A COMPARISON OF VARIOUS METHODS
I doubt that anyone will try to outdo Jessica Fridrich by devising a solution with still more algorithms. But there are other approaches. For example, the solution described on this web site places all edge pieces in the correct position/orientation before placing any corner piece. And perhaps the ultimate will not be obtained by increasing the number of algorithms but by reducing them. Would you believe two series?
"The Ultimate Solution to Rubik's Cube" first places all 12 edge pieces using a single series (the Edge Piece Series). This series is neither new nor unusual. Jake Olefsky uses a similar series in Step 3 of his solution. However, I use a more direct approach. For example: F R' F' R would cause the three edge pieces which are adjacent to the TFR corner to move in a counterclockwise direction about that corner. Its mirror image would cause these same three pieces to move in a clockwise direction. But I deviate even further from Jake and his friends. I use a word description of the series rather than a series of letters.
Fig. 1 Start Fig. 2 Step One Fig. 3 Step Two
Once all edge pieces are in place the corner pieces are moved into correct position/orientation using a second series (the Corner Piece Series). This series has eight turns. Again it is not described by a set of letters but by a word description which leads the cubist through the set of turns. It is progressive and symmetrical. One form moves three corner pieces in a clockwise direction about a triangle on the top face of the cube. It's mirror image sends three corner pieces in a counterclockwise direction about a triangle which is a mirror image of the first.
Fig. 4 Step Three Fig. 5 Step Four Fig. 6 Step Five
Again it is not new. You can find it in Don Taylor's "Mastering Rubik's Cube" (diagram b, page 24) and Jonathan Bowen's "The Rubik Cube" (part 6 series vi) on the Internet.
Two series. The ultimate solution! Does it work? Of course it does. A consecutive series of 100 scrambled cubes required an average of 65 moves (or 70 turns) to restore the cubes to their original state. The minimum number was 40. The average can be reduced to about 62 moves by using the approach of placing corners and edge pieces simultaneously in the first two layers. But this destroys the simplicity and gains very little. In fact it always takes me longer to solve the cube this way because one must locate two subcubes simultaneously and then ascertain how they will be dealt with as a pair.