About Lemmas

Lemmas is a training tool for competition math: AMC, AIME, and HMMT. It gives you real contest problems just above the level you can already solve, and it brings back the problems and formulas you missed until they stick.

Where the problems come from

The bank holds 6,190 problems. 5,727 are official contest problems:

Every official problem shows its source attribution and links to the original. The other 463 are Lemmas Originals. 90 were written for Lemmas, with answers computed and checked by a program rather than typed in by hand. 373 were generated with AI assistance; each was solved again independently and kept only if the two answers matched, and each carries a short note on the idea behind it and on why its wrong choices are tempting. They are always labeled as originals and never presented as past contest questions.

How difficulty is measured

Each problem has a difficulty rating from 1 to 100 on one scale shared by every contest, so an AMC 8 problem and an AIME problem can be compared directly. Practice shows it as a percentile against every other problem in the same subject, so the 90th percentile means harder than 90% of them. Lemmas does not yet have enough student attempts to rate problems by how often people solve them; when it does, this page will say so.

What makes us different

Lemmas is made by high schoolers, not a company. We’re two students who were recently exactly where you are, trying to get better at contest math without much to go on: no coach to ask, no clear idea what to work on next, and a lot of guessing about what was actually worth our time. We built the tool we wished we had.

A lot of good prep costs money, and we understand why. Teachers and programs have to get paid somehow. We don’t have that problem. Lemmas is free, there’s no card to enter, and we’re not trying to make money off you. The only reason it exists is that we think more people should get a real shot at competition math, not just the ones who can afford it.

Who made Lemmas

Lemmas was founded by William Sun and Surya Raghavan.

• William Sun, co-founder. Three-time AIME qualifier.
• Surya Raghavan, co-founder. Four-time AIME qualifier.

Get involved

Lemmas is still small, and the people who use it shape it. There are a few ways to help:

• Tell us what to fix or build. Post on the Feedback board to report a wrong answer, a confusing problem, or a feature you want, and vote on what others have posted.
• Share a solution. Once you have solved a problem, you can post your own approach for others to read.
• Bring Lemmas to your team or club. If you coach or run a math circle and want to use Lemmas with students, write to lemmas.official@gmail.com.
• Help with problems. If you hold rights to contest problems, or want to write original ones, get in touch through the contact page.

Questions

What does it cost?

Nothing. An account needs a username, an email and a password, and there is no card to enter.

I’m new to competition math. Where do I start?

Start anyway. You choose a focus subject, and a ten-problem first set in it places you (you can skip it). After that, problems begin a little above what you can already solve. If that is early AMC 8, that is where you start.

Who runs Lemmas

Lemmas is a two-person project, run by its co-founders in New Jersey, US. They choose and check the problems, build the site and read what people send. Questions, corrections and rights requests can go to either of them, to lemmas.official@gmail.com, or through the contact page.

• William Sun: will.sun0411@gmail.com
• Surya Raghavan: suryaraghavan10@gmail.com

See the privacy policy for what an account stores, and the terms for how the problems may be used.