualifying through the AMC.
Related guides
- AMC 10 vs AMC 12: Key Differences and Which to Take
- HMMT: Format, Dates and How to Prepare
- ARML: Format, Dates and How to Prepare
Donald A. Kroll holds a Master's degree in Mathematics and has spent years helping students prepare for competition-level problem solving. Based in the United States, he writes about study strategy, test readiness, and the habits that turn steady practice into real results.
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