If this question as I wrote it was originally unclear to some people, I expect that the visual image added to the question in the edit by Steven Kay should make it clear and justify reopening it.
If the question were about how to use a particular GIS software to test a polygon feature class to determine if any polygons within it meet your criteria then I think it would be ready to re-open.
If I were to try and answer the question it would need to be about using ArcPy to do it, but I am sure there are many other GIS software products and those with expertise within them, that would be able to provide an answer too.
By not specifying a particular product, or asking for an algorithm, you are effectively asking multiple questions (how to do in any of many products) which I think makes it too broad and/or unclear (because you have not specified a product).
If you are only interested in this as a general geography question then please be aware that this is the GIS Stack Exchange and it may or may not be on-topic for the Earth Science Stack Exchange (review their on-topic page before asking).
A Meta GIS SE discussion that I believe to be relevant to your question as currently asked is Is geography trivia on topic?