Four-Dimensional Rubik's Cube Craziness

roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."

Great.

Heck with solving it. There are some things that just aren't worth solving. Now where can I find a software rendered four dimensional analog of a hammer and nail?

Re:Great.

instead of greasing it to make it go faster, you ad space-time fabric softener.

Is this actualy 4D ?

I don't know. It looks like a more complex 3D version that's just real togh to build with plastic.

Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.

Re:Is this actualy 4D ?

Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.
The 4th dimension is whatever you define it as. There's no "true" 4th dimension. Einstein had the idea that time could be treated in a fashion similar to that of the spatial dimensions, and so, in his work, he defined the 4th dimension as the temporal dimension.
However, for this program's purposes, it's assumed that we're talking about the 4th *spatial* dimension. You can (kinda) visualize it if you think of the progression of first 3 dimensions: a line (1st d) can be rotated 90 degrees to itself to form a square (2nd d) which can be rotated 90 degrees to itself to form a cube (3rd d). The 4th dimension is thus hypothesized as the space defined by a cube rotated 90 degrees to itself.
(Granted, I'm no mathematician, so if someone has a better understanding, please correct me.)

Re:Is this actualy 4D ?

If you've ever read the story "And He Build a Crooked House" by Robert Heinlein, it contains a very good description of what a four-dimensional hypercube would look like. Imagine a small cube in the middle, six cubes surrounding it (one on each side, squashed together so that they share faces), and one big cube on the outside. Alternately, imagine two intersecting cubes (one corner of each cube is in the middle of the other cube), where each face of one cube is connected to each face of the other cube by another cube. Confused yet? So am I! Read the story, it's quite interesting.

This puzzle uses the first model mentioned above, except that you can only see seven cubes at once (the outer cube is hidden so that it won't block the view of the others). If you rotate the model (with Shift-left or Shift-right click), the outer cube comes into view.

Re:Is this actualy 4D ?

Here's a Java animation that will show you a 2D projection of a 4D hypercube:

http://dogfeathers.com/java/hyprcube.html

It's really tough to wrap your head around another spatial dimension. Books like Flatland and Realware make the comparison to a 2D person's world being interrupted by one of us.

For example, if you were 2D, living on your flat plane, and a 3D person passed an orange through the plane, you would perceive it as a round shape which grew out of nothingness, got bigger and changed shape for awhile, then shrank and disappeared.

A 3D person could also see into your house, because a 2D person would just build four walls and no ceiling or floor. Similarly, a 4D creature could see through all of us and our buildings, because we only build in three dimensions.

nooo

it took me long enough to finish the real thing.

Re:nooo

Haha, it only took me a minute to solve the 3D version!

I'm sure this 4D version will be just as easy...

Although I'm not sure how I'll peel off the colored stickers and rearrange them with this software version.

Hmmm

Re:nooo

Rubik's makes a special cube [rubikshop.com] for "less intelligent puzzlers". You might want to pick up one of these.

Jason
ProfQuotes [profquotes.com]

Not interested...

I can't even figure out the regular one. Hell, I am lucky I can tie my shoelaces in the morning!

Re:Not interested...

You sound like you could borrow my Rubik's Square. It only took me about half an hour to solve, once I realized that all the squares are the same color.

Technique number one

Apply a screwdriver to it; reassemble in the proper order.

Um, though that may be a little hard with the program, I'll admit.

Maybe if I apply the screwdriver to the ~~++5#Q%NO CARRIER

Re:Technique number one

That's a violation of your End-User License Agreement and the DMCA.

Please lie face down on the ground, with your legs and arms apart. BSA agents will be arriving shortly to take you into custody.

Schwab

damn it....

you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve. Anyone have any clue how long it would take a computer to solve your standard rubics cube through brute force?

Re:damn it....

Check out http://jpbrown.i8.com/cubesolver.html [i8.com]

He made a software/hardware 3D rubics cube solver using LEGO mindstorms, a quickcam, and VB.

Re:damn it....

you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve.

Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.

Re:damn it....

Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.

Kinda funny -- I've inadvertently subjected myself to this same trick as a child. It always took so long to scramble the thing, it was easier to take it apart and put it back together in random order. Little did I realize there was a very good chance of creating an unsolvable cube.

Furthermore, I went so far as to buy a "how to solve the rubik's cube" book. Followed every goddamn step in that thing, and was pissed when it wasn't working. Eventually I tried it on my sibling's and it worked, and I came to the conclusion that mine was defective. Not sure how long it took me to figure out how mine became defective, but the blame was fully mine. :)

Gotta say, trying to solve an unsolveable puzzle sure kept me busy. It may have gotten my frustration tolerance up high enough that I can stand to debug those really nasty programs....

You were close...

