Deadhouse Gates

This may sound like a joke at first, but it’s in fact an interesting logical puzzle based on a story by Raymond Smullyan. A man walks into a bar, sees a woman that he’d like to know and asks her,

Will you promise to give me a photograph of yourself if I make a true statement?

Feeling this to be a flattering and benign request, she promises. The man then states,

You will neither give me a photograph nor will you sleep with me.

Here’s the dilemma: the woman can’t give the man a photograph of herself, since if she were to do so, his statement would be false and she would have broken her promise to give him a photo only if he made a true statement. Therefore, she must not give him a photograph under any circumstances. But if she also refuses to sleep with him, his statement becomes true, and this would require her to give him the photo. The only way she can satisfy her promise is to sleep with him so that the statement becomes false. The woman’s seemingly innocuous promise ensnares her. Fortunately or unfortunately, I suspect that the class of people for whom this seduction technique would prove effective is probably rather small. Nevertheless, it might make an interesting premise for a Star Trek episode, or perhaps form a part of a logician’s dating manual.