Fermi problems

Princeton University Press sent me a copy of Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin, by professors Lawrence Weinstein and John A. Adam. The book is a compendium of Fermi problems -- that is, problems which are simply stated and whose answers can be estimated at the order of magnitude level through simple logic from a few factual inputs.

The classic Fermi problem is: How many piano tuners are there in Chicago?

When I took my oral exam as a first year graduate student at Berkeley, theoretician Geoff Chew (a former student of Fermi's) asked me:

1. How many blades of grass are on your front lawn?

2. What is the ratio of paved to unpaved surface area in Iowa? (He had earlier asked where I grew up.)

Luckily I got them both right. The experimentalist in the examining pair, Paul Richards, held up a cylindrical metal device of some sort and asked me what it was. He let me hold it; it was heavy. I stared at him blankly. To this day, I still don't know what the gizmo was :-) I suppose I was destined to be a theorist!

Physicists are constantly solving Fermi problems in the course of their work, because it's the first step in sizing up any potential project, theoretical or experimental. When I talk about entrepreneurship I emphasize the same kinds of problem solving in business or technology: how many servers will we need? how fast will sales grow? how much capital should we raise? ...

Watching someone work out a Fermi problem in real time reveals a lot about their brainpower. Wall Street firms, consultancies like McKinsey, Microsoft, and even small startups have been known to ask these kinds of questions of job applicants. This book discusses similar problems in a business context.

The difficulty of most Fermi problems is limited, unless the problem requires some specialized knowledge. But I like them slightly better than puzzles or brain teasers which rely on esoteric tricks that the solver either gets or doesn't get. A former collaborator of mine came up with the following (slightly broadening the genre) one evening while I was visiting U Chicago:

1. If the sun stopped radiating energy, what temperature would the surface of the Earth cool to?

2. In the above scenario, could humans survive using current technology if given enough time to prepare?


Weinstein and Adam's book is a nice collection. None of the problems require any specialized knowledge of math or physics; the level is appropriate for a bright kid or moderately technical reader.