Introduction
Computers have been around for a long time now, and the development of artificial intelligence led to a lot of progress in the field of mathematics. Group theory was one of these fields under research, and the Rubik’s cube was a fascinating problem in this subject.

Hungarian sculptor, Erno Rubik, invented the Rubik’s Cube in 1974. Since then, it has progressed as a puzzle that has baffled many minds and intrigued many more on finding methods on how to solve it. Over the years, many people created their own methods and logical approaches towards solving the cube, such as Jessica Fridrich with her CFOP method, Gilles Roux with his Roux method, and many other notable people.

Erno Rubik, A Professor of Architecture

Why Computers?

Naturally, these processes of finding methods to solve the cube had inefficiencies of their own, since they were invented by humans and had very logic-based approaches. If a computer was given the same task, would the approach be the same? Would a computer solve a 3x3 cube layer by layer? Would a computer solve it using the Roux method? This question began to make mathematicians and statisticians across the world ponder.

It is useful to note that there are over 43 quintillion possible permutations on the 3x3, and the more you can grasp, the more in-depth your method of solving it will be. So, it was only obvious that a computer designed for this application would be able to solve it in far fewer moves, using methods that would only seem vague and senseless to humans.

The Search

So, in 1981, the search was begun, with multiple computers around the world trying to figure out the least number of moves needed to solve any random state of the Rubik’s Cube. Initially, this number was set to be anywhere between 18 and 52, but over time, with about 35 CPU-years of idle computer time donated by Google, the number has been found to be exactly 20, with no deviation. This was termed to be “God’s Number” and it gave us rigorous proof that any state on the cube could ALWAYS be solved in 20 moves or less.

The Superflip, proven to require a minimum of 20 moves to solve

Once we had this development in 2010, we understood that computers might be our best source and tool to find new algorithms for a myriad of different cases! Soon enough, public as well as private tools were developed for this purpose, and we started improving on current algorithms with lower move-counts and better efficiency.

The Uses

This led to the creation of “algsets”, which are sets of algorithms to solve a certain part of the cube, of much higher precision and more use. For example, ZBLL is one such set that solves the entire last layer using just one algorithm (after orienting the edges). It consists of 493 total algorithms, developed by Zbigniew Zborowski and Ron van Bruchem. The use of computers and programming to come up with algorithms has been intensive throughout the development of algorithms for cubing.

A ZBLL Case

An Event In The WCA?

An official WCA event analogous to this process of finding the shortest solutions for certain states of the cube is FMC (Fewest Moves Challenge), where each competitor is given an hour to find the shortest possible solution to a given scramble, to the best of their abilities. The current World Record Single for this is an impressive 16 moves, held by Sebastiano Tronto of Italy! This shows how much our understanding of the cube has progressed since the advent of computers in our search for better solutions, to a point where even a human is capable of finding solutions under 20 moves!

A Sample of FMC sheet

That’s Not All!

Another aspect where computers have made a vast difference is scramble generation. Scrambles are sequences of moves that are performed by all speedcubers while practicing and they result in one of the over 43 quintillion possible states upon completion. The generation of these scrambles is done by software, and put together in online timer websites such as cstimer.net and . For official competitions, the WCA uses a software called TNoodle to do the same, and this shows just how much we rely on computers to generate unique and legal scrambles!

While one may scramble a cube by hand, find an algorithm by tedious hit-and-trial, calculate the number of permutations on the cube by mathematics and find methods to solve the cube on their own, it is clear how much of an impact the involvement of computers has had in the progress of speedcubing today. It is fascinating to see, and an amazing feat that is now accepted as the norm across the world.

The Software

The best part about all this is that nearly all of the software is open source and free to use, which makes it that much more friendly to cubers. It is useful to note that this only covers the software part of speedcubing, since the hardware part related to manufacturing and processing of the cubes themselves are also done by computers that have been constantly upgraded to serve the purposes that the speedcubes of today do.

A Look At The csTimer+ Interface

Image Courtesy: csTimer+

Conclusion

Thus, we see that computers and the improvement of Artificial Intelligence (AI) have together created an ecosystem, whether it be online or offline, for a  better speedcubing experience for all. They have brought about changes that make our lives easier and also help loads with learning and self-improvement! Together with the advancement of technology, this implies many bright avenues for the future of speedcubing, which is just as exciting as speedcubing itself.

The GAN Robot 2.0, a cube scrambling and solving robot

-Akshaansh Chilakapati

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