In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as a basis for discussion of the nature of mathematics, for development of problem-solving skills and confidence, and as a means of engaging students from a broad range of mathematical backgrounds. I suggest a consistent use of puzzles in a low-pressure setting as a possible means of fostering inquiry and a positive learning mindset among students.