It is one of the most popular Fermi questions and you could face it during the 1st round, when math and problem-solving skills are usually tested deeply. I will propose a quick solution, in order to give later some detailed considerations.
Let's estimate the number of windows in Seattle.
- No. of residents in Seattle: you do not have to know that Seattle has almost 750k residents, but a good candidate should infer that it is a big city in the US and that can be assumed it has 1M residents.
- No. of windows per residents: you are actually interested in the number of facades to clean; a small window has 2 facades, the inner one and the external one, while bigger windows have 4 or more facades. Let's assume that an average residence in Seattle has 2 people and 40 window facades. So we have 20 residential facades per inhabitant. Let's assume to have other 20 commercial window facades per resident, including e.g. bars, offices, stores.
-> 1M residents x 40 window facades, we have a total of 40M facades to clean.
Now let's evaluate the charge per facade.
- Facades per hour: the time requested for a wide window of a store will be much higher than the service window of a little house. Let's assume an expert cleaner will take 1 min for a medium-sized window, i.e. 60 facades per hour.
- Charge per hour: let's assume an hourly rate of $10. We should also consider the cost for infrastructures, tools, products, and insurance: let's estimate other $5 per hour.
-> in an hour: $15 / 60 facade, that gives 25 cents per window facade.
--> Therefore to clean all the windows of Seattle you could charge $10M ($0,25 x 40M).
Remember: in consulting nobody knows the number of windows in Seattle and maybe neither in window-cleaning companies :) What will be valued is not the accuracy of this type of numbers, but the reasoning you make behind them and your common sense (you should always wonder if numbers you estimate have sense or not). In addition, when you complete an estimation (e.g. the no. of residents in Seattle) you can ask the interviewer whether you can proceed with that number or she has something more accurate.
The solution proposed will be considered great and will allows you to pass the round. But in order to really crack it and impress the interviewer, you should be more curious, proactive and come up with creative considerations, potentially based on personal experience. Some examples:
- When you calculate the no. of windows in town you can make some comparisons with your city, e.g.: "in Manhattan, I feel lucky with just one window at home, but I know that Seattle is more residential, houses are bigger and they usually have beautiful views on surrounding gardens and parks. Therefore let's assume an average house has 4 little windows (2 facades each), 4 medium (4 facades each) and 2 big (8 facades each)."
- Think out of the box: ask the interviewer if you should also consider the car windows.
- When you evaluate the cleaning speed you can say, with a bit of healthy self-irony: "A medium-sized facade take me at least 3-4 minutes to clean it. But I know to be a disaster :) I assume an expert cleaner with professional tools can handle it and move to the next one in 1 minute."
- In the end, to consider other risks not covered in the discussion, you could also introduce a safety factor, e.g. "the time evaluated do not consider the time to put up and put down the infrastructure and the time needed to wait for residents to free up windows. For these and other possible risks we should consider an increase of 10% of the estimate."