1. Introduction This blog describes two findings related to the structure of the state space graph of the 3×3×3 Rubik cube puzzle. In addition to the above, the method of cube representation and the "direction value mappings" are new. “Rubik cube” here means the 3×3×3 Rubik cube. There are Rubik cubes of other dimensions but they are not discussed here. 2. Background The Rubik cube puzzle has around 4.3×10 19 possible states. Finding the optimal sequence of moves to go to the “Goal state” from a random state is an unsolved problem. (Here the optimality is with respect to the number of moves in the sequence) The Idea: In a graph like the n-dimensional hypercube, it is easy to find the optimal path from one node to another, however large the graph may be, since we know the structure of the graph . Likewise if we know the structure of the state space Graph of the Rubik cube puzzle, we could find optimal solutions to any configu...