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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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    $\begingroup$ en.wikipedia.org/wiki/Fermi_problem $\endgroup$ Jul 30, 2010 at 16:54
  • $\begingroup$ This may be of interest. $\endgroup$ Jul 30, 2010 at 20:10
  • $\begingroup$ I voted to close because I don't think this question is math-related. No math-related answers either. $\endgroup$
    – Larry Wang
    Jul 31, 2010 at 9:03
  • $\begingroup$ In my defense...it was CW $\endgroup$ Aug 3, 2010 at 18:01

3 Answers 3

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

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    $\begingroup$ I see what you did there... $\endgroup$ Jul 30, 2010 at 16:46
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    $\begingroup$ I find it bothersome that out of all answers I posted on this site, this "smartass answer" is by far the most up-voted. $\endgroup$
    – rgrig
    Jul 31, 2010 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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  • $\begingroup$ This seems more like a factor-label problem to me, but I like it $\endgroup$ Apr 8, 2011 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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