Whenever I got stuck on math homework while growing up, I would go looking for my mother. Often I would find her on the living-room couch unwinding after work, catching up on the news with both the local Cantonese news station blaring on the TV and The Economist open in her lap.“I don’t know how to do this,” I would complain, settling on the carpet by her feet.“Read me the question.”I would recite: “Sarah takes six hours to paint a fence, and John takes 12 hours to paint the same fence. How long will it take to paint a fence twice as long if they work together?”She wouldn’t even look at the page.“How many hours do you think it’ll take them?”“I don’t know, or I wouldn’t be asking you!”“Single digit? Tens of hours? Hundreds of hours?”“Mommm …”
I love Fermi problems, and making estimates. These days, I do it a fair bit for work, and I also do it a fair bit around chemical employment as well. How many professors do you think work on this problem? Maybe 1, maybe 10. How many working industrial medicinal chemists are there in the United States? I dunno, definitely 1000, definitely not 100,000, probably closer to 5,000. How many chemical plants are there in the United States? Well, that's probably a number less than 5000, but more than 100.
Readers, what are your favorite Fermi-type questions and how do you go about solving them?