The story of upper and lower bounds does not really stop with the number twenty. The story above namely supposes that one move consists of turning one side completely freely, that is, 90 degrees in one direction or 180 degrees in any direction.
If we restrict ourselves to moves of exactly 90 degrees, we get a different analysis. Mathematicians like naming things, and this is often called quarter-turn metric instead of half-turn metric.
This creates a much more difficult problem, because a move of 180 degrees now counts as two moves instead of one. The story about upper and lower bounds evolved similarly, and in August 2014, the problem was finally solved.
It was again Tomas Rokicki and his collaborators who found the answer: With quarter-turn metric the answer is 26.
New records for speed cubing are continuously being set. If we take a look at the website of World Cube Association, a great resource for competitions and registered cube records, we see how the records of the regular 3x3x3 cube has evolved from 2004 to 2016:
In the graph above you find all of the official records, but also the tenth and hundredth places. It is clear that we are approaching a limit to how quickly the cube can be solved. The current world record for solving the regular 3x3x3 cube was made by the American 14-year old Lucas Etter in November 2015 at 4.90 seconds.
Here in Norway, it is Jonathan Hamstad and Morten Arborg who compete for the Norwegian record. Since October 2015 it is the former who holds the record at 6.33 seconds. To see all the records, I recommend the website of the World Cube Association. The Norwegian Cube Association (in Norwegian) provides information on cubing in Norway.
It is perhaps no surprise that robots solve Rubik's Cube faster than humans. But just how fast can a robot solve the cube?
In January 2016, a new world record in robot cubing was set. At that time, a robot was able to to see, analyze and completely solve the cube in no more than 0.887 seconds.
Finally, it must be noted that there are many variations to how the cube is solved and to how similar cube puzzles are constructed. In the video above you can see a little of this fascinating universe of varieties.