Yeah I got that, but it's really not as interesting as it seems. Let me explain why. Say we have an array p[1], p[2], ..., p[n] with all possible rubiks cube c

Yeah I got that, but it's really not as interesting as it seems. Let me explain why. Say we have an array p[1], p[2], ..., p[n] with all possible rubiks cube configurations Then this function will solve the cube: move(1) = p[1]^(-1) move(i) = p[i]^(-1) * p[i-1] In laymans terms, the resulting algorithm is: assume the initial configuration is p[1], then solve it. If it wasn't, undo those moves then solve as if the initial position was p[2], etc... So, yeah. Those fixed solving sequences / hamiltonian paths are actually very common. We can make one for any permutation of the group elements. So I posed a more interesting question: what is the simplest sequence of moves that has this property?