Let In be the graph of the unit n-dimensional cube. Its 2n vertices are all the n-tuples of zeros and ones, two vertices being adjacent (joined by an edge) if and only if they differ in exactly one coordinate. A path P in In is a sequence x 1, …, x m of distinct vertices in In where x i is adjacent to x i+1 for 1 ≤ i ≤ m-1; P is a circuit if it is also true that x m and x 1 are adjacent. A path is Hamiltonian if it passes through all the vertices of In . Finally, for vertices x and y in In , we define d(x, y) to be the graph theorectic distance between x and y, i.e., the number of coordinates in which x and y differ.