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A fun question I ask students or interviewees (in engineering) is:

This is not my question, this is an example:
Using only what you know now, how many cans of soda would you estimate are produced per day (on average) in the United States?

For this question, the result doesn't matter so much as the process you use.

In this theme of estimation, what's your favorite question?

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This may be of interest. –  Tom Stephens Jul 30 '10 at 20:10
    
I voted to close because I don't think this question is math-related. No math-related answers either. –  Larry Wang Jul 31 '10 at 9:03
    
In my defense...it was CW –  Michael Haren Aug 3 '10 at 18:01
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closed as not constructive by BlueRaja - Danny Pflughoeft, Ben Alpert, Akhil Mathew, Larry Wang, BBischof Jul 31 '10 at 17:35

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4 Answers

"How many estimation questions are asked in interviews across the world during a typical 24h period?"

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I see what you did there... –  Michael Haren Jul 30 '10 at 16:46
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I find it bothersome that out of all answers I posted on this site, this "smartass answer" is by far the most up-voted. –  rgrig Jul 31 '10 at 13:16
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One that I remember from some book (I think it was Innumeracy by John Allen Paulos) was "How fast does your hair grow, in miles per hour?"

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This seems more like a factor-label problem to me, but I like it –  Michael Haren Apr 8 '11 at 2:58
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I like "how many licks does it take to get to the center of a tootsie roll pop".

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What is the mass of the atmosphere?

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