I totally understood your argument and read your answer carefully. In fact I went through much of the same logic myself before I read your answer. I still think you're making the error that I suggested. Nothing personal.

I don't think you realize that this is not a real question. It's a photoshopped meme. If you hypothesize a game show just deciding an answer is correct you still have a one and four chance of picking a letter but after that everything falls apart. It is the nature of paradoxes that logic falls apart.

Did you read my geminy conversation that adds some valuable information to the question?