I’m posting all these puzzles because Yat said he thought that logic puzzles are becoming stale, and I’m trying to prove him otherwise.
There are two types of inhabitants in the world: humans and vampires. Humans always tell the truth and vampires always lie. Also, inhabitants can either be sane or insane. Someone who is insane has all of their beliefs backwards; everything true they believe to be false, and everything false they believe to be true.
For example, if you ask an insane vampire, “Is the sky blue?” he will insanely think that it isn’t and then lie and say that it is. He will answer, “Yes.”
Here’s the problem: insane vampires and sane humans will give the exact same answer to any question (as will sane vampires and insane humans), so how are you supposed to protect yourself from vampires in this world if you can’t tell them apart?
Ask any inhabitant if 2 + 2 = 4. If the answer is yes, is he a sane human or an insane vampire? If he answers no, is he an insane human or a sane vampire? There’s no way to tell!
…or is there?…
What is a single yes or no question that you could ask to any inhabitant to determine if he is a human or a vampire?
Please use rot13 to encode your answers so as not to ruin the puzzle for anybody else.