From a puzzle-solving point of view, these very large cubes aren't that interesting. When you increase the cube size, there are new things to figure out, but only up to a certain point. Figuring out how to solve a 4x4x4 when you know how to solve a 3x3x3 takes some significant work. I think I spent a whole weekend to successfully solve a 4x4x4 the first time I got one, despite being reasonably good at solving the 3x3x3. Solving a 5x5x5 for the first time took just a couple of hours, there wasn't much new to learn. The 6x6x6 was easier still. When I got to the 7x7x7, there wasn't really anything new at all. I could solve it immediately, it just took more time.
Anything beyond 7x7x7 is pretty much the same. It's just more annoying, because the puzzle gets physically harder to handle, and because you have to do the tedious work of counting how many layers away from the centre a piece is. The 7x7x7 is the biggest cube used in official competitions, for a good reason.
The motivation for making enormous cubes like the 34x34x34 is just the engineering challenge, and breaking records. Nobody is going to want to solve such a thing, at least not more than once.
That all sounds like fun but I'm still working through solving a 64-disc Tower of Hanoi puzzle right now and won't be able to get to another puzzle for a bit.
I'm still waiting for my Moment of Glory when a puzzle room or something has a Hanoi tower and I can slam out the solution as quickly as I can move the pieces, thus justifying all my formal Computer Science education once and for all.
(There is a very easy-to-remember algorithm that can be trivially executed by humans given here in a Mathologer video, with a time-code link to jump straight to it: https://youtu.be/MbonokcLbNo?si=ey8bv4T9KbDxgB7N&t=650 )
in particular, "bandaged cubes" in which certain faces have fused blocks to limit your available moves, and "constrained cubes" in which certain faces can only rotate in one direction, and only by a certain amount.
Just to elaborate: Solving a 5x5x5 or a 7x7x7 is basically just turning the cube into a 3x3x3 by lining up the edges and fill in the centers. Which is a new thing, but quite easy to figure out. And then solve it as if it was a 3x3x3.
That's not the only way to solve big cubes, but it's indeed the most common way (known as "reduction"), and what most people naturally come up with if they try to solve 4x4x4 or bigger on their own. In addition to what you said, there is also the issue of parity (basically, when you reduce a 4x4x4 to a 3x3x3 by solving centers and edges first, you will often end up with a 3x3x3 cube in an unsolvable state, and you need to figure out some tricks to convert it to a solvable state), but if you know how to solve parity problems on a 4x4x4, you can do it for a cube of any size.
The moves to fix parity made the 4x4x4 less fun for me. The recommended solution is long.
The hollow 3 has a similar problem. Because you can’t see the central piece there’s a way to rotate the core and a couple of edge pieces so they look like they violate parity.
Just out of curiosity (no rubiks cube affinity at all), but how can there be an unsolvable state when there are 'tricks' get in a solvable state? Does that not imply that there are no unsolvable states at all? Or is that maybe related to a certain method of solving?
The reduction method means reducing a big cube (NxNxN for N>3) to a 3x3x3 cube by first solving the centers (the central (N-2)x(N-2)x(N-2) square on each face) and the edges (the inner N-2 pieces along each edge of the cube). You are then essentially left with a 3x3x3 cube that you can try to solve by only turning the outer layers (which won't break the centers and edges you solved in the first stage).
The problem with this is that you may end up with a 3x3x3 cube that is not solvable. For instance, you can get a state where the entire cube is solved, except for two edges that need to swap locations. This isn't possible. In group theoretical language, only even permutations are possible. You can swap two _pairs_ of edges, but not just two edges.
When you end up in such an unsolvable 3x3x3 cube, you have to temporarily turn the inner layers of the cube and break apart the centers and edges you built in the first step, and then reassemble them again to a solvable 3x3x3 cube.
