Varsity Guessing

Two of the AP Physics students and I were off playing with the jazz band at the U Delaware jazz festival last Friday, so I left the remaining folks to do some Fermi problems. 

In addition to finding a flashlight that was lost in a huuuuuuuge box of packing peanuts early in the week, they came up with this estimate of the amount of land area allotted to each person in the world (well, really, the number of people per square km):

The guess is pretty close.  There are a few wonky estimates (fraction of the Earth that's land and size of the Earth), but they more or less normalize to give a pretty close answer, which is pretty much the idea of a back-of-the-envelope calculation.     

It's not about super-accuracy, but about finding the right order of magnitude for the answer, which they rocked.