The Stripy Strudel's Journal

You have most probably read someone's recommendations on interviewing job candidates, or, conversely, on attending interviews as a candidate. Starting from year 2000, when Joel Spolsky published “The Guerrilla Guide to Interviewing”, these recommendations often include the advise to to ask an impossible question. The numerous advisers reprinting this recommendation from each other's articles offer various ways to pose such a question, but Spolsky has several examples in his article, including this: “How many piano tuners are there in New York?” (I think if I hear this in an interview, I'll reply “Just as many as there are cliche users in Novosibirsk”.)

It turns out that the author of this question is Enrico Fermi. Here is the original version of the problem as well as the solution: Fermi's Piano Tuner Problem. The solution is similar to what Spolsky describes, and the answer comes out to be 150. I'll quote the last paragraph from Fermi's solution.

This method does not guarantee correct results; but it does establish a first estimate which might be off by no more than a factor of 2 or 3 — certainly well within a factor of, say, 10. We know, for example, that we should not expect 15 piano tuners, or 1,500 piano tuners. (A factor of 10 error, by the way, is referred to as being ‘to within cosmological accuracy.’ Cosmologists are a somewhat different breed from physicists, evidently!!!)

In my opinion, this last paragraph about interpretation of results is the most important. Without realizing what such a solution is and what it is not, the solution turns into guesswork, and the problem becomes something like a test for quick wit. Joel says that a candidate who starts solving such a problem is a good candidate; I'd rather say that one who immediately starts estimating how many gas stations there are in Moscow and cheerfully answers, say, 2500, is either self-assertive (you can't verify if the result is correct anyway) or reads too much Joel Spolsky.

Quotation out of context is a powerful tool indeed. If only for the well-known Lenin's pronouncement: “The most important of all arts for us is cinema”, the full context of which is: “While the nation is illiterate, the most important of all arts for us are cinema and circus.” Seems like Joel isn't a stranger to it as well.

Thanks to rimpocha for the food for thought.

See also:

• Wikipedia: Fermi problem
• A collection of Fermi problems

UPDATE: Mr. Spolsky has left the advise to ask an impossible question out of the third revision of his article.

По-русски: Об интерпретации результатов и о выдёргивании из контекста