A fun application of these types of problems is that you can show that there are far more molecules of air than lungfuls of air, which means that the air you breathe right now is extremely likely to be comprised of atoms that were once breathed by/part of any famous person in history from 80+ years ago.

How many piano tuners are in Chicago?

Yeah, Fermi problems are rather interesting. Same here. I love them and I hate them. I love the thinking it requires, but I hated that my chemistry teacher back in the day absolutely forbid us from looking up exact numbers and required that we generalize with everything, even if we knew the exact numbers. For example, we had to guess the population of Chicago and the average number of pianos per household.