Algorithms in Speedcubing
Speedcubing seems impossible to those who don’t know the “secret,” and that secret is the algorithms. When I first learned how to solve the Rubik’s cube, I realized that I just had to recognize less than a dozen sequences of moves and apply them based on recognizing the location of the stickers.^{1} However, I am still amazed by ingenious solutions devised by mathematicians and early speedcubers like Jessica Fridrich and Ernő Rubik himself. The former popularized a method of solving the cube known as CFOP, an extensible and efficient method that I use along with a majority of speedcubers. Many “beginner’s methods” are derived from simplifying CFOP, and many of which focus on reducing the number of algorithms that need to be memorized.
Memorizing algorithms is definitely a tedious part of speedcubing which scares away many aspiring cubers. I only had to memorize a total of 78 algorithms (21 PLLs + 57 OLLs) to get the gist of the CFOP method, allowing me to solve the cube in under 20 seconds (with a lot of practice). And it was not as scary as I initially thought; most of the memorization came down to muscle memory, allowing me to retain over a few hundred moves in my memory without every thinking about it (muscle memory is very powerful). But sometimes I still wonder whether algorithms are necessary and whether there are methods easier than popular beginner methods that do not require algorithms and are equally as straightforward.
While searching for the simplest and most intuitive way to teach basic speedsolving skills (on the original Rubik’s Cube) to my friends, I came across many methods attempting to minimize the number of memorized algorithm. When evaluating these methods, it is important to consider a few things.
 How compatible it is with mainstream speedsolving methods, which determines whether it gives a good foundation should the aspring cuber want to go further into speedcubing.
 What it defines as intuitive and “not an algorithm.” Also note that there is a tradeoff between intuition and speed, and that there is a difference between intuitive recognition and actively figuring out cases solely by intuition.
 How easy it is to teach. Having few algorithms is definitely an advantage, but there is some methods are still more straightforward and direct than others. This is important to consider because the method should cater to complete beginners with no prior knowledge in cubing or puzzle solving.
This search of methodology happened a few years ago, and I cannot entirely recall my thought process; however, one method that stood out to me was ColorfulPocketsVlog’s HFBeginner Method (also embedded below), a variation of the Hexagonal Francisco method (also an uncommon method). It suprised me that this method really only had 3 algorithms (although learning the inverses of some algorithms that have an order greater than 3 can really help reduce time) yet the intuition was simple and stragihtforward. Mastering the intuition within this method also has several benefits (such as keyholing) for more advanced speedcubing methods.
So far, I believe a variation of this method would be the way to go for teaching the art of speedcubing to beginners based on the criteria considered (presented above). This will definitely be my goto method, and I will update on this once I have the opportunity to try teaching this method.

It is important to note that solving the Rubik’s cube “without algorithms” is equally as difficult as figuring out your own solution to the Rubik’s cube. It is very hard to search for a specific case of an algorithm (without machine assistance). However, you could experimentally find algorithms that act on a certain set of stickers and grouping them together, and that process effectively creates algorithms. So algorithms are a very necessary part of solving the Rubik’s cube, but they act like a “black box” by obscuring the solution to the cube to noncubers. Many aspiring cubers would follow logical steps to assemble the first two layers (F2L) on a 3x3x3 (standard Rubik’s cube), only to wonder: “what do I do from here?” The answer usually will be “then do this algorithm, and apply that algorithm after recognizing this case, etc.” ↩