> How many molecules from Socrates’s last breath are in the room?
We can estimate the number of air molecules in the room by using Avogadro's number (6.022e23), the rough chemical composition of the air (roughly 80% nitrogen, element 7, and 21% oxygen, element 8), and the room's volume (which can be hard to estimate by eye unless it's a very small room).
We also need the total mass of the atmosphere; we can estimate it from the Earth's surface are and atmospheric pressure, but we need to convert 1 atm to kilos per square meter. Would an average student remember that conversion rate? I certainly don't. (Turns out that 1 atm ~ 10,330 kg/m^2).
That's quite a few constants to remember from physics and chemistry.
(I'm aware that Fermi estimates are only one of many kinds of example questions in the post.)