Fermi questions


Fermi questions are fun math questions that serve very practical purposes; they give exercise in using numbers, opportunity to learn more about the world around us, and can be used in practical, every-day questions.


So, … let's learn more about them.


Questions without answers

Fermi questions are named for the Italian-born physicist Enrico Fermi who used to pose them.

One example was his estimation of the strength of the first atomic bomb by simply seeing how the blast blew a few strips of paper. Actually, he did a pretty good job of it.


The basics of a Fermi problem, or Fermi question, are simple.


The goal is, in fact, to come with an estimated value, not necessarily a single, completely accurate one.


What! Not a single, accurate answer? Math heresy! What's the point?

The point is that if one makes reasonable assumptions and estimations, the answer should at least be in the ballpark to the correct value.


If your result is not too far off, then you very likely understand the problem and the information to solve it.

If you're way off, don't get frustrated.

It just means that at least one of your assumptions may be off. Rethink the problem, or look up real values until you have an answer in the general neighborhood of the real. The point is not just to get a value, you can easily look it up or use a calculator. The object is to exercise your mental muscles and to learn about the world around us.


Allow me to demonstrate

Consider a couple of examples:


How many piano repair businesses are in Los Angeles?


So I estimate there would be 200. An internet search showed a total of 114. Rather close, especially for a bunch of guessing.


Part of the power of this estimation process is that the individual assumptions may be too high or too low, but as long as the assumptions are reasonable, these differences will tend to smooth out the result.


**Disclaimer – I confess, when I first worked this out, my result was way too high. But after cutting the total population in half I got the result seen. So even Homegrown Professors need to learn too.


How tall is the tallest man?

Below is a picture of Robert Wadlow, the world's tallest man on modern record.

From the picture above, how tall is Mr. Wadlow?


So I estimate that he is 9 feet tall.


His actual height, 8 feet 11 inches. Very close!


Actually, a very common example of Fermi questions, not going by that name, of course, is employed in the game show "The Price is Right," particularly in the final round called the "Showcase showdown."


The object, for the benefit of anyone not familiar with it, is for two contestants to guess the value of a set of prizes. The mental adding of prize values is, in fact, a Fermi question; some prize values may be guessed too high and some to low, but the values tend to smooth out. Of course, being a game show, there is more to it – the contestant must come the closest to the actual value without going over. But the math follows the same type of game.


Go, and do likewise

Below are some questions to consider tackling. They're fun to do as a group.


Try some. It can be a fun group project that builds math skills that can be useful in life.


On the web

Several sites go through different problems:


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