Free Olympiad Math Practice — Untimed, with Stepwise Solutions

Olympiad-level practice with detailed stepwise walkthroughs. Type your answer to check, or reveal the full numbered solution on demand. Untimed · single problem at a time · no signup.

Free math olympiad practice problems with stepwise solutions

If you're prepping for AMC, AIME, USAMO, IMO, RMO, INMO, Pre-RMO, or Putnam, the single highest-leverage activity isn't watching lectures — it's solving real past problems and then carefully reading the worked solutions written by strong solvers. This page gives you that, free, untimed, in your browser.

Each session loads a fresh random problem with the math rendered in KaTeX and any geometry diagrams pre-built. Type your answer (with smart matching for fractions, radicals, decimals) or click Peek to compare with the official answer. When you're ready, expand the stepwise walkthrough — every solution starts with a key-insight paragraph explaining the technique, then numbered steps with all the algebra shown. Use the Print button to save problems as offline worksheets or PDFs.

Math olympiad pathways covered

The pool spans the major competition tracks. Use Next problem until you land on something from the path you're targeting:

AMC 10 / 12 path
US entry contest — 25 MCQ, 75 minutes. Try the timed mock.
AIME path
Integer answers 0–999, 3-hour invitational. Timed mock available.
USAMO / USAJMO
Proof-style problems. AIME-qualifiers' next step.
IMO & IMO shortlist
International Math Olympiad — the top of the global pyramid.
RMO / INMO (India)
Pre-RMO → Regional → Indian National → IMOTC selection.
Putnam
Undergraduate-level US competition — harder algebra and analysis.

How to use it

  1. Try the problem cold first. If it has a single boxed answer (about 56% do), type your guess and hit Check. Wrong is fine — that's how technique sticks.
  2. Reveal the walkthrough. Click Reveal stepwise solution to expand the full numbered solution. Read the key-insight line first; it usually names the technique.
  3. Trace your own attempt against the steps. Where did you diverge from the solution? That divergence is where the learning is.
  4. Click Next problem. Fresh random problem every time. Your session stats (attempted / correct / streak) save in your browser.
  5. Don't optimize for the streak. Stats are there to nudge consistency; revealing isn't failure. The point is learning, not raw accuracy.

Topics in the pool

The pool mixes the four major olympiad strands. Build the foundational toolkit with these free helpers:

Algebra & linear algebra
Polynomial identities, matrix work, vector tricks.
Geometry & trig
Power of a point, mass-point, identities, coord-bashing.
Combinatorics
Counting, pigeonhole, casework, generating functions.
Number theory
Modular arithmetic, Diophantine equations, parity tricks.

Frequently asked questions

What level are these problems?

Olympiad and pre-olympiad difficulty — AIME, USAMO, IMO-style training problems plus RMO / INMO / Pre-RMO and Putnam material. The pool draws from real past competitions across algebra, geometry, number theory, and combinatorics, with detailed numbered solutions written for instructional clarity.

How is this different from the AMC and AIME mock tests?

The AMC and AIME pages are timed competition emulators with scoring. This page is untimed practice — one problem at a time, full stepwise solutions on demand, no clock pressure. Useful for learning new techniques and reviewing worked examples.

Can I check my answer if it's a fraction or expression?

Yes. The Check button uses smart matching — fractions can be typed as 1/2 (matches \frac{1}{2}), radicals as sqrt(5), and decimals automatically compare against fractions. For matrix or vector answers, click Peek to see the expected answer rendered in math and compare on paper.

Can I print a problem with its solution?

Yes. Click Print on any problem. The print view includes the question and full stepwise walkthrough at print-friendly typography with an 8gwifi.org/math/olympiad source line — useful as offline worksheets or saved PDFs.

Does this cover the Indian Math Olympiad path (RMO / INMO)?

Yes — the pool includes RMO, INMO, Pre-RMO, and IMO-shortlist style problems alongside US olympiad material. Difficulty mix is random so you'll see a range; use Next problem until something at the level you want shows up.

Are my stats saved across sessions?

Yes — attempted / correct / streak / best-streak save in your browser's localStorage. Nothing is sent to a server. Click Reset on the stat bar to clear them any time.

How do I get a different problem?

Click Next problem. The engine picks a fresh random problem from the pool — and swaps to a different random shard once you've seen half of the current one, so you keep getting variety.