Rubik's Cube™

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The article God's Number is 20 describes the demonstration that every position of Rubik's Cube™ can be solved in twenty moves or less. With about 35 CPU-years of idle computer time donated by Google, a team of researchers has essentially solved every position of the Rubik's Cube™, and shown that no position requires more than twenty moves.

"We have known for fifteen years that there are positions that require 20 moves; we have just proved that there are none that require more. Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions, yet there are probably more than one hundred million such positions. "