Sort of. The 3x3x3 and 5x5x5 both have fixed, immovable centers. Red is always opposite orange, blue is always opposite green, and yellow is always opposite white. The 4x4x4 doesn't have fixed centers. When you build the central 2x2 squares on each side (the first step of the reduction method), you have to be careful to have the colors arranged in the correct locations relative to each other. In a certain sense, this is trivial, but it forces you to remember exactly where all colors are on a solved cube in order to solve a 4x4x4 (or other even sized cubes). Odd sized cubes don't have this problem.
Another annoying thing about 4x4x4 compared to 5x5x5 is that you have two possible types of parity issues on the 4x4x4. On the 5x5x5, only one of these can occur.
Nevertheless, if you know how to solve a 3x3x3 and no bigger cube, a 4x4x4 is certainly the easiest next step.
I've read that the minimum number of moves for solving a 3x3x3 cube in its most scrambled state ("God's number") is just 20 moves, and this was verified through brute force search. I'm uncertain as to whether there is an algorithm for solving an arbitrarily scrambled cube in just 20 moves, or if it's just known that it is possible to be solved in 20 moves, but probably the latter. Anyway, I can't seem to find a corresponding God's number for the 4x4x4 cube but it seems perhaps the lower bound is in the 30-40 move range. I not a cuber (?) by any means so I don't know if there's any sort of formula to even approximate the lower bound for solving successively higher level cubes, but if there is, I'd be very curious to know what the approximate God's number is for this 34x34x34 beast.
Anyway if we were to go with just a very naive guess that each higher level takes 1.5x the moves of the previous level so 3x3x3=20, 4x4x4=30, 5x5x5=45 and so on, that would yield 34x34x34= 5,752,532 moves (or 5,817,104 if you round up 1 at every fractional result), which at a second per move, would take over 2 months to solve. I suspect that in practice, any algorithmic means to solve such a cube would take somewhat longer, so much so that a thoroughly scrambled cube might never be unscrambled.
A few days ago, my younger daughter was trying to have fun and suggested that we watch an important video about solving a 1x1x1 Rubik’s Cube. I went along, and we spent some time moving up the numbers; that’s when we needed to search for the largest number of NxNxN possible, and we landed on this video and the article.
3D printing technology is amazing now. I used to struggle with my ABS prints warping 12 years ago with a PP3DP --- I couldn't even print a giant 3x3x3 rubik's cube that worked. Now there are lots of 3D printers that are essentially just zero configuration and everything works out of the box. I even printed a lens mount for my camera and it came out quite well aligned. So it is very nice to see some regular consumer 3D printers being good enough for a functional 34 x 34 x 34 cube.
(Snark warning, but even more than that, I find myself amused and amazed by the overall story)
Ah, yes. Ruwix, the beloved Rubik's cube tutorial site that abused and cheated their way to the top of SEO rankings[0] in ethically dubious manner by directly victimizing end-users.
There are a lot of methods, optimized for different purposes. Some are easy to learn, but take a very large number of moves to solve the cube. Some are exactly the opposite: Difficult to learn, but enables you to solve the cube in just a few seconds. Others are optimized for solving the cube in the fewest possible number of moves, but requires so much thinking that they are not suitable for fast solutions. Others again are optimized for blindfolded solving.
My two favorite methods are Roux and 3-style.
Roux is the second most common method for speedsolving. Compared to the more popular CFOP method, Roux is more intuitive (in the sense that you mostly solve by thinking rather than by executing memorized algorithms), and requires fewer moves. Roux is much more fun than CFOP, if you ask me, and for adults and/or people who are attracted to the puzzle-solving nature of the cube rather than in learning algorithms and finger-tricks, I think it's easier to learn. Kian Mansour's tutorials on YouTube is a good place to start learning it.
3-style is a method designed for blindfolded solving, but it's a fun way to solve the cube even in sighted solves. It's a very elegant way to solve the cube, based on the concept of commutators. It takes a lot of moves compared to Roux, but the fun thing is that it can be done 100% intuitively, without any memorized algorithms (Roux requires a few, though not nearly as many as CFOP). It's satisfactory to be able to solve the cube in a way where you understand and can explain every single step of your solution. As an added bonus, if you know 3-style, you can easily learn blindfolded solving, which is tremendously fun, and not nearly as difficult as it sounds.
