Most software developers have either been asked a Fermi question in an interview or know of someone that has been asked this type of question. Companies like Microsoft and Google are notorious for asking these questions.
Why do interviewers ask this type of question?
Most developers I've talked to generalize the purpose of these questions as "They want to evaluate your critical thinking skills." Wikipedia's definition states that a Fermi problem: is an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one's assumptions.
More specifically, the interviewer wants to determine how adept you are at creating quick, reasonably accurate estimations. People who possess this skill augment a team's ability to quickly arrive at solutions when time and effort required to gather hard data is costly, impractical, or impossible.
Here's a few links, so you can brush up on your Fermi skills:
http://www.soinc.org/events/fermiq/fermiguide.htm
http://www.vendian.org/envelope/dir0/fermi_questions.html
http://www.physics.uwo.ca/science_olympics/events/puzzles/fermi_questions.html
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