There is a common interview question that asks the candidate to estimate the amount of manhole covers in North America.
This is a particularly nice interview question, as there are a dozen different ways to approach it, no clear right answer, and no easily searchable result online. Here I present my quick take on it, and some assumptions that could impact results. I will make every effort to avoid searching anything online (during my guess phase), and present purely my guesstimates for all values. To do this, I decided to try out a very nice online tool: getguesstimate.com
To get an easily tweak-able, reasonable value, I decided to start with the population of North America. Taking the percentage of the population that lives in urban (or suburban) centers, I figure out how many people have sewer access. I then work from the other direction, and count the rough amount of sewer mainlines needed per person. Lastly, I make a wild guess (and this is the part people should take a peak at) that there are 1-5 manhole covers per mainline.
This gives me a rough answer of 22 million Manholes in North America, with reasonable lower to upper bounds of 19-46 million.
The result above is very sensitive to final “Manhole Covers per Mainline” step. My reasoning to take a 1 to 5 guess is:
- Each mainline should have at least 1 manhole to check for issues/do repairs
- Each mainline would stretch at most 5 km, more that this and likely 2 or more mainlines would connect togeter
- In the 5km case, a maintenance worker would not be expected to walk 2.5km underground, in full gear.
- Ideally, the worker would have to walk a maximum of 1km. Hence, 5 covers for 5km mainline.
The other values and explanations are listed in the model. Take a look at the model here: https://www.getguesstimate.com/models/7449
Manholes Guess & Check
The EPA estimates that there are about twenty million manholes in the United States [*]
If we take EPA’s 2012 estimate to be accurate, we are getting roughly 16 people per Manhole. This would give us (if we take US numbers to be fairly average for North America) about 29 million manholes in North America. This means my guess above turned out to be a fairly accurate, a 30% error!