How many public playgrounds exist in the United States? How to answer using statistics and probability?

Question

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?

Answer 1

Randomly select at least 30 US cities.

Choose rich ones, choose poor ones, choose small ones, choose big ones, choose highly populated ones, choose scarsely populated ones, choose ones on the east, West, Midwest, north,south, Northwest, Southwest, southeast, northeast, etc etc etc

Record the population and # of playgrounds in that city.

Do least squares regression to logx vs y, get a logarithmic function to predict how many playgrounds based on population.

You also may be able to do proportionality hypothesis tests proportion of # of playgrounds per 1000 people.