In 2006, Silviu Radu further improved his methods to prove that every position can be solved in at most 27 face turns or 35 quarter turns. Daniel Kunkle and Gene Cooperman in 2007 used a supercomputer to show that all unsolved cubes can be solved in no more than 26 moves (in face-turn metric). Instead of attempting to solve each of the billions of variations explicitly, the computer was programmed to bring the cube to one of 15,752 states, each of which could be solved within a few extra moves. All were proved solvable in 29 moves, with most solvable in 26. Those that could not initially be solved in 26 moves were then solved explicitly, and shown that they too could be solved in 26 moves.