The Rubik’s Cube® is a simple, inexpensive puzzle with only a handful of moving parts, yet some of its simplest properties remain unknown more than 30 years after its introduction. One of the most fundamental questions remains unsolved: How many moves are required to solve it in the worst case? We consider a single move to be a turn of any face, 90 degrees or 180 degrees in any direction (the ‘face turn metric’). In this metric, there are more than 36,000 distinct positions known that require at least 20 moves to solve [9]. No positions are yet known that require 21 moves. Yet the best theoretical approaches and computer searches to date have only been able to prove there are no positions that require more than 26 moves [4]; this gap is surprisingly large. In this paper, we prove that all positions can be solved in 22 or fewer moves. We prove this new result by separating the cube space into two billion sets, each with 20 billion elements. We then divide our attention between finding an upper bound on the distance of positions in specific sets, and by combining those results to calculate an upper bound on the full cube space.