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## Four-Dimensional Rubik's Cube Craziness296

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."
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## Four-Dimensional Rubik's Cube Craziness

• #### Great. (Score:5, Funny)

on Monday June 09, 2003 @12:03AM (#6147619) Homepage Journal
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. (Score:5, Funny)

on Monday June 09, 2003 @12:05AM (#6147630)
instead of greasing it to make it go faster, you ad space-time fabric softener.
• #### Is this actualy 4D ? (Score:5, Interesting)

<kevinforge&gmail,com> on Monday June 09, 2003 @12:31AM (#6147754) Homepage Journal
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 ? (Score:5, Informative)

on Monday June 09, 2003 @01:01AM (#6147862) Homepage
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 ? (Score:5, Informative)

on Monday June 09, 2003 @01:20AM (#6147908) Homepage
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 ? (Score:2)

Read the story, it's quite interesting.

I just read that story! Found it at a used book store a couple of weeks ago. It was in a collection of short stories entitled "6 x H". Doubt if that one is still in print, but it might be worth a look around the net for it.

Not only is it a fascinating look at someone building an impossible house, but it's especially fun for anyone who has ever bought a house before it was built. :)
• #### Nope... (Score:3, Informative)

Those are only descriptions of a hypercube that is projected onto a three-dimensional space or intersected with a three-dimensional space.

A real hypercube looks like a hypercube, not a cube with lines or anything else... of course you need to be five-dimensional to perceive the whole thing at once.

In general you need N+1 dimensions to perceive an N-dimensional object; for example, we can only fully perceive two dimensional objects all at once. Three dimensional objects we only see a particular side of, an
• #### Re:Is this actualy 4D ? (Score:2)

which would make for some fucked-up mechanical ideas... imagine an engine that runs in the 4th dimension....
• #### Re:Is this actualy 4D ? (Score:2, Interesting)

A better way to visualize a hypercube (and to draw one on paper) is as follows:

1. Expand each vertex in a direction you haven't used yet. (Draw a horizontal line from the dot, and put a dot at the end of it.)

Now you have a line, one dimension.

2. Expand each vertex in a direction you haven't yet, and connect them. (Draw vertical line from each dot, and a horizontal line connecting the two new dots.)

Now you have a square, two dimensions.

3. Expand ea
• #### Re:Is this actualy 4D ? (Score:3, Interesting)

after taking calc III, Ive come up with a great way to describe 4d objects.

Example, take a room, it has 3 standard dimensions, now lets add another dimension, lets say temperature. Now we have a 4d object, we could even try and make a function to model temperature based on postion, temp = f(x,y,z);

You can even do neat things like make 3d objects out of 4d objects by taking a level surface of the 4d object. In simpler terms, take all of the points in the room that are one temperature, that will form a 3d o
• #### Re:Is this actualy 4D ? (Score:5, Interesting)

on Monday June 09, 2003 @02:05AM (#6148011) Homepage Journal
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 (Score:5, Funny)

on Monday June 09, 2003 @12:03AM (#6147622) Journal
it took me long enough to finish the real thing.
• #### Re:nooo (Score:5, Funny)

<robNO@SPAMelitemrp.net> on Monday June 09, 2003 @12:06AM (#6147636) Homepage
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 (Score:2)

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

Easy. Just write a hack to it. The source code seems to be available [superliminal.com]. Scroll down, and you wont miss it.

• #### Re:nooo (Score:3, Informative)

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

Bah, as long as one minute? You are slow.

Check out this site [speedcubing.com], especially the multimedia section. There are videos of guys that solve the cube in less than 20 seconds!

• #### Re:nooo (Score:2)

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

"Marty -- You're not thinking forth dimensionally."

• #### Re:nooo (Score:5, Interesting)

on Monday June 09, 2003 @12:48AM (#6147810)
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]
• #### Re:nooo (Score:2, Funny)

Right. So you get a blank cube and a set of stickers...

Why are the Do-it-yourself instructions needed?

