Riddles can teach us psychology when we stop to consider the psychological principles that make them “work”. This paper studies a particular class of riddles that we call stumpers, and provides analysis of the various principles (some familiar, some novel) that inhibit most people from finding the correct solution – or any solution – even though they find the answers obvious ex post. We restrict our analysis to four stumpers, propose the psychological antecedents of each, and provide experimental support for our conjectures.