The best way to solve a given cube is called "God's algorithm" to us Rubik's geeks (I can average about 50 s. solving a cube, which is ok, but not phenomenal). It's 18 moves [www2.vo.lu]. The method behind it is far too complicated for a person to do without a computer to assist, but using a rather simple method [olympus.net], a person can very easily solve a cube in around 65 moves, but slowly. The record-breaking solution times are closer to a hundred moves, but rather than remembering a move-efficient but thought-intensive way to solve it, one remembers many more algos that whose situation can be recognized much more quickly.

And for the previous posts asking how long it takes a computer to do it... it's very, very low. Under a second. Many people can do it, manually (a computer just has to give the moves, it can ignore the time required to actually turn the cube) in under 20 seconds [speedcubing.com] (For the people out there in disbelief, Dan Knights has a video of him actually doing it in 17, it's for real. I won't post the link, because I'm not going to be responsible for slashdotting his site).

There's a huge difference between a computer solving it "brute force", and a person or computer solving it through established algorithms. By brute force, just twirling the cube until the solution popped up, it would take on average however long it takes your computer to process half of the possible combinations. That's quite a long time. However, a computer solving a cube how we would, focusing on time rather than least amount of moves, could easily solve more than one a second.

thats an easy one

and there is also a running competition for the most efficient solution.

duh...just peel off the stickers.

*Four* dimensional Rubiks Cube?

What, you have to step into the future to solve it? :-D

Be pepared...

Just a word of warning to the foolish and brave. Before you tackle the 4^4 hypercube, make sure you buy an ergonomic mouse and mousepad. My guess is you'll probably develop super-carpal tunnel syndrome before you even you match one side of the damn cube. Also be sure to stockpile a few extra mouses, there's no knowing how many of them you'll be throwing against the wall.

Anyone remember "Cubey"?

For those spared this atrocity, it was a Saturday morning cartoon featuring, I kid you not, a living Rubik's Cube. It was an idea that filled me with loathing even at that age, and I can't tell you what it was about because I always switched to something else as soon as it came on.

The 1980s certainly seemed the nadir of American animation...

Re:Lego Solution

Ahhhhhhhh!

It's LEGO, not LEGO's, not Lego's, not lego's, not lEGO's, not leGO's, not legO's, not lego'S, not LeGo's, not lEgO'S.

It's not LEGOS, legos, LEGOS'.. ITS LEGO

"I have one LEGO, I have two LEGO, I have many LEGO. I enjoy playing with LEGO"

1 LEGO = LEGO
2 LEGO = STILL LEGO

No farking S!!

Ok I feel better now. :)

When I was a kid

I memorized the solutions to the Rubik's Cube so everyone would think I was smart! Haha, fooled them!

Now I just get drunk and masturbate a lot.

Most efficient solution

1) Click OPTIONS
2) Click SOLVE

Two clicks... anyone do better?

Re:Most efficient solution

1) Click OPTIONS
2) Click SOLVE

Two clicks... anyone do better?

Umm..
3) PROFIT?

Rotates too fast

My problem with this is that it rotates so fast, that I can't figure out what the effect of a rotation is supposed to be. The speed also makes learning by observing it solving itself useless ... just some flashes and 0.25 seconds later it's done. Any way to slow it down?

Movie References

Puzzled by the cube? Try renting two (relatively low-budget, unknown) sci-fi flicks. - Cube [imdb.com]: Buncha people, trapped in a buncha cubes, with a buncha deadly traps. - Cube 2: Hypercube [imdb.com]: Buncha people, trapped in a hypercube, with less deadly traps but more confusion as to wtf is going on. Both movies are fairly puzzling in their own right, with that sort of "unknown" sci-fi ending that is commonly found in lower-budgeted movies (e.g. Pi).

1-D Rubik's Cube!

I found this great 1-D Rubik's Cube, here, I can embed it here on this page:

.

The interface is simple: just look at it. Quantum mechnaics dictates that observing it changes it's state so just assume it's solved.

Here is a magnified version:

.

If you still have trouble with it, my book will be coming out pretty soon.

Hofstadter's the best source for rubik weirdness

Douglas Hofstadter wrote a couple of excellent columns on Rubik's cube and variations on the theme for his Metamagical Themas column in Scientific American back in the eighties (you can buy his collected columns in this book [amazon.com]). In particular, he talks about the various ways you can modify the basic 3x3x3 cube concept - for example, 4x4x4 cubes, 3x3x3 tetrahedra, alternate colour schemes, and so on (along the way, investigating the spark of inspiration that encourages people to try out different variations on a theme - something he refers to elsewhere in his books as 'conceptual slippage' - this hypercube would be a 'slip' along a different axis to those hofstadter explores - I'm sure he'd appreciate it :) ). He goes into plenty of detail about the mathematical approaches you can use to solving the cube, and some intriguing analogues to subatomic physics that crop up in the maths of rubik... anybody wanting an introduction to the kinds of topics the people behind this hypercube are exploring could do worse than to read those articles.

There's also some excellent stuff in that book on Lisp, quantum mechanics, chaos theory, Alan Turing, and nuclear war... great selection of articles by an extremely interesting mind.