Hmm, who are these people who open the box and say "What no directions?! How will I tell which yellow sticker goes where?"
• #### Not interested... (Score:4, Funny)

<rosewood&chat,ru> on Monday June 09, 2003 @12:06AM (#6147633) Homepage Journal
I can't even figure out the regular one. Hell, I am lucky I can tie my shoelaces in the morning!
• #### Re:Not interested... (Score:5, Funny)

on Monday June 09, 2003 @12:36AM (#6147770)
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.
• #### Re:Not interested... (Score:2)

are those Rubik's shoes, perchance?
• #### Re:Not interested... (Score:3, Funny)

There's your problem...a Rubik's cube isn't to be used to tie your shoes. Pshhh some people.
• #### Technique number one (Score:5, Funny)

on Monday June 09, 2003 @12:06AM (#6147634) Homepage Journal
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 (Score:2)

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

My favorite "solving" technique was a lot simpler... peel off the stickers and arrange them into the solution.

neurostar
• #### Re:Technique number one (Score:3, Funny)

Here's a solving technique that works everytime: Simply twist and turn the cube until all sides match up. No additional tools required or embarassing adhesive related situations to deal with...
• #### Re:Technique number one (Score:2)

That only works for a short time, until the glue starts to give out, the stickers fall off. and you end up with an all black cube (admittedly easier to solve).
• #### No it won't (Score:2, Funny)

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

No it won't, we just have to wait for someone to come up with a software implimented 4 dimensional hammer...there's probably already one written for emacs...
• #### Re:Technique number one (Score:5, Funny)

on Monday June 09, 2003 @01:13AM (#6147895) Homepage Journal

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

• #### Re:Technique number one (Score:2)

BSA agents will be arriving shortly to take you into custody.

The Boy Scouts of America have a DMCA enforcement merit badge now?

• #### Re:Technique number one (Score:2)

This is what disassemblers were made for ...
• #### damn it.... (Score:5, Interesting)

<animemeken@hotmail.com> on Monday June 09, 2003 @12:06AM (#6147637) Homepage
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.... (Score:5, Informative)

<robNO@SPAMelitemrp.net> on Monday June 09, 2003 @12:15AM (#6147687) Homepage
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.... (Score:3, Informative)

thank you, that side eventually led me to my answer [t-online.de]
• #### Re:damn it.... (Score:5, Informative)

on Monday June 09, 2003 @12:19AM (#6147713)
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.... (Score:5, Funny)

on Monday June 09, 2003 @01:01AM (#6147860)
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....

• #### There's a math problem in here somewhere (Score:2)

I wonder how many possible combinations of the cube are solvable (if you put the pieces together in all possible combinations?)

Furthermore, any solvable combination will just be a permutation of any other solvable combination (i.e. you don't have to take the cube apart to create another solvable combination from one). So all these "solvable" states can be collapsed into 1.

So then I wonder how many unique combinations there are, of which only one is solvable. The answer is left as an exercise to a reade
• #### Re:damn it.... (Score:2)

Yeah, but it's trivial to figure out that a cube has been messed with this way. In solving a cube, you would solve the bottom layer (easy), edge pieces of the middle layer, and then the top layer, which was the hardest. In solving the top layer you had to do three things- get the corner pieces in the right places, rotate the corner pieces to be in the correct orientation, and then move the edge pieces.
For doing all these things, there is a predefined operation you perform on the cube. There is one that rota
• #### Re:damn it.... (Score:3, Funny)

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.

Way back in the mists of time I tried that on my school's Rubik's wizard. I took three pieces and rotated them. Gave it to the wizard and waited. Five minutes later he returned the almost complete cube, pointing out the _one_ piece he was unable to get right as it had been rotated.
• #### Re:damn it.... (Score:2, Informative)

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?

A regular computer would solve it in less than 10 seconds. Really a messy scramble of the 4D cube took only 6 seconds to solve. And it wasn't even backtracking.

http://www.kinnetica.com/cioxx/hypercube.png [kinnetica.com]

• #### Re:damn it.... (Score:2)

I've solved it a couple of times, but I have yet to memorise all the ending tricks, so I have to cheat a bit at the end.

The best method I've found for solving is by Lars Petrus [lar5.com]. I also found another method eight corner [alexfung.info] which IMHO is harder, but it's good to check it out to get a grasp of what you're doing when you are twisting the cube. (It's like a mathematical descition of rotational operations.)

