I'll invite you to help me with this challenge, namely by providing the challenges. Enrico Fermi was famous for being able to estimate physical quantities even in situations where he did not (and, possibly, nobody) knew what the actual answer was. This is enormously helpful in science. One of the things we need to know is whether the answer we got back from our observing system or calculation was reasonable. When you start working in brand new areas, it's much harder to know what is reasonable. A Fermi estimate gives you that first guess. As Fermi also was a Nobel Laureate and did a lot of creative, original work, it might be a good thing if we practiced this skill ourselves.
Fortunately, you don't have to be a Nobel Laureate to do it, and the subject needn't be one on the frontiers of human knowledge. I made some use of it, for instance, regarding the company 'Joe the Plumber' wanted to buy. (After doing so: it isn't a small company.) The classic example is to estimate how many piano tuners there are in New York city. But I've seen that one a bunch of times, and don't have a piano, so it lacks something for meaning. The reason I need your help is that anything that leaps to my mind to create an example from will be in some area that I know something about already. So, what number -- about the world -- would you like to see estimated? No 'guess what number I'm thinking of' or 'what is the tangent of a trillion'? But something about how many, how big, how hot, ... of something in the observable universe.