The Hangman's Paradox
Here is one of my favorite paradoxes:
A hangman is stationed on a
road at the crest of a
hill. He asks each passerby where he or she is going. If the passerby lies about his
destination, he/she is hanged.
A
man comes up to the hangman. The
hangman asks "Where are you going? Answer truthfully or face the
gallows."
The traveller replies, "I have come here to be put to
death by you."
The traveller was replying truthfully. So the hangman shouldn't hang him. However, he had come to the hangman to be hanged. If the hangman let him go, the traveller would be lying, therefore he should be hanged.