This unsolvable puzzle question has occupied the internet for years

This conundrum in the form of a “Who Makes a Millionaire” question has plagued the internet for over a decade. The question is:
If you randomly chose an answer to this question, what are the chances that you got it right?
* Answer A: 25 percent * B: zero percent * C: 50 percent, or * D: another 25 percent.
With four possible answers, it would seem that 25 percent would be the right answer.
But there is a problem: there are two choices: answer A and answer D.
Anyone who now thinks that there is no solution would have to choose answer B: zero percent.
But that contradicts itself: Because if B were correct, there would be a correct solution, but then logically answer B cannot be correct either.
Now only answer C, i.e. 50 percent, remains.
But answer C also contradicts itself. Because the probability of randomly selecting this is 4 possible answers, 25% and not 50%.
Thus the question, as it is posed, cannot be solved in the sense of a paradox. The puzzle was published in a Cambridge University blog in 2011 as an example of a probability paradox.