Trying to solve it "just by trying" is not going to get you anywhere. Or at least extremely hard. Both of the
• #### thats an easy one (Score:5, Funny)

on Monday June 09, 2003 @12:07AM (#6147639)
and there is also a running competition for the most efficient solution.

duh...just peel off the stickers.
• #### Re:thats an easy one (Score:3, Funny)

Wouldn't that be a violation of the DMCA ?
• #### Umm (Score:2, Funny)

by Anonymous Coward
Can someone plz send me a link to a trainer for this. Thx. also no-cd version much appericated.
• #### *Four* dimensional Rubiks Cube? (Score:5, Funny)

on Monday June 09, 2003 @12:09AM (#6147652) Homepage Journal

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

• #### Re:*Four* dimensional Rubiks Cube? (Score:2)

the fourth dimension can also be in/out, though it usually refers to time
• #### Re:*Four* dimensional Rubiks Cube? (Score:2, Funny)

by Anonymous Coward
• #### Re:*Four* dimensional Rubiks Cube? (Score:2)

Whether Time is a dimension (or even exists as our temporal cortexes perceive it) is questionable.

• #### I solved the 4th Dimentional Cube! (Score:2)

Two years from now, but the continents all bunched together, and Hillary Rosen is president-dictator!

That's what you get when you mess with the timeline!

• #### Tried it a while back. (Score:2, Interesting)

by Anonymous Coward
Neat game. It's been around a while. I've been able to solve 7 random twists. The first thing you have to do is start with a ordered cube and see what happens when you twist it different ways. Not consistently, though. The trick is to figure out what the last move probably was, reverse it, the one before it, reverse that, and so on. After 3 random twists, you might be able to make a bad guess and recover from it. After 7, one wrong turn is a good reason for starting over. Never was able to solve a r
• #### Is it me (Score:2)

or is that page black text on a dark brown background? Some people...
• #### Be pepared... (Score:5, Funny)

on Monday June 09, 2003 @12:13AM (#6147678) Homepage
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.
• #### Re:Be pepared... (Score:2)

What do you mean extra mouses? I may just go see the page and.... oops, there goes my mouse, trowing itself against the wall. And I though quake 3 arena was bad for it....

• #### Anyone remember "Cubey"? (Score:4, Interesting)

<lawrenceperson@[ ]il.com ['gma' in gap]> on Monday June 09, 2003 @12:14AM (#6147679) Homepage Journal
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:Anyone remember "Cubey"? (Score:2)

Yes, I remember (I try to blot out the memory but it keeps COMING BACK!!) But I still think the MC. Hammer cartoon was worse. Anyone remember Mr. T's show?
• #### Not "Cubey", (Score:3, Informative)

Information on the "Rubik, The Amazing Cube" television show

Premiered on ABC: September 10, 1983-September 1, 1984.

The series ran for 1 year, and had a total of 12 episodes. It was
originally broadcast as "The Pac-Man/Rubik, The Amazing Cube Hour"
on Saturday mornings in colour with each Rubik segment lasting
22 minutes.

The Plot
--------

Rubik is discovered by a young boy (Carlos) who brings the colourful cube
to life - after he aligns all the cube's sides - an sets out on a magical
• #### Re:Anyone remember "Cubey"? (Score:2)

Oh, you bastard, why did you have to remind me of that? Yes, it was awful.

Now I've got the sound bite of him saying "Rubik" in that attempted-cute way stuck in my head. ARGH! Actually, kind of analagous to Pikachu saying his own name in delight and sense of accomplishment. But Rubik was worse.

How am I supposed to go to sleep with that stuff in my head? Now I'll have to watch some porn or something...
• #### Bastardly Deed for the Day (Score:2)

> Now I've got the sound bite of him saying "Rubik" in that attempted-cute way stuck in my head. ARGH! Actually, kind of analagous to Pikachu saying his own name in delight and sense of accomplishment. But Rubik was worse.
>
> How am I supposed to go to sleep with that stuff in my head? Now I'll have to watch some porn or something...