Edit: If you do decide you want to learn, make sure you get a good modern cube. The hardware has advanced enormously since the 1980s, modern cubes are so much easier and more fun to use. There are plenty of good choices. Stay away from original Rubik's cubes, get a recent cube from a brand like Moyu, X-man or Gan.
I used to be able to solve the 3x3 in high school using memorized algorithms and then I lost interest since there was no reasoning involved. Your comment makes me want to pick it back up and learn 3-style, so thank you for the clear explanation!
Like you, I learned the 3x3x3 in high school via memorized algorithms, and that was only so interesting. Years later my brother got me a Megaminx (the dodecahedron equivalent to the 3x3x3 cube, third one in the top row there) and I was absolutely fascinated by learning to solve that by porting what I knew from the cube. From there I got all those other shapes as well. The most interesting ones to search by name: Dayan Gem 3 (the one that looks like the Star of David), Face-Turning Octahedron (last one in the second row), Helicopter Cube (to the right of the 3x3x4), Rex Cube (right from the Helicopter Cube).
Even with CFOP, there is a large amount of intuition needed in order to break below the 25 second limit, mostly because of lookahead. During that phase, you need to train your fingers to do moves while your brain anticipates the next moves. There are no real formulas involved, it's really about intuition, pure skill, and multitasking.
Congrats, that's an awesome average! I wish I was that fast. I don't time myself often, but when I do, I usually end up somewhere around 15 seconds. My efficiency is not bad, but my hands are just too slow.
I agree about beginner tutorials. There are some decent Roux tutorials, but they are mostly not targeting complete beginners. I believe it should be possible to make a Roux-based beginner method that is even simpler than the popular layer-by-layer beginner methods most new cubers learn. If you think about it, it seems almost obvious. If efficiency is not a concern, the first two blocks of Roux have to be simpler than the first two layers of a layer-by-layer approach, since you are solving a subset of the first two layers. CMLL is also obviously simpler than the CFOP last layer. The only thing that remains is the last six edges, and that's simple enough that I think beginners could figure out by trial and error. With the right simplifications (at the expense of efficiency) and good pedagogy, I therefore think Roux is ideally suited for teaching to complete beginners. Unfortunately, nobody has done it yet.
IMO, the firstmost source is your own observations. 3x cube is very tactile, so some moves are just natural.
It helps also to develop some sort of notation for yourself. This way you can track and repeat your moves.
Solving by layers is kinda logical. So solving one side (first layer) is not hard. Then some experimentation with rotation sequences which temporarily break the solved layer/face and then re-assemble it will lead to discovery of moves to swap the edges into the second layer.
The hardest then is to solve the third layer. Again, the notation and observations help charting your way through.
A curious discovery may be about some repeated pattern of moves which may be totally shuffling the cube yet, if continuing it, eventually returns the position to the beginning state. It's kind of a "period".
Solving by layers is logical, it's what most beginners learn, and it is kind of how CFOP (the most popular speedsolving method) works. Nevertheless, it's not what I would recommend. The problem with solving layer by layer is that you are sort of painting yourself into a corner from the beginning. After you have finished the first layer, you can't really do anything without breaking the first layer. Of course it is possible (and necessary) to proceed in a way where you keep breaking and repairing the first layer while progressing with the rest of the cube, but the limited freedom of movement still makes the solution process needlessly complicated, and increases the move count.
In my opinion, it's better to start by solving a part of the cube that still leaves you with a significant amount of freedom of movement without breaking what you have already done. There are several ways to do this. My favorite method (Roux) starts by not making a full layer, but just a 3x2 rectangle on one side. This rectangle is placed on the bottom left part of the cube. You still have a considerable degree of freedom, you can turn the top layer and the two rightmost layers without breaking your 3x2 rectangle.
