Puzzles and codes have multifaceted uses in practices of concealment, especially for militaristic purposes, corporate secrecy, or national security.The term ‘Enigma’ is perhaps most recognisable in modern history and contemporary culture as the name of a cipher device used by the German military to send messages during World War II. This chapter moves to the historical context of the twentieth century and shows how humans sometimes deliberately engineer enigmas to serve their own purposes. The author focuses on the mathematics underpinning the story of the Enigma Machine, setting out the process both of the code’s creation and of its decryption. Following the story of Alan Turing, a mathematician and one of the code breakers at Bletchley Park, the chapter emphasises both the necessity of collaborative labours to solve challenging problems and the importance of individual research and investigation to resolve crucial pieces of a much larger puzzle.