Introduction
When I first tried to solve Rubik’s Cube on my own, I was immensely frustrated. Not only did I fail, but I also could not grasp the concepts required to accomplish this task. I eventually gave up and looked up tutorials on Youtube, from which I learned to complete the puzzle. Only after practice and repetition did I understand the basic arrangement of a Rubik’s Cube, and how that can be used to solve it without memorizing many algorithms. So yes, a Rubik’s Cube can be solved without using pre-known algorithms, and this can help you gain a better sense of how the puzzle functions.
The Approach
There is a multitude of different approaches: you can start with corners first, by block building, by orienting all edges, among many others. The easiest and most common method used in CFOP is the cross + First 2 Layers. None of these steps require any algorithms, as they are intuitively solved.
The cross involves creating a foundation of four edges on one side. Then, matching corner and edge pieces are paired up and inserted into their correct slots between two cross edges. Alternatively, block-building is an excellent option. This gives you the freedom to pair up whatever pieces are available instead of building a restrictive foundation. However, in the end, it comes to the same thing: the first two layers are solved and the third layer remains.
The Third Layer
Visualizing what needs to be done to take your cube into its solved state is a useful way to structure the process in your head. It can be broken down into solving the edges and corners separately: doing this by orienting and permuting both the edges and corners. Orienting means that the pieces are facing the correct way and permuting means the pieces are in their correct, solved location.
In CFOP, the last layer is solved using OLL and PLL algorithms, which have to be memorized. Solving this step without using these algorithms is tricky because of the few pieces left, but it is certainly possible. In events such as FMC (Fewest Moves Challenge), competitors frequently do not use OLL and PLL algorithms because they are inefficient compared to more flexible methods like using commutators.
Commutators
Commutators are a specific set of moves that only move around a few pieces on the cube while keeping everything else intact. They are of the form: A B A’ B’, where A and B are two move sets and A’ and B’ are the inverse of the move sets. Some of the most common commutators are for moving around 3 corners and 3 edges, and a few might be very well known to you despite the unfamiliar name.
For example, the commutator of R U R’ D2 R U’ R’ D2.
In this case, A = R U R’ and B is D2.
Hence, the full commutator that cycles 3 corners will be A B A’ B’ = (R U R’) D2 (R U’ R’) D2.
This technique of using inverses means that all the pieces affected except the ones involved will go back to their solved state. When the pieces to be solved are not in the position you desire, a few set-up moves can easily be performed before and reversed so that everything goes back to being solved. This is, in fact, one of the fundamental rules behind methods for 3x3 blindfolded solving.
So, for the last layer, a combination of commutators can be used to orient and permute all the pieces. The advantage of this is that it is highly flexible and requires absolutely no memorization of algorithms. Instead, it takes a very simple concept and makes it so that a few pieces can be solved without disturbing others.
Conclusion
The Rubik’s Cube can most definitely be solved without memorizing any algorithms. After all, Erno Rubik had to solve it on his own the first time he scrambled his puzzle! Commutators are a very useful tool in this case. You might be wondering, what is the point of learning these techniques? Well, commutators are the basis of 3x3 blindfolded solving as well as many FMC successes. Furthermore, they help develop a proper spatial understanding of the Rubik’s Cube that might help you in improving in other events as well!
About the Author
Pranav Prabhu
Pranav Prabhu is the current 3x3 Fewest Moves (Single) National record holder from Chennai. He started cubing when he was 14 and has 5 years of cubing experience. Besides cubing, Pranav enjoys reading books, writing, and playing the piano. He has participated in 36 competitions and won 30 podiums including 8 gold medals and 1 National record.
