Hard math questions, with answers
- What are the last two digits of 7²⁰²⁶? Answer: 49, because 7⁴ = 2401 ends in 01 and 2026 = 4·506 + 2.
- How many zeros does 100! end with? Answer: 24, from 100/5 = 20 plus 100/25 = 4.
- What is 1 + 1/4 + 1/9 + 1/16 + …? Answer: π²/6 (the Basel problem).
- What is ∫₀^∞ e^(−x²) dx? Answer: √π / 2.
- In the Monty Hall problem, should you switch doors? Answer: yes; switching wins with probability 2/3. Work through cases like it with the probability solver.
- Is √2 rational? Answer: no. If √2 = p/q in lowest terms, then p² = 2q², so p and q are both even, which contradicts lowest terms.
How to approach a hard problem
- Try small cases and look for a pattern.
- Draw a picture, even for algebra.
- Work backwards from what you need.
- Look for something that never changes: parity, a sum, a remainder.
- Test the extremes: zero, one, very large values.
Paste your own
Type or paste any hard problem, from a test, a textbook or an olympiad. The solution shows its reasoning step by step, so you can follow it and spot a weak step. For easier practice, start with these math problems with answers.
Questions students ask
Can AI solve olympiad problems?
Often, but not always, and proofs are where AI errs most. Read every step critically and ask about any that skips reasoning.
Can I get a hint instead of the full answer?
Yes. Ask for "a hint only", and ask for the next one when you need it.
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No. You can type or dictate problems without signing in. Signing in with Google or Discord is free; it keeps your chats beyond 3 days and lets you attach a photo, PDF or Word file.