Cubing Algorithms

Cubing algorithms have been present from the genesis of the cubing community. The cube algorithms expressed as notation R U F D L etc are the primary way we share and communicate common knowledge that exist in various solving methods. For instance, in the CFOP method, we have an algorithm list of OLLs that is pretty useful as anyone on the internet can download it and start executing and try out all the cases. Cubing algorithms and cubing theory are still in their infancy, there are a lot of things that are still not fine tuned that can be put into a rulebook and coached to a beginner. There is a lot to cubing algorithms rather than just having R U R’ U’ written out. There are various short hands, ways to optimize reading, ways to understand better by grouping into triggers and memorizing it using Yo notation. All these algorithms are classified on various sites like speedcubedb and various other sites online. New cubers and seasoned cubers can check these resources out and get value out of it. This article is divided into various categories: the first section addressing how to bracket moves to make algs look more sensible. The second section talks about grouping moves to see visible patterns within the algorithm. The final two sections talk about new ideas that are being brought up like visualizing the algorithm in the form of a picture, or try to break down an algorithm into words and make sentences out of them. I voice my thoughts about the cubing algorithm in the end and conclude this article. Let the brainy ride of reading this article begin.

Bracketing moves

Bracketing cube moves is important. It helps divide a long sequence in a few chunks that our brain can understand easily. One basic example that I can give of the Tperm algorithm that everyone is familiar with. The algorithm goes like R U R’ U’ R’ F R2 U’ R’ U’ R U R’ F’. Just reading this alg can sound tough and unfamiliar so it is better to group them in groups. So we can make our life easier by breaking up the alg into chunks and try and understand each part of it. One way to go about it is (R U R’ U’) R’ F R2 (U’ R’ U’) (R U R’) F’. So the triggers R U R’ U’, R U R’ and U’ R’ U’ are well known to most CFOP solvers, so breaking down the alg into this form makes it more understandable.

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Grouping moves

Grouping algorithms or sets of algorithms is another careful task. If you see any common algsheet like OLL and PLL, you see that they are classified beautifully with the OLL being classified by the shape that they form, number of edges oriented. If you take the set of say F2Ls, there are just too many ways you can categorize them, some categories go like orientation of corners, orientation of edges, slot location, piece closeness. 

Pictorial representation of algorithms

Pictorial representation of cubing algorithms

Algorithms as pictures is something that we do not come across when we start learning algs in cubing. is a great and unique site made 2 years back by a speedcuber Derek Nash. The motive behind the creator is unique. He wants to find a visual way of seeing each algorithm. So any face turn, slice turn can be coded up as an arrow. This makes a big algorithm just a series of images that you can understand if you go through the arrow diagrams from left to right. There can be other ways of visualizing algorithms but this is an unexplored field. A lot of ideas can be realized but as of now we only have the cushan web applet to get a better pictorial representation of a 3x3 algorithm.

Yo notation

The popular cube notation that every speedcuber knows is called singmaster notation as it was devised by a mathematician David Singmaster. This notation is good to generate scrambles and stuff, but not good enough for memorization of long algorithms. One of the major hurdles that I see in newer speedcubers is that they do not have a mechanism to learn algorithms or the stamina to revise and get familiarized with a complete algorithm set. 

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Yo notation is a way to encode face turn, slice turns and wide turns of a 3x3 uniquely as a letter. The main objective of creating such an encoding system is that it makes learning algorithms much easier. 

This ‘Yo notation’ system makes memorizing algorithms simpler. Let me explain my point. In this system, we are able to encode each face turn as a unique letter U=a, U’=b, U2=c and so on, and the entire algorithm string can be broken down into groups of 4 to be memorized as images. So for example, R U2 R’ D, becomes jckd in Yo notation, which is just the letter quad for ‘justin kid image’. So a sequence of moves that do not have a common trigger embedded inside it like (R U R’ U’, R U2 R’, R’ F R F’ etc), can be remembered as an image if we encode the face turns into yo notation and make an image out of it.

Yo notation

Fig. A snapshot of how cube algorithms are organized in popular online sites like

Final thoughts

The larger the island of knowledge, the longer the shoreline of wonder

- Ralph Sockman

There are a lot of things to learn about cubing algorithms even after you start out and learn the face turn notations. There are various ways of improvement and each way of improvement has its own caveats. Cubing algorithms have come a long way and have become a lot more accessible now, especially the algorithms from the CFOP method. There are a lot of things, ideas and improvements that can be explored to make a better way of encoding a sequence on a rubik’s cube. This article tried to address this and I hope I ignited your thinking neurons and you get started with your ideas and get more out of cubing and understanding cubing algorithms better and become a much more sounder cuber. Remember, that if you are fast, it does not mean that you are a person who has tried many ideas. There is a thin line between grinding solves and getting ideas, and a good cuber needs to do both in order to improve in the long term. Cubing is a creative sport and not a repetitive task. Delving into cubing algorithms is one way of expressing cubing creativity!

See you in the next article.


-Abhijeet Ghodgaonkar

Abhijeet Ghodgaonkar is the current 4x4 Blindfold (single) National Record holder from Mumbai. He started cubing when he was 13 and he has an overall competitive experience of 8 years. His main events are 5BLD and MBLD. He has been developing concepts like letter quads and 5-style since 2017, to make blind-solving events more structured. He has participated in 50 competitions in a total of 3 countries and won 105 podiums with 51 Gold medals, 2 Asian Continental Records, and 3 National Records.  He also has a World Ranking of 29 in 4x4 Blindfolded Single.

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