Preliminary Ideas for a Rubik’s Cube Club

“Speedcubing,” the act of trying to solve a Rubik’s Cube or related twisty puzzles in the shortest amount of time possible, was a hobby that I picked up years ago. Back in middle school, I certainly found Rubik’s cubes very cool, and it changed my life as I revolved around it. I would often have my Rubik’s cube and not my phone or wallet, but never vice versa. My dream has always been to one day create a club that shared my passion for this weird, stereotypically “nerdy,” twisting puzzle that apparently makes no sense (and seems like magic) to the uninitiated. Learning to cube was not the easiest process for me, but throughout many years of cubing I’ve discovered this rough concept of “cube intuition,” the ability to develop an understanding and make predictions about solutions to certain states on cubes or other twisty puzzles. After playing around enough with the cube, one could imagine shifting certain cube states to get others in their minds, and sometimes find solutions on the cube without any help. I was also amazed by our abilities as humans to reverse up to seven or eight random moves on a cube, placing it in a semi-scrambled state, with this intuition. So, I thought that there might be a better way to teach how to “cube” (solve the classic 3x3x3 Rubik’s cube) for long-term development. The ideal method of pedagogy would definitely differ between varying demands: someone who just needs to restore their cube without peeling off the stickers would benefit from a few inefficient but easy to replicate and remember algorithms that utilize repetition, whereas someone who is considering the lustrous career of being a speedcuber would benefit more from learning some of the mathematical theories behind cubing and developing “cube intuition” earlier on before too many bad habits or wrong ideas are formed. Of course, personally, I went through the one of the standard “beginner’s methods” and took many wrong turns along the way, but the goal was to minimize these inefficiencies for serious, aspiring cubers through clever pedagogy.

There were many technical setbacks to starting a club. Most notably, the pandemic prevented in-person meetings and halted many of the official processes required to start clubs at both Phillips Academy and my old school ISB.¹ Furthermore, at ISB there were many restrictions on middle schoolers and high school freshmen trying to start clubs. However, after CoVID-era restrictions and policies were rolled back at Andover (though the era has not fully passed), the gate of opportunity has finally been re-opened, and this idea could become a reality! Partnering with a talented speedcuber, Jaylen Doyle ‘25, who averages around ten seconds with single bests in the low 6 second marks, I am overjoyed to be a part of the creation of this club. Surprisingly, Phillips Academy hasn’t hosted a Rubik’s cube club in recent years, despite its popularity among curious and nerdy young minds. The set-up process for the club is not at all resources-intensive; I could easily enumerate the short list of necessities:

• A room to hold club meetings,
• A dozen decent beginner speedcubes for people to try out,
• And access to a printer, that’s it!

Although Jaylen and I will have to work out many more technical details, I will outline the preliminary ideas and goals that I have for this club.

First, as mentioned above, I want to design a new way (which may just be a combination of many existing beginner methods, taking the parts that fit our purpose/rationale) to teach cubing. In terms of pure cube intuition, methods like Petrus and the Heiss method are solely based off this concept, the latter requiring zero algorithms! However, these methods tend not to be friendly to beginners because they are extremely labor-intensive. In my opinion, they take our goal of “teaching speedcubing to beginners in a way that initiates development of cube intuition” into “asking beginners to have cube intuition so that they could solve the cube.” This struggle and lack of progress could easily demotivate aspiring cubers. Years ago, I have written a post on this very blog about what I thought to be an algorithm-free way to approach speedcubing for beginners. I still stand by that algorithms should be taught sparingly to beginners, even though “pros” rely on large algorithm sets (COLL, ZBLL, etc.) to speed up their solves. One who thinks speedcubing is simply about memorizing algorithms and executing them quickly with the help of fingertricks is neither set up for either long term success nor equipped with transferrable skills in other cubing events or other activities altogether.² To find the best balance between difficulty, development of intuition, and succinct use of algorithms requires much more investigation and experimentation, which I hope to achieve to some extent through this club.

I might also take the opportunity at some point to introduce two lesser-known WCA events that are both considerably more difficult and more technical: the 3x3x3 blindsolve and the Fewest Moves Challenge (FMC).³ Most WCA events are the same as the 3x3x3 speedsolve but with different sized cubes or different twisty puzzles altogether. However, these events are both based off the most common 3x3x3 cube, but they are assessed much differently. In the former, you are timed as you collect information about the cube in the first stage before you are required to put on blindfolds to prohibit gaining any more visual information and solve the cube from memory, while in the latter, you are given notation for an initial scrambled state and asked to find the shortest solution you can in an hour, assessed by move count.

The Blindsolve relies on mathematical, algebraic concepts known as commutators. These allow us to identify individual pieces that we want to swap, create “cycles,” use memory techniques to remember them, and then directly act upon this information to “unravel” the scramble piece by piece back to the original state. This method is the least memory and computation intensive: after remembering the correct information through your memory device, assuming that you have amply practiced the conversion between that information to one of various sets of commutator algorithms, you won’t have to compute any state information and could simply rely on the memorized sequence. There are many skills to unpack and learn in this event, and besides, it looks so cool! Surely a great way to impress friends and family while deepening your understanding of the theory of cubes. After all, cubes are but an algebraic group of states and permutations.

On the other hand, the FMC requires a much deeper dive into the technical world of cube theory. We start off by re-establishing norms in conveying solutions through notation designed for Rubik’s cubes. Then, we put aside the speed-optimized solution methods with which we are familiar and learn various move-optimized methods to achieve a lower move count. After that, we learn about the algebra of cube permutations and how the scramble’s twin, its inverse scramble, could miraculously help us generate better solutions that wouldn’t be possible with normal, linear solution searching methods. The same knowledge about commutators (as from Blindsolving) is required, but less memorization and execution, and more on the theory of commutators and their typical move counts.

Both events offer valuable and transferrable skills both within cubing and towards algebra-oriented mathematical fields. If I get the opportunity, I would definite try to create something to the effect of a lecture series attempting to cover these two events through a math-centered perspective. Admittedly, though I could say that I know how to do them, I am not good at either of those events at the moment. I will likely write follow up blog posts documenting my journey towards better performances in those events before I go on to try to instruct.

1. International School of Beijing (webpage). ↩

2. Fingertricks are ways to speed up the execution of algorithms, mainly by preventing repetitive use of the same finger and allowing some moves to occur naturally in sequence or even parallel to one another. This is a more recent occurance as it usually follows improvements in cubing hardware (the physical cubes). Read more here. ↩

3. The World Cube Association (WCA) is an organizing body that regulates the competitive world of speedcubing. It recognizes most popular and unambiguous events involving twisty puzzles, some of which are not based on minimizing time. There are 17 WCA events, and these events are widely recognized as “official” whereas many derivative events are still held but are lesser known and absent in official competitions. ↩