The next step is to build a symmetrical 3x2 rectangle on the lower right side of the cube. This is quite easy to do by just using the top layer and the two rightmost layers, thus avoiding to mess up the left hand 3x2.
After finishing the two 3x2 rectangles (commonly known as the "first block" and the "second block"), the next step is to solve the corners on the top of the cube. This is the only algorithmic step of Roux, you use a number of memorized algorithms. However, the algorithms are shorter and simpler than those for the top layer of a layer-by-layer approach, because the algorithms are allowed to mess up everything along the middle slice (which hasn't been solved yet) and the edge pieces on the top of the cube.
After finishing the top corners, you are still free to move the middle slice and the top layer without messing up what you've already done. Fortunately, this is enough for solving (intuitively!) the remaining pieces. You can finish the solve by using only these non-destructive moves.
The Roux method, therefore, allows you to keep the maximum degree of freedom of movement (without destroying what's already been solved) all the way until the end. This is what allows it to have a very low move count, and what's makes it easy to learn. It also gives you a lot of creative opportunities compared to CFOP and other layer-by-layer methods. Because of the increased freedom, there are more ways of doing things, and bigger scope for clever shortcuts, especially when building the first and second blocks.
Don't start with algorithms. Figuring out how to solve them is half the fun. If you want to be a speedcuber you could always look up algorithms later but you can't unlearn the algorithms once you learn them.
Perhaps it worked that way with you, but I'm not smart enough to figure out a 3x3 on my own, and wouldn't have had the many many hours of enjoyment that I did have, if I wouldn't have learned any algorithms.
It's not like memorizing algorithms makes it trivial - there's still recognition/look-ahead and finger tricks to learn, if you want to get faster. And finding the optimal cross (in CFOP method) during the 15 second inspection takes some thinking. I'm bad at that.
I’m having a really hard time to understand even the “beginner’s method” on that wiki.
For example, it entirely glosses over how to solve the „first two layers“ (F2L) on the left and back faces. It only ever explains F2L for the front and right faces. However, I can’t possibly achieve a „yellow cross“ that way. I wonder why I can’t seem to find any source that actually explains it.
From the original article on the 34x34x34 "record":
> It took about 1 year, and 1000 work hours to make the cube.
Imagine doing all that work, all the planning, designing, printing, assembly, and feeling the title will be yours soon, knowing the record has stood unbroken for 7 years, confident you're the only person even trying...
... And then 4 weeks before you finish a guy appears on YouTube with his 49x49x49...
In the 49x49x49 video, he goes over previous world records of "Highest Order nxnxn Twisty Puzzle", and I thought it was weird he didn't mention the 34x34x34. But in the youtube description, he links to this forum post where he announces it on August 10 (a few weeks before the video, but still well after May 10): https://www.twistypuzzles.com/forum/viewtopic.php?t=39559 There is a comment from the creator of the 34x34x34:
> Ah there's so much I want to say, where to begin? Well, soon after finishing the 34x34, I notified Greg, who immediately notified me about the 49x49. At that point, Preston had already checkered the 49x49, so I did not consider the 34x34 a world record. It seems nobody noticed this, but nowhere in any of my videos did I claim the 34x34 was a world record :lol: But still, everyone just assumed it was :lol:
I’m sorry I was not good with my search. I actually found a 33x33x33, and then the next highest that popped up was this 34x34x34. Next time, I will see if I should spend more time searching for higher records in any record-breaking event.
Anything beyond 7x7x7 is pretty much the same. It's just more annoying, because the puzzle gets physically harder to handle, and because you have to do the tedious work of counting how many layers away from the centre a piece is. The 7x7x7 is the biggest cube used in official competitions, for a good reason.
The motivation for making enormous cubes like the 34x34x34 is just the engineering challenge, and breaking records. Nobody is going to want to solve such a thing, at least not more than once.
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