Time for my bastardly deed for the day:

"Oh, Rubie! (clackclackRubik!clack) Yeah, Rubie, that's it! (Rubik!clackclack) Twist it there Rubie! Oh, Rubie, (R

• #### heuristic search (Score:2)

I suspect that this could be solved in a reasonable amount of time with a heuristic search algorith, such as ACO or a genetic algorithm using the number of matches as a heuristic.

Obviously, brute force, even at a massively parallel execution, is completely out of the question.
• #### When I was a kid (Score:5, Funny)

by Anonymous Coward on Monday June 09, 2003 @12:17AM (#6147701)
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.

• #### Already done it. (Score:2)

I solved a Rubiks' Clock on the way home from the swapmeet I bought it at. That's it, right? Like the Rubik's Cube, but about time...
• #### Re:Already done it. (Score:2)

Yeah, Rubiks clock is fairly easy. I solved it in about 20 minutes or so IRC.
• #### cube? (Score:2)

it's not really a cube is it? i mean, that implies n^3 but this is n^4 so is it really a rubiks quartic?
• #### Re:cube? (Score:2)

No, it's a Rubiks hypercube.
• #### Re:cube? (Score:2)

So, it's a hypercube (4-dimensional), but we can't visually comprehend that so we look at the 3-dimensional shadow...well, actually a 2-d perspective of a 3-dimensional shadow...on a 16-bit OS on a 32-bit computer, etc, etc, 2-bit company that can't stand one bit of competition?

I'm so confused. I'll go play with that triangular pyramid puzzle...at least I could occasionally solve it without consulting a cheat book.
• #### On a similar note... (Score:2)

I've found a very sparce selection of downloadable Go [fc.ul.pt] games for GNU/Linux, (GNU Go [gnu.org] is the only one I know of). I'm surprised there's not more renderings of this awesome ancient game.

Still, when you got a four-demensional rubik's cube goin' on, life is pretty good :)
• #### 2D representation (Score:2)

The software is just a 2 dimensional representation. I find it almost impossible to solve the normal cube in the software version and I can solve a physical cube in under 5 minutes. A 4D cube might be interesting but not a 2D representation of one. I like the 4x4x4 and 5x5x5 cubes at rubiks.com.

Jason
ProfQuotes [profquotes.com]
• #### Not complete (Score:2)

Actually this is not a complete 4D rubik's cube. A hypercube had 8 sides, each of which are cubes, you can only see seven at any time in this program. The eigth one is there though; when you rotate a side, you will see cubies being rotated in from off-screen, they just don't show it. But since they don't show it, you cannot actually rotate that face. That would be like having regular 3D rubik's cube and not be able to turn the white face.

Still I love this program. I'm a big fan of rubik's cubes and o

• #### Re:Not complete (Score:3, Informative)

That would be like having regular 3D rubik's cube and not be able to turn the white face.

Not quite. It's like having a physical 3D rubik's cube and not being able to see all 6 faces at the same time. You can however turn a physical cube around so you can see the hidden face. It's a similar idea in this one. The way to see the hidden "face" is given in the FAQ:

Q: I can turn a real cube around so that I can see the hidden faces, can
I do something similar to see the invisible eighth "face"?
A: Yes. If yo
• #### Most efficient solution (Score:5, Funny)

<`moc.amrakduab' `ta' `todhsals'> on Monday June 09, 2003 @12:50AM (#6147820) Journal
1) Click OPTIONS
2) Click SOLVE

Two clicks... anyone do better?
• #### Re:Most efficient solution (Score:5, Funny)

on Monday June 09, 2003 @01:10AM (#6147886)
1) Click OPTIONS
2) Click SOLVE

Two clicks... anyone do better?
Umm..
3) PROFIT?
• #### Re:Most efficient solution (Score:2)

Umm..
3) PROFIT?

No. You forgot the ??? part.

• #### Re:Most efficient solution (Score:2)

Two clicks... anyone do better?

I can do it in one click, but I'm not allowed to describe it, since it's patented.

• #### Re:Most efficient solution (Score:2)

Funny, I just clicked 'solve', so I guess I've got you beat.

