Math Riddles

These are competition-level problems. The math itself might be accessible — you won't need calculus or linear algebra — but the insight required is non-obvious. Infinite series that telescope. Probability paradoxes that break your intuition. Recursion that maps to Fibonacci.

The two-envelope paradox is a good example of what makes these hard. The naive calculation says switching always improves your expected value. But if that were true, you'd switch forever. The resolution requires understanding where the probability assignment went wrong — and that's a genuinely tricky idea, even for people comfortable with probability.

Don't expect to solve these quickly. Use pen and paper. Work through the hints. Read the proofs even if you solved it — the proof might show a cleaner path than the one you found. If you can consistently solve Einstein riddles, you're genuinely good at mathematical problem-solving.