How many piano tuners work in a city the size of Chicago? Just estimate
Physicist Enrico Fermi was famous for cracking seemingly unanswerable questions by breaking them into smaller, roughly-estimable pieces instead of looking anything up. The piano tuner question became the classic teaching example: how many people live in the city, what fraction own a piano, how often does each piano need tuning, and how many tunings can one tuner complete in a year? Can you work out a plausible number using only reasoning like that?
Reveal the answer
There's no single 'correct' figure — the point of a Fermi problem is that careful order-of-magnitude reasoning (roughly: 3 million people, 1 in 20 own a piano, each tuned once a year, one tuner completing 1,000 tunings a year) lands within a factor of two or three of the true answer, around 150 tuners, which is what matters. Fermi set problems like this for his students at the University of Chicago to train exactly this kind of estimation under uncertainty.