

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


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informatimago
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/](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-...](http://www.chinamarketresearchreports.org/report/global-and-china-
door-knob-industry-2014-market-research-report.htm) (don't forget to divide
the number of doorknobs by two to get the number of doors (ignoring revolving
doors)).

~~~
sneakpeek
This is also assuming that the doorknob manufacturer manufactures doorknobs
for house doors. What about cabinet doors, curio cabinet doors, and trap
doors. Also, would car doors count?

------
basseq
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".

------
harperlee
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?

~~~
ljk
what about a doggy door on a real door?

