A Rubik's Cube Can Always Be Solved in 20 Moves or Fewer

The quest to find the most efficient solution for any scrambled Rubik's Cube led mathematicians to a concept known as "God's Number." This isn't an average number of moves, but the absolute maximum required for the most difficult configuration possible. For decades, the search for this number was a major challenge in computational mathematics. Early estimates were in the fifties, but as algorithms improved and computers grew more powerful, mathematicians and programmers gradually lowered the upper limit, proving it was no more than 29, then 25, then 22.

The final proof for the number 20 arrived in 2010, when a team of researchers, using donated idle computer time from Google, completed a monumental analysis. They didn't need to check every single one of the 43 quintillion scrambles. Instead, they used mathematical principles of symmetry and group theory to cleverly sort all possible positions into 2.2 billion sets. By tackling these sets, they were able to prove that no position required a 21st move to be solved. This confirmation closed a thirty-year-old puzzle, perfectly blending abstract theory with immense computing power to find the ultimate speed limit for solving the cube.