I have a goal of estimating how many public playgrounds exist in the United States.
There are many methods of gathering real data about playgrounds, but, unfortunately, there is no single authority that can answer this question or provide a comprehensive list.
Contacting every city in the nation would be too prohibitive, and other options such as working with regional park & rec departments have proven to show how little information those departments have. (Edit: I should also note that parks != playgrounds, but playgrounds may be contained inside parks).
This problem is akin to the old interview question: How many gas stations are there in Los Angeles?
How would one go about constructing a valid estimate on the total number of public playgrounds in the United States, with a margin of error <= 5%?
Can the community think of such a methodology that is purely grounded in math?
If you propose a solution, can you calculate what your result is for comparison with the others?