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 )
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.
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.
Thanks for explaining. I assumed this was the case, but want sure. Even the photo of the guy with it annoyed me. Just looked obnoxious, fake, and self-promoting. The guy's YouTube channel also appears to target audience aged 12-14, with obnoxious, juvenile thumbnails to match. Awful.
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.
A few months ago I learned to solve the classic 3x3x3 using the beginner's method [0]. Basically, you memorize a set of algorithms based on the current state of the cube and what overall stage of solving you're at (you first solve the white layer, then the middle layer, then the final layer).
What's funny is that I feel no compulsion to learn other methods, no compulsion to get faster at it, no compulsion to move up to larger cubes like 4x4x4 etc.
I just find it soothing and meditative. In fact, doing a few cubes has replaced some amount of doom-scrolling for me. Hard to describe exactly. Scratches some hand-eye / brain-motor itch.
Yes, i understand perfectly this is exactly what i do with my cube, it is sitting in my desk and i give it a few solves daily, it really helps to keep my mental in a good state.
I will probably buy another this time stickerless to not worry about them deteriorating over time
(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.
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.
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...
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.
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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.
(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 )
https://ruwix.com/twisty-puzzles/bandaged-cube-puzzles/
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.
Deleted Comment
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.
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.
Maximum number of moves scales as n^2.
it has been proved only that the lower bound is 31, while the most probable value is considered to be 32
https://oeis.org/A257401
Now someone should build a robot to actually work that thing.
https://www.youtube.com/watch?v=ocy09pzME4E
The stop motion of the build was very satisfying. It’s also amazing how smoothly it moves, even being as heavy as it is.
What's funny is that I feel no compulsion to learn other methods, no compulsion to get faster at it, no compulsion to move up to larger cubes like 4x4x4 etc.
I just find it soothing and meditative. In fact, doing a few cubes has replaced some amount of doom-scrolling for me. Hard to describe exactly. Scratches some hand-eye / brain-motor itch.
[0] This is the guide I used: https://assets.ctfassets.net/r3qu44etwf9a/6kAQCoLmbXXu29TTuA...
I will probably buy another this time stickerless to not worry about them deteriorating over time
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.
[0]: https://news.ycombinator.com/item?id=27427330 ("How I uncovered a black-hat SEO scam")
That, and clearly money.
https://m.youtube.com/watch?v=4ZeylpCG3IE
> 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...
Ooof.
I'm so glad he was beaten by the 49x49x49.