Guesstimate - How many workers did it took to build the pyramids?

Question

How would you solve this?

This would be my structure (for simplicity just focusing on one pyramid in Egypt)

Number of workers = workers in quarry + workers transporting stones from quarry to pyramid + workers actually building pyramid + other workers

workers in quarry

workers in quarry = required stones per day / required workers per stone per day

required stones per day = required stones total / time to build pyramid

required stones total = Volume Pyramid / Volume average stone

I would need to estimate

Volume Pyramid
Volume average stone
time to build pyramid
required workers per stone per day (this one is tricky, further breakdown??)

workers transporting stones from quarry to pyramid

they were using some kind of sleds to transport stones so

workers transporting stones = required sleds * workers per sled

required sleds = number of stones per sled per day * required stones per day

number of stones per sled per day = Max number of stones fitting on one sled * number of rides per sled per day

I would need to estimate

Max number of stones fitting on one sled
number of rides per sled per day
workers per sled

All of them seem tricky and might require further breakdown.

workers actually building pyramid

workers actually building pyramid = required stones per day * required workers per stone

I would need to estimate

required workers per stone (might requires further breakdown)

Other workers

e.g. planners, other logistics, food, maintenance, etc.

I would just use something like 10-15% of total workers to add.

I feel like this is quite complex even with the assumptions that Im making which could be broke down further. Am I overthinking? Do you like the structure?

Case was asked during an interview of a boutique consultancy and I dont know what additional infos they were providing during the case. I assume they helped a lot otherwise the case is to long / doesnt provide recruiters so much insights to justify time spend for this case.

thanks!

Answer 1

Hi there,

Can't believe this actually came up in a real interview!

The most comprehensive answer would have to consider the fatality rate of slaves ('workers' is a bit of a euphemism), which is a weird thing to talk about in a business case. Hence, I really find this somewhat distasteful from said boutique firm.

Anyways, a couple of things you missed in your structure:

Dividing volume of pyramid by volume of 1 stone won't give you the number of stones since pyramids aren't solid - you have to divide the exterior from the interior architecture
Pyramids have complex and intricate interior architecture and design (think of all the paintings and sculptures) - needs to be accounted for

Lastly, I picked up on one of the estimate, which is time to build pyramid. How are you going to estimate that? An educated guess? The approach is fine, it's just that it all hinges on that (more time, fewer ‘workers’ of course) and it could be 5 or 50 years for all I know. You must point this out in the interview.

Hope this helps a bit! Best of luck!

Answer 2

Just a short note to add to Moritz's answer. The way to avoid being stuck with the time issue is to actually estimate the number of man-years of work,i.e., make the calculation assuming you would build it in one year (which means many more workers than in reality), and only at the end dividing by the number of years it took to build the pyramids.

So for example you would reach 100,000 man-years of work. If you assume it took 20 years to build, then the answer would be 5,000 workers (for 20 years).