The Enigma machine was used by Germany in World War II to send coded messages. It has gained fame because it was an excellent coding device for its day and because of the ultimately successful efforts of the British (with considerable aid from the Poles) to crack the Enigma code. The breaking of the code involved, among other things, some very good mathematics developed by Alan Turing and others. One part of the machine consisted of three rotors, each containing the letters A through Z. To read an encrypted message, it was necessary to determine the initial settings of the three rotors (e.g., PDX or JJN). How many different initial settings of the three rotors are there? The naval version of the Enigma machine had four rotors rather than three. How many initial settings were made possible by the rotors on the naval Enigma machine?


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