(the linux client doesn't have an "options" menu, it just has all the buttons along the bottom of the screen).
• #### Great (Score:2)

Now if someone would only release a patch to stop that infernal beeping when you click in the wrong place on the window. xset and setterm seem to have no effect.
• #### key to the universe survival (Score:2)

wasn't there a place [imdb.com] where hot and sultry female villians are willing to perform, erm, certain acts, in return for a rubix cube like that? Maybe this is the updated version of the intergalactic somethingoranother - beware if women on the street starts to act suspiciously intimate once you start solving this thing!
• #### Other 4D games (Score:2)

I wrote a two player web based 4d three-in-a-row [meta.net.nz] game one evening when I was bored.

I didn't find it particularly hard to play, but some people do. I think it's a good way to practise thinking about things abstractly.

Anyway, find a friend, and play a few games, see how you do. The rules are slightly different, you play until you fill the board, and the person at the end with the most numbers of three in a row wins.

• #### Open Source? Open sores! (Score:2)

I guess you haven't tried to get it compiled? No luck with a straight ./configure && make under FreeBSD nor Debian.
• #### Interesting(evil) trick(torture): (Score:2)

If you pop off a corner of a solved Rubiks cube, rotate it 120 degrees, and pop it back on, it becomes unsolvable. You should try it on someone you hate, or someone you know who won't murder you repeatedly. >.>
• #### Rotates too fast (Score:3, Insightful)

on Monday June 09, 2003 @02:30AM (#6148056)
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?
• #### Popular? (Score:2)

... popular three-dimensional version.

Popular? Do people still play with this? I haven't even seen one in the last 15 years or something (I'm in Europe). My impression was that after the initial 'craze' everyone got collectively sick of it somewhere in the mid-eighties and it kind of faded away. It was an interesting puzzle though, not that I ever really tried to solve it.

JP

• #### Movie References (Score:5, Informative)

on Monday June 09, 2003 @03:18AM (#6148143) Homepage
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).
• #### Ok, where's the 5D and 6D? (Score:2, Funny)

Heck, It was just too easy.. solved it in less than a minute.

But I won't submit my entry into the hall of fame, otherwise the FBI will come looking for this "human computer" that can perform 10^30 trops, and exceeds export regulations :P

• #### 4D analogs for mathematics behind Rubik's cube? (Score:2, Interesting)

Another way of viewing the 3D Rubik's cube (for the mathematicians out there) is as a group on 6 generators, meaning that any reachable configuration could be gotten by merely repeating the same 6 operations in some order (I believe the 6 generators being rotating the two outer 3x3x1 squares 90 degrees clockwise along any of the 3 axes).

Using this group, you could do various things like find the odds that a random arrangement of stickers is actually solvable (take the size of the group divided by the n
• #### 1-D Rubik's Cube! (Score:5, Funny)

on Monday June 09, 2003 @05:29AM (#6148467) Journal
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 (Score:5, Informative)

on Monday June 09, 2003 @06:10AM (#6148579)
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.
• #### Whooptee-Doo (Score:2)

I'm not interested in 4D. Let me know when they get to 5D, so I can get my Rubik's Tesseract.
• #### Douglas Li Needed a Challenge (Score:2)

I actually know one of the people on the hall of fame, a young man named Douglas Li. A couple of months after he completed his solution, he and I competed together on Michigan's all-star high school math team for ARML (American Regions Math League). He's quite good with mathematics in general, and both he and I scored about par for the course in the individual portion of the competition.

What I'll never forget, though, is that on the bus ride from Michigan to Iowa, he would take particular challenges on his
• #### Bookmark to make the page easier to read... (Score:2)

Try the following bit of code...

If you copy and paste that into a bookmark, that book mark will have the function of removing all colors from a page. Any page.

The 4D cube page has TERRIBLE coloration. This helps.

Rudy

javascript:(function(){var newSS, styles='* { background: white ! important; color: black !important } :link, :link * { color: #0000EE !important } :visited, :visited * { color: #551A8B !important }'; if(document.createStyleSheet) { document.createStyleSheet("javascript:'"+styles+" ' ");
• #### Oh my eyes! (Score:2, Interesting)

The colours, the horrible colours!