Estimate a number, then read the working
A Fermi problem asks for a number nobody has memorised: how many piano tuners a city supports, how much a cloud weighs. You give an estimate, then the game walks through the arithmetic that produces a defensible figure.
A Fermi estimate is right when it lands within a factor of ten, because the point is the chain of assumptions rather than the final digit.
The game scores the estimate and then shows how the same chain is built properly.
The question has a real answer that nobody carries around, and it can be reached by multiplying a few quantities you can guess. Population, frequency and rate are usually enough. If a question can be answered by looking it up in one step, it is not a Fermi problem.
Each assumed quantity carries an error, and those errors compound. A chain of five guesses that are each within a factor of two can land within a factor of thirty of the truth. Scoring by power of ten keeps the game honest about how precise a guess can be.
After you commit, the game lays out one route to the figure: which population was assumed, which rate was applied, where the rounding happened. A different route often reaches a similar place, which is the useful part of the exercise.
A streak counts consecutive questions that land within the accepted range. Because each question is a different domain, maintaining a streak means your general estimating instinct is calibrated rather than your knowledge of one topic.
A question, a scoring band and the reasoning.
Each question is chosen so that no single search answers it. The number has to be assembled from parts you can reason about.
Your estimate is compared logarithmically rather than by percentage. Being within a factor of ten counts as a hit, which matches how estimation actually works.
Every round ends with the assumptions spelled out in order. You can see exactly which step your own estimate diverged from.
Consecutive correct estimates build a streak that carries across unrelated subjects, so the counter reflects a general skill rather than one topic.
Three steps, repeated for every question.
Identify the two or three figures you would need to multiply. Population, per-person rate and time span cover most problems.
Round each quantity to something you can multiply in your head. The combined figure is your answer, not any single assumption.
The solution shows one valid chain. Check which of your assumptions was furthest out and adjust the instinct for the next question.
Three players on the habit the game builds.
I used to refuse to answer without data. Now I write the chain first and only then estimate, and the result is usually within the band.
The worked solution is the reason I stay. My number was wrong by a factor of forty because I assumed a rate ten times too high, and I could see it immediately.
The streak counter is the honest part. It cannot be gamed by knowing one subject well, because the next question is always from somewhere else.
Scoring, difficulty and what counts as close.
