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We give new algorithms for generating all n-tuples over an alphabet of mletters, changing only one letter at a time (Gray codes). These algorithms arebased on the connection with variations of the Towers of Hanoi game. Ouralgorithms are loopless, in the sense that the next change can be determined ina constant number of steps, and they can be implemented in hardware. We alsogive another family of loopless algorithms that is based on the idea of workingahead and saving the work in a buffer.

Loopless Gray Code Enumeration and the Tower of Bucharest