Loopless Gray code enumeration and the Tower of Bucharest

Abstract We give new algorithms for generating all n - tuplesover an alphabet of m letters, changing only one letter at a time ( Gray codes). These algorithms are based on the connection with variations of the Tower of Hanoi game. Our algorithms are loopless, in the sense that the next change can be determined in a constant number of steps, and they can be implemented in hardware. We also give another family of loopless algorithmsthat is based on the idea of working ahead and saving the work in a buffer.