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How Many Fish are in all the World’s Seas?

Riccardo asked on Feb 15, 2018 - 3 answers

How would you structure your approach to solve that question ?

3 answers

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replied on Feb 16, 2018
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I will use the following approach:

1) Take the Sea you know and try to calculate it's Volume. You may use the speed of a plain as the benchmark and assume that the Sea is 1/2 of a Sphere:

  • It takes X hours to fly from A to B over the Sea
  • The average speed of a plane is Z
  • Thus the radius of the Sea is 1/2 * X* (Z-1) (Because it takes extra hour to take off and land)
  • The volume of the sphere is 4/3 * p* rˆ3
  • The volume of the Sea is 1/2 * 4/3 * p * rˆ3 (Half of the sphere)

2) Make assumptions about the number of fish per 100 mˆ3

3) Calculate volume of fish in the Sea using your assumptions about the fish

4) Calculate the other seas using the assumption about their relative size

5) Sum up the numbers


Hi Vlad, thank you for your answer. Do you know if is a prerequisite, during an interview, to know how to calculate the volume of a sphere ? I don't open a geometry book since when I was in the middle school — Riccardo on Feb 16, 2018

Juan Pablo replied on Feb 15, 2018
I did my internship in consulting and now I am preparing actively for interviews

What they want to understand is what is your approach to that brainteaser. In this case i would suggest in a general perspective to do the following:

Start saying that in each KM3 there are x Number of Fish, then you can proceed by calculating the numer of fish in each ocean, having in mind that there are a lot of differences in the composition of the Atlantic´s ocean than the Dead sea.

Based on that, you should calculate the volume of each ocean and then making multiplying it by the number of fish in each of them. if you want to go further in your analysys, you could come up with the fish born seasonality, which could impress your interviewer but at the same time could mean much difficult calculations.

Hope it works.


Juan Pablo Montoya

replied on Feb 25, 2018
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I would drastically simplify how to calculate the size of the sea by starting with assumption that there is a maximum sea depth that is compatible with most life, call it 30, 50, 100 meters. Once you agree on that you can approximate all seas to a composition of cuboids vs. spheres, making calculations faster and smoother. Once calculated the volume, apply assumed population per cubic kilometer and voila, done.

hope it helps,


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