Guess. Check. Learn.

Your scale accuracy

The result first shows your estimate, the checked estimate, and the factor between them. Being 1.3 times low is close; being 10 times high means you missed by one order of magnitude. That plain-language gap is the main feedback on every challenge.

Your Results combines those attempts into a personal accuracy history so you can see which subjects and problem types fit your mental models best. No account is required; a passkey is optional when you want to save progress across devices.

Why this improves numerical intuition

Being full of it can feel exactly like being right until a number forces the comparison. Committing to an estimate before seeing the answer makes hidden assumptions visible and gives you feedback your intuition can reuse next time.

The arithmetic can be simple while the assumptions are revealing. A factor-of-100 miss may come from population, price, time, density, conversion, or a physical constraint. The checked reasoning helps identify which piece of the mental model needs attention.

What is a Fermi problem?

A Fermi problem asks for a useful estimate when exact data is missing, delayed, or impractical. You break a big question into quantities you can estimate, keep the units straight, and check whether the result is plausible. The method is named for physicist Enrico Fermi, who was known for turning fuzzy questions into tractable approximations.

The goal is not false precision. These challenges target the right scale, normally using no more than two significant digits and scientific notation. The reference page collects useful facts, formulas, and notation habits.