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Comment by Tomminn | Hacker News Reader

If you've never learnt the algorithms required to solve a Rubik's cube-- don't. Understanding and solving a cube by brute effort is a great little challenge to come back to over the years.

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If you have learned them, it's not too late. Martin Gardner mentioned an algorithm that doesn't work layer by layer, but instead starts off with all manipulations available, and gradually restricts which ones are admissible. In principle, just at the point no moves are admissible, the cube is also solved.

In that oh so distant future when I have nothing else to do, I'd like to try to work out this approach for myself.

Sounds interesting, do you have any source on this? tried googling but couldn't find anything...

I messed up. Upon referring to http://martin-gardner.org/MGSAindex.html , I've learned it was a Hofstadter column: https://www.scientificamerican.com/article/metamagical-thema... (paywalled)

Does http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers... provide enough information? (At least it gives you some better search terms.)

> "indeed it is not visually obvious that any progress at all is being made until the cube is almost solved."

I do the edges first and then the corners. I changed it up for novelty and to force myself to come up with a different solution. So I've got permutations to manipulate edges that also mess with the corners, followed by ones that manipulate the corners.

I've wondered if there is a way to do it by restricting to smaller and smaller subgroups, but that'd probably be a lot of work to figure out.

Apart from the fact that you get the happiness of having solved it without help. What else does it give?

Probably not much. A bit more intuition about non-commutative transforms, perhaps.

But you don't gain anything much from learning to solve them either. It's a fun party trick once or twice, but you'll likely feel uncomfortable not acknowledging that you read the answer, at which point it's comparatively unimpressive.

Is there any game or challenge that actually makes you smarter or better or helps you out in any practical way?

Of course. Games like go can help reduce the effects of Alzheimer[1]. I'm sure there are studies for chess too.

Sports are games with obvious health, mental and social benefits.

On a more intuitive level (aka I don't know if it's been researched), I would be surprised if most board games don't improve, at least a bit, the analytical thinking useful for many engineering fields (or even day to day life).

Challenges is a term too broad, you can imagine countless ones that have practical benefits. Learning-to-play-an-instrument-in-a-month challenge for example. 100 push-ups a day for a month. Read one book a month.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4548213/

Depends upon what one considers practical? I had some nice (here: both informative and entertaining) conversations with someone I'd consider a genius, not via the more evidently practical skill of juggling, but because we'd made each others' acquaintance due to a mutual interest in Rubik's Cube.

If you haven’t seen it, you may be interested in https://youtube.com/watch?v=q6AsllXpKBU, which combines solving Rubik’s cube with juggling (1 minute, 41 seconds per cube)

Speedcubing. It is very ignorant to claim that all you need is to know a bunch of algorithms. It is on par to claim that to win a basketball match you need to throw a ball into the basket. You need to think how to optimally solve the cross (or maybe to do extended cross), you need to be quick to spot the pieces for F2L and to choose optimal way to place them, you can choose different ways to solve the last layer to maybe gat an OLL or a PLL skip.

Millions of years of evolution and the presence of play in mammals suggests yes

> A bit more intuition about non-commutative transforms

Most (almost all?) state machines one encounters in software are non-commutative. Cosets and conjugation are cromulent CS concepts.

Edit: Grand Corps non Commutatif https://www.youtube.com/watch?v=SZXHoWwBcDc

Oh, for sure, I don't mean to suggest that non-commutativity isn't an important concept. But just as I think throwing a ball around is of limited value beyond a bit of intuition in studying aerodynamics, I don't think playing with a Rubik's cube is going to fundamentally advance your understanding of transforms.

If you can explain the various algorithms and how they work it may still seem impressive.

In my opinion, you don’t understand the Rubik’s cube if you don’t know how to solve larger ones. I’ve never held a 5×5×5 or larger in my hand, but I know I can solve it or any larger one easily.

Variants such as dodecagons can be a little trickier, as knowledge doesn’t transfer as easily, but if you understand the cube, you still should be able to solve them reasonably quickly.

> But you don't gain anything much from learning to solve them either.

It is very useful to be able to solve the cube yourself.

This allows you to start from a solved state easily, and then experiment with different patterns, move sequences, etc.

I was not one of those people who could completely track the state of the cube in my mind. But it was easy for me to see what I've done if I started from the solved state.

Telling people what kinds of intellectual effort are worthy of your respect is both obnoxious and interesting. Please stop.

Isn't that the whole point of puzzles?

That depends if you are doing the puzzle for the love of puzzles, or if you are doing the puzzle for your father's love of puzzles.

When my oldest was about six or seven, I showed her the Rubik's Cube. She was enthralled with it. But she had no drive to solve it, and showing her how (no algorithms) really didn't interest her. Now, at thirteen, she's picked it up again. And she absolutely loves solving it.

I am so glad that I've never pushed her to learn things, rather just having just _exposed_ her to interesting things without pushing her. Now she has the intrinsic drive to learn.

I have a cube sitting on my desk; it helps me think. Over time I've learned more and more algorithms for it; I almost know all the PLLs. Honestly it's a lot of fun!

Because once you learn them, you will never unlearn. I took a cube in my hands after some 30+ years break and my hands just instantly knew the sequences...

I remember about 80% of them by muscle memory, but... I've forgotten some, so my party trick now is to get a cube 'nearly' solved in about 50 seconds, then give it to someone else, and say "I've done all the hard work already, you can finish it off".

Generally that's true for things learned as children, not as adults.

I managed to forget most of them after about 5 years of not doing it. I can intuitively get the first two layers now, but the top seems too difficult without knowing the sequences.

I like messing about with a Megaminx also, and it's the same for that. I can get the first couple of layers just thinking about it intuitively, but then I get stuck on the top layer.

At some point I'll relearn the sequences again, but I haven't yet.

Also picked up a 2x2 cube recently, and that one has me pretty stumped. You'd think it'd be easier to figure out but I haven't figured it out yet.

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