Your logic is flawed (as is nearly every "solution" to one of these problems I've seen). The question wasn't "How many barbers should there be?" It was "How many barbers are there?" This is an important distinction as your approach shows the appropriate number of barber shops that can reasonably be operated and have no shortage of customers due to hair growth speeds. I would approach the problem from the opposite direction. How many distinct professions are there in San Francisco? What is the current population? What are the percentage breakdowns of those professions? At that point, you can easily get the number of people employed as barbers. Now, did they want individual barbers, or the number of barber shops? You then only need to infer the number of barbers per shop, rather than estimating a lot of data that isn't readily available.