Consider the following multiple choice question:

> 
> If you randomly chose and answer to this question, what is the probability that you are right?
> 
> 
> * a) 17%
> * b) 0%
> 
> 
> 

Note that when I heard about this question, there where more, and more plausible answers compared to how the question is formulated here. However, I'm only interested in answer b) and thus chose for a) some random probability. I hope most people will agree that a) is not possibly the right answer.
If you care to see a slightly different formulation and tons of tons of confused people, simply google the question or check out this [link](https://plus.google.com/+RaymondJohnson/posts/CSXeyftovTJ).

So back to the question: If you randomly chose one of the answers, then each of them is chosen with a probability (that depends on the number of answers and is in this case) of 50%.

Suppose that there is a correct answers to this question. Obviously a) is not the right answer. Also b) is not right, since, if there is a right answer the probability to choose it randomly is 50%, which is not the value that is given by the answer b). Therefore, to suppose that there is a right answer leads to a contradiction.

Well then, suppose that there is no right answer. If there is no right answer, the probability to chose the (non existing) right answer is 0%, which is the value that is given by the answer b). So b) is the right answer and again this leads to a contradiction.

It seems that b) is right and wrong at the same time which makes me wonder if it is not the question that is ill posed. But what exactly is not ok with this question? 

I understand that the status (right/wrong) of an answer actually depends upon which answer you choose, so that this is somehow a recursive problem. Nevertheless, does this make the question invalid?

Is this a known type of question? And what actually interests me the most: Are there other examples of such questions, ideally not statistical ones?