We consider two closely related word puzzles, and show that each of these is based on an operation that can be interpreted mathematically as a derivative. While the appearance of this mathematical structure in such a context might be surprising, the identification arises quite naturally in both cases, and the resulting derivatives are in the same family as the derivative defined in type theory. We construct the derivatives appropriate to each of these word puzzles, and show how they can be used to frame these puzzles and to motivate some additional related questions.