Fermi estimation step by step: break the problem down, set bounds and multiply orders of magnitude.
When someone asks you something you don't know, the temptation is to blurt out a random number. There is a much better way, and physicists used it long before computers: break the question into pieces you can reason about and multiply them. It's called Fermi estimation, after Enrico Fermi, who was famous for working out almost anything on a napkin.
Fermi used to ask his students how many piano tuners there were in Chicago. Nobody knows, but you can reason it out:
Each step could be off by a factor of two, but the errors tend to cancel out: some push you up and others push you down. The result usually lands in the right order of magnitude, which is what really matters.
1. Break the question down. "How many traffic lights are there in a city?" is unknowable, but "how many intersections with lights are there in my neighborhood?" and "how many neighborhoods like mine does the city have?" can be pictured. Each piece should be something you've actually seen.
2. Anchor each piece in something you know. Your street, your home, your day. You don't need the exact figure: you need a number you wouldn't be embarrassed by.
3. Set bounds. If a piece won't come, ask yourself the lowest number you'd believe and the highest. More than 10? Surely. Less than 10,000? Also surely. Then the best bet isn't halfway (5,000) but the middle in times: 10 times 10 is 100, times 10 is 1,000, times 10 is 10,000. The center is about 300, equally far, in times, from both ends. That's the geometric mean, and it's the right way to split the difference when you don't even know how many digits the answer has.
4. Check it backwards. With the result in front of you, ask whether it squares with anything else. If you conclude your city has more traffic lights than cars, one of the steps went wrong.
When you guess by eye, an error just stays there. When you multiply five pieces, each with its own error, some go up and some go down, and they usually cancel out in part. It's the same reason the average of many people beats almost any one of them (more on that in the wisdom of crowds).
GutGuesser's scoring measures exactly this: not how many units you're off by, but how many times. Going over by double costs the same as landing at half. That's why Fermi's method fits so well: it doesn't chase the exact number, it avoids being off by ten. Get the order of magnitude right and you've won half the game.
Four questions a day, one minute. Nobody knows the number; whoever gets closest wins.
Play today's challenge