Can anyone estimate the total number of doors in the world? How?

Why? :-)

Assuming it's a question asked by a doorknob manufacturer, we actually want to count the "real" doors that have doorknobs, not the moral doors that you may conceptually have at the entrance of some shack. We could also evaluate entrances and such.

Let's take the population per continent:

http://www.ecology.com/world-population-continent/

    Current World Population by Continent
    Population estimates as of 2010. 
    Source: Population Reference Bureau
    Asia             4157300000
    Africa           1030400000
    Europe            738600000
    North America*    461114000
    South America     390700000
    Australia**        36700000
    Antarctica***             0

Now, we'll estimate the number of houses per person, for each continent (related to family size, existence of work office and administration buildings), along with the number of doors per house/office.

  #| Asia           |# (+ (* 4157300000 (+ 1/4 1/12) 4)
  #| Africa         |#    (* 1030400000 (+ 1/6 1/30) 4)
  #| Europe         |#    (*  738600000 (+ 1/3 1/2)  6)
  #| North America* |#    (*  461114000 (+ 1/3 1/2)  6)
  #| South America  |#    (*  390700000 (+ 1/4 1/12) 4)
  #| Australia**    |#    (*   36700000 (+ 1/3 1/2)  6)
  #| Antarctica***  |#    (*          0 (+ 1/6 1)    8))    

Which gives an estimated total of 13,070,390,000 doors, about 1.9 door per person. (The number of doors in Antartica is grossly underestimated, sorry).

PS: If you want to know if I'm right, you'll have to pay USD 2200.00 ;-) : http://www.chinamarketresearchreports.org/report/global-and-... (don't forget to divide the number of doorknobs by two to get the number of doors (ignoring revolving doors)).

This sounds like a (bad) case interview question. Which are, of course, more about the approach and rigor of thinking than a "correct" numerical answer.

Quickly, my approach would be something like:

1. Let's agree on a definition of "door". For the sake of estimation, let's assume these are human-sized hinged openings. E.g., cabinet doors, garage doors, doggie doors, and other definitions don't count. Since this is a total swag, let's ignore things like double-hung doors. This still leaves open the idea of things like transportation (bus doors, car doors, train doors, elevator doors, etc.) that we could estimate by a similar method, but let's ignore that, too.

2. To get to a total number of doors, let's estimate the average number of unique doors an individual could interact with. We could probably draw a graph that resembles a reverse exponential curve: e.g., there are a large number of people who interact with zero or one doors per day (e.g., people in rural areas of developing countries) and a very small number of people who interact with a lot of doors.

3. To get to an average number of doors, we can thinking about residences and work locations. We can probably ignore other door locations, as a retail location you would go, for example, is someone else's work location. So thinking about my own experiences:

3A. I have 22 doors at home, which I share with my wife. So 11 attributable to me. (Aside: count the number of doors in your house, apartment, etc.: it's higher than you probably think. Even a studio apartment might have 4+.)

3B. Work is harder because no doors are "mine" (no office). I could go through and think about what percentage of a door is "mine", but I don't think it would be more than 0.5. Let's round up to 1. It might be more like 2-3 for some people at the end of the curve.

4. Let's say I'm at, effectively, the far right on the curve with 12 doors. (After all, if we compare to global wealth distributions, a salary of $50k puts you in the top 1% worldwide.) The interesting thing about exponential curves is that the median is going to be in the first quintile, but the mean is going to be around the 50% mark. So we can assume the global average is 6 doors / person. (Note: this is the step you would nitpick, because it's a giant assumption. Not to mention that my 50% comment isn't accurate: totally depends on the shape of the curve. :) )

5. With a global population of about 7 billion people, the total number of doors is 42 billion.

Now we can argue about my assumptions and definition of "door".

Yes! But as inputs for the estimate we would need the purpose, and, closely related to it, the definition of door in that context. Do the doors of my Lego car count? What about doors in the painting on my wall, or the one on the microwave?