After more than three decades of search, experts were finally able to determine the smallest number of moves necessary to solve any start configuration of the famous Rubik's Cube. The new calculations demonstrated that the so-called “God's number” for the 3D puzzle is 20.
Over the years, countless algorithms and methods have appeared on the Internet, and in scientific journals, all of which aimed at reducing the amount of time and moves necessary to solve any scrambled cube. The Friedrich method is for example the most widely-used approach in “speedcubing” today.
The method proposes a series of algorithms for solving a scrambled cube, beginning with a cross-like pattern on one of the faces – most often the white one – and continuing with all three layers progressively. It is used by participants in most competitions, and it grants the user very low solve times, after considerable practice.
But mathematicians are not interested in solving the cube fast. They want to know the most efficient way to solve it. In other words, they wanted the smallest number of moves necessary to resolve even the most difficult configuration. For years, the number oscillated between 15 and 20.
Now, a massive computer simulation crunched up all possible starting points of a scrambled cube. The algorithm used demonstrated after using 35 CPU years on supercomputer that the smallest number is 20. There are exactly 43,252,003,274,489,856,000 possible positions a cube can exist in at first.
What the recent study shows is that 20 moves is all it takes to solve the Rubik's Cube. “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,” the researchers behind the study write on a
website dedicated to their work.
The research team was made up of Kent State University mathematician Morley Davidson, Google engineer John Dethridge, German math teacher Herbert Kociemba, and American programmer Tomas Rokicki. They divided the algorithm between a large number of Google-owned computers, and the final results came in a few weeks later.
“It took fifteen years after the introduction of the Cube to find the first position that provably requires twenty moves to solve; it is appropriate that fifteen years after that, we prove that twenty moves suffice for all positions,” the team concludes.
For Cube enthusiasts, here is the algorithm that leads to the most difficult-to-solve scramble:
F-U-F2-D-B-U-R-F-L-D-R-U-L-U-B-D2-R-F-U2-D2 (Singmaster notation)
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