Is solving a Rubik's Cube intuitive?

[Wertm]

The Origin


The Rubik's cube, by far one of the most fascinating puzzles to be created in modern times.


Erno Rubik, inventor of the puzzle, who first developed it in 1974, Hungary, behind the Iron Curtain, teaching architecture and design at Budapest College of Applied Arts. He developed the cube as a way to illustrate spatial relationships in 3D to his students. It took a young Rubik a little over a month to solve his own creation.


He found trouble finding a manufacturer at the time, but it was eventually picked up by Ideal toy company and officially released in 1980... side note, before officially sold as the Rubik's Cube, Rubik called his invention the Magic Cube.


Rubik's cube today


In 2021, Rubik's cubes still have a vast popularity. Despite being close in age as the internet itself, this fascinating puzzle is still booming across the globe. And now more than ever this cube shines its importance in the form of competitions.


"The World Cube Association has a global footprint, with 30 separate regional organizations covering countries—and even entire continents—worldwide. Around 700 competitions are held annually and draw 20,000 competitors each year, according to the WBUR report." - https://en.m.wikipedia.org/wiki/World_Cube_Association


Now, I watch a lot of videos stemming from various competitors from these competitions, and everyone that I've seen says that these competitions are very useful for socializing, learning new techniques, and just having a great time... and maybe break a few records.


Intuition or mathematician?


After getting into an interesting bout with my English teacher on how a Rubik's cube is more intuition than mathematician. I, who averages a time of just under 42 seconds would testify that using the beginner solving method CFOP (Cross F2l OLL and PLL) allows for the first two layers to be very intuitive, whilst the last layer requires you to use some of your memory bank,


"Intuitive solving consists in solving the Rubik's cube without using any algorithm that you do not understand. In most methods, for example for the last layer, most algorithm are used in such way that there is an input cube in some state, then you apply the appropriate algorithm that you learnt by heart, and quite magically, the cube is in the desired state." - SpeedSolving.com.



Now, algorithms are where things get a little messy, since you'll need to be able to 'learn' an algorithm, but remember, learning a simple algorithm is easier than learning algebra. Now thanks to the SpeedCubeShop Discord community I was able to ask two speed solvers, Leapo, and Blade, who both average under 15 seconds what their opinions were. The two answers I got were pretty unexpected. For me at least, Leapo said, "After looking at a few example solves and explanations, algorithms became easy to memorize and do on my own."



And Blade said, "For me I just looked ahead and thought about where other pieces would go by moving the ones I had my focus on."



What Blade said, I believe, is showcased terrifically in "Scrambled" , a short animated video by the Rubik's YouTube channel Link:

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Final thoughts



For me solving a Rubik's cube the first time was fairly simple and wildly intuitive. But as I saw first hand in the community, that subject is very diverse and complicated. And varies from person to person and their ability to think outside the cube.


I posted this to see how many people agree with intuition over mathematician, let me know what you think.

 

[unirox13]

Very cool post. I think that it kind of comes down to who is solving the puzzle and how they're learning to do so. Honestly, I believe that age may be a factor as well.

I learned to solve the Rubik's cube over 10 years ago. I was around 20 years old or so. I learned using the beginners method book that came with the puzzle. At the time I didn't understand how the moves that I was doing were actually effecting the puzzle. It almost seemed like magic, I did the moves correctly and poof! something happened. Honestly, I wish I'd learned from a person rather than from text.

Having been solving for many years now, I understand how the pieces of the puzzle move. Where they go during certain moves and how they're able to be put in places without messing up the rest of the puzzle. The commutator was so foreign to me for years after I learned to solve. However, now, I understand how to build a commutator for a lot of different uses. I wish that I had learned more about the mechanics of the puzzle before attempting to solve it. I feel as though had I understood how the pieces moved in relation to one another, I may have stood a better chance of solving the puzzle on my own.

So I guess, in my opinion, the mechanics of the puzzle are less intuitive than the actual solve itself can be. If I had been given a run down, by a seasoned solver, of the very basics of how the pieces moved the entire solution would have made more sense. At the time of learning the solution just seemed like a bunch of moves that worked. Now I am able to see what they do and why they work.

Also, I feel as though had I learned the puzzle now, I may have taken a completely different approach. I think that I would have looked at it from a mechanical standpoint. Taken the time to watch the pieces.

Hopefully this made a little bit of sense. As far as your initial question. I do think that solving the puzzle can be seen as intuitive, but only once you truly understand how the pieces are being moved.

 

[Cuber2s]

I would honestly say no except for maybe f2l

 

[Christopher Mowla]

Everyone who has used a guide of some kind to solve it should vote no. (If it was intuitive for you all who voted yes, you wouldn't need help of any kind to solve it.)

This poll should only be for those who actually solved it with absolutely no help from anyone or anything (if we want to be completely honest with ourselves) . . . but I guess I will vote no since I didn't solve it without help. Those who happened to do so using group theory (not just commutators, but actually looking at a group theory paper and applying the knowledge logically from what was observed in that mathematical work) would naturally vote no (as they solved it based on logic rather than intuition). Those who happened to discover commutators but have no idea what group theory is should vote yes.

