There is a school of thought that says that if by its very nature a question is unanswerable then the question is meaningless. Some would say that by this criterion the question, “Do I see the color green differently from you”, is meaningless. Personally, I think this is a bit extreme.
There are some unanswerable questions that arise from mathematical paradoxes. For example, Bertrand Russell’s paradox. Consider the set of all sets that are members of themselves. For example the set of all sets is a set and so is a member of itself. Now what about the set of all sets that are not members of themselves. Is it a member of itself? If you think about this for a moment you will see that you get a contradiction either way.
Another math paradox is to consider the smallest number that requires more than twenty-five words to describe. Surely such a number must exist. However, if it does, then it can be described as “the smallest number that requires more than twenty-five words to describe”, which is obviously fewer than 25 words.