I've been reading this book called "What is the name of this book?" and it has inspired me to come up with this riddle: Suppose you have two buttons, labeled "A" and "B", and you know that pressing one button will release something bad (e.g. anthrax) and pressing the other button will release something good (e.g. a million dollars). Furthermore, each button has an inscription on it, and you know that exactly one of the two inscriptions is true. The inscription on "A" is "This button does not release something good" The inscription on "B" is "Exactly one of the two inscriptions are true." If one must press exactly one button, can one figured out which button one should press to release something good?

If you want a small hint, the small hint is make sure you read the exact wording of the puzzle. There is a trick in there somewhere.

If you want a big hint, the big hint is that "Press 'A'" is incorrect.

If you want a huge hint, the huge hint is look closely at the sentence which reads "you know that exactly one of the two inscriptions is true."

The correct answer is no, you cannot figure out which one you should press.

Here's the trap that I was expecting most people to fall into: They would look at the inscription on "B" and consider what would happen if it were false: It's negation would be true. Its negation is "Either both or neither of th inscriptions are true", and since we're already considering the scenario that "B" is false, it cannot be that both inscriptions are true, so both inscriptions must be false. Therefore "A"'s inscription of "This button does not release something good" must be false, which means "A" must release something good.

Most people would then consider what would happen if the inscription of "B" is true. In that case, only one inscription must be true, and we've already assumed that "B" is true, so "A" must be false. So once again, "A" must release something good.

The problem with this is that they assume "B" must be either true or false. They fail to consider the case where "B" may be "paradoxical". Consider the case where "A" is true. Then the inscription of "B" can be neither true, nor false. Notice that my exact wording in the puzzle was "Exactly one of the two inscriptions are true". The trap is to then automatically assume that the other inscription must therefore be false. "One true, one false" is certainly one possible configuration for the truth-value of the inscriptions, but so is "one true, one paradoxical".

Thus we can have a consistent solution where "A" is true, and a consistent solution where "A" is false, and so, no, it's not possible to figure out which button you should press.