Intuition Intuitive or mathematician mathematical logical

 

[ruffleduck]

Without any help except from my dad (who also had no prior knowledge of how to solve the cube), I learned that I should not solve face by face, but should place pieces in their correct positions relative to the centers. After a couple months, I even figured out how to solve F2L and edges of the last layer, all without help. But I never was able to solve the corners of the last layer. If I knew about commutators (which are intuitive) I would have been able to solve the puzzle with no help. I consider the Rubik's cube to be intuitive, but not trivial.

 

[carcass]

When you say intuitive, I think of it meaning being able to be understood without aid. Very few people can solve such a puzzle without assistance, so I said it was unintuitive; people usually think you solve one side at a time.

 

[cuberswoop]

When I first had a 3x3, I came up with my own method, or so I thought. I figured out the layers, like some other people, and I even figured out some basic commutator and come break and repair ideas, like sune and anti-sune. I got to PLL with my method, but I couldn't figure anything really after that.

 

[qwr]

I always wonder if hypothetically I somehow forgot how to solve a cube I could figure it out on my own. When I learned I was an impatient child who just wanted the answers. I'll never know the answer but maybe.

 

[IsThatA4x4]

It was not intuitive for me off the start, and I didn't know the workings of the beginner's method and what things actually did. But now, with more experience in speedcubing, methods like Heise that are a mix of blockbuilding and commutators are supposedly intuitive.
However, I would not necessarily say that commutators are really that intuitive. If we look from a beginner's perspective, it is certainly not clear that if we do A B A' B' (where A is the interchange, B is the insert) that it will not just mess up the whole cube. On top of that, you have to know certain rules for commutators, such as:
- the interchange move cannot affect all three pieces at once
- the insert must preserve the interchange layer
And for edge commutators (at least from my experience), a slice move interchange means you cannot use slice moves in your insert, something a beginner most likely could not figure out on their own.
I definitely do not think solving a rubik's cube is mathematical. It could be maybe if you really wanted it to, but that's some really advanced maths.

 

[qwr]

I think figuring out commutators can be intuitive if you've had a little exposure to either puzzle solving or group theory. Commutators and conjugation come up in introductory group theory. The intuitive part is you realize if a cubie is not touched by both moves in a commutator like A B A' B', then it is eventually reset. I'm guessing the most intuitive way to solve is like beginner 3BLD using buffers which is also how you'd solve sliding puzzles too.

 

[Tony Fisher]

I solved the cube 100% on my own in 1980 and I am amazed that most others haven't done the same. The commutators I devised were just common sense and I understand exactly what is happening. There's two moves though that I guess are less intuitive. One is orientating three corners and the other is swapping two corners while preserving orientation. These were discovered by breaking up the completed face and then restoring it with slightly different moves. I wasn't looking for these specific results, only things that would be handy. So for those two I simply memorised the moves without knowing why they do what they do.
It would be an interesting challenge to do the cube entirely by intuition as long as I could write moves down to keep track. The three corner orientation move can easily be replaced by commutators so that would leave a single algorthym to discover, swapping two corners while preserving orientation. I guess that could be achieved by devising a commutator but I am not sure. That's not a question BTW since I need to figure that out myself if I ever try.

 

[Mike Hughey]

Not sure where I would fit in this. While I figured it out on my own, I did get help in that I read (completely read some of it, skimmed some of it because I had never actually held a Rubik's cube before, so some of it didn't make a lot of sense) the first Scientific American article about it back in 1981. I did not memorize any of the commutators at all, since they really didn't make any sense to me. I didn't even fully understand how commutators worked or how to construct them. But I did read enough to figure out that repeating a small sequence of moves could result in a useful "algorithm", and that with luck, some small sequences of moves could result in a relatively efficient useful algorithm.

So then I went out and bought a Rubik's cube. I had read the Scientific American article in the library, so I didn't have access to the article while I was learning to solve it. I spent the entire first week trying to maintain the cube in a solved state. I would perform several moves repetitively until the cube was restored to a nearly solved state, and see which pieces moved. I would then undo that "algorithm", and try something different. I kept going until I had "algorithms" to (if I recall correctly) cycle 3 edges, cycle 3 corners, and swap 2 edges and 2 corners. Once I had those, I scrambled the cube, and took another week before I finally solved it. I would solve the first layer completely intuitively, then use those 3 algorithms to swap pieces until it was solved. I remember figuring out how to twist 2 corners was too confusing for me, so initially I actually would just rescramble and solve again if I got 2 twisted corners.

So I didn't figure it out with commutators (exactly), and I didn't really have a lot of help, and I'd say I mostly solved it intuitively. But knowing that you could create algorithms by repetitive move sequences was a big hint that I got from the article, so I'm not sure I can claim I really figured it out entirely on my own.