LemmaTry the trainer
V1 · Building in public

Competition math, open to everyone.

The training ground that used to live inside elite prep schools — AMC, AIME, and MATHCOUNTS practice with adaptive problems, worked solutions, and AI-guided hints. Free, forever.

Try the trainer →See a sample problem
AMC · AIME · MATHCOUNTS
Contest-grade problems
$0
For every student
Handwritten geometry proofs, series identities, and Fibonacci spiral in navy ink on cream paper
Problem set · 2026
Preparing forAMC 8AMC 10AMC 12AIMEMATHCOUNTS

§ 01 · The gap

No student should be priced out of loving a hard problem.

Competition math has become an arms race of paid coaches, private classes, and $2,000 summer camps. A curious kid with an internet connection can find last year's AMC in a PDF, try three problems alone, and quit.

Lemma is the coach and the practice room, free. It generates fresh problems at your level, gives you a nudge when you're stuck, and shows the elegant solution when you're done — the way a good teammate would.

§ 02 · How it works

Four steps. One loop.

  1. i.

    Choose your problem

    Pick a contest, a topic, and a difficulty — from AMC 8 warm-ups to late AIME.

  2. ii.

    Work it, timed

    Answer on the real format — A–E bubbles or AIME three-digit entry — with a running timer for real contest pacing.

  3. iii.

    Submit your answer

    Type in your answer and get instant feedback on whether you got it right.

  4. iv.

    Review the solution

    Every problem comes with a full worked solution, so you learn the technique, not just the answer.

§ 03 · A taste

A taste of what's inside.

Every card in Lemma looks like this. Try it before you tap for a hint.

Try the full trainer →
AMC 10Number theory · Middle (#11–20)
#00512

What is the remainder when 1! + 2! + 3! + ⋯ + 100! is divided by 1001?

⏱ avg. 6 min

§ 04 · Who's building this

A note from the founder.

Justin Puno

Founder · Class of 2026

I qualified for the AIME six years running and got a perfect score on the AMC 8 in 2022. What I noticed along the way is that the biggest barrier to competition math isn't talent — it's cost. Coaches, camps, and problem books add up fast. Lemma is the tool I wish existed when I was starting out: unlimited practice, smart hints, and clean solutions, free for anyone who wants to try a hard problem.

6×
AIME Qualifier (2021–2026)
Perfect
AMC 8 Score (2022) — top ~131 nationally
Cum Laude
Phillips Academy Andover, 2026

§ 04 · Mission

“The kids who'll qualify for the AIME next year already exist. Most of them just haven't been handed the right problem yet.”

Lemma is free for students. Always.

§ 05 · Feedback

Let us know what you think.

Building this in public. Tell us what's confusing, what's missing, or what you'd want next.