Rubik's Cube Distilled

[Tunnelcat]

It's been found that every possible solution to the Rubik's Cube can be performed in only 20 moves or less!

http://videogames.yahoo.com/events/plug ... on/1407748

[SirWinner]

I must assume that you are talking about the 3 by 3 version. The 3 by 3 version the centers are always oriented in the same position.

The 4 by 4 Rubik's Cube the centers can be moved from their original positions. It has been a long time since I worked on the 4 by 4 version. The trick is to get all the centers and the edges properly oriented... then it can be solved using the 3 x 3 methods.

Interesting article.

[Stroodles]

Wow, that's pretty amazing.

I'm also curious to know just how good those Google computers are.

[Lothar]

More detail:

http://www.cube20.org/

[Tunnelcat]

The article's referring to the 3 X 3 version. Hey, I've got a few versions that are not cube shaped. I went into a collecting frenzy when they were popular years ago. One's a ball shape, one's a tetrahedron and I think the other is an octahedron, plus the 4 X 4 biggie cube. I'll take a pic of my collection for everyone after I dig them out of storage.

[Spidey]

Sniff…is that mothballs I smell?

[AlphaDoG]

Sniff…is that mothballs I smell?

I'm curious, did you hold the moth by the legs or by the wings?

[Isaac]

Sniff…is that mothballs I smell?

I'm curious, did you hold the moth by the legs or by the wings?

aww... nuts..

[null0010]

I've seen some disgustingly complicated variations of the rubix cube on youtube.

[Tunnelcat]

Veeeeeeery funny boys. I have a convenient basement with all sorts of collectibles stored in boxes, but sorry, no moths. You'd like my Star Wars and Raiders of the Lost Ark stuff.

But I did find my Rubik's collection. Bought most of it in the late 1980's. Some pretty weird shapes here, but the original is in the middle:

[Foil]

At a recent LAN event, one of the attendees brought his 7x7 Cube, and I watched him solve it in around fifteen minutes. Highly impressive stuff.

[Tunnelcat]

Stumbled into this accidentally. Programmable matter.

Universal Rubik's Cube

[Grendel]

You are missing the 2x2x2 cube.

[Isaac]

Can every one here solve these? I can't.

[snoopy]

I never had the patience to learn how to solve them.

[Isaac]

Oh, so it's something you learn.

[null0010]

It's all about algorithms and move combinations. It's not hard unless you're trying to put together a standard process, or figure out you \"own\" way to do it. Too many guides all over the Internet to really call it hard.

[AlphaDoG]

Stumbled into this accidentally. Programmable matter.

Universal Rubik's Cube

Now that is awesome. Thanks for posting.

[snoopy]

Oh, so it's something you learn.

Yeah, you learn how to break it down into steps, and learn how to make progress without messing up what you already have.

[SirWinner]

You can learn to solve any of them with a lot of patience and learning the methods to solve them.

The 3x3 there was a book out a long time ago.

The trick is to do like Computer Programming and divide and subdivide the seemingly impossible into small solvable parts. The when you do each small part properly you can solve it.

The way I solve the 3x3 cube is pretty simple.

Given that the centers don't move on a 3 x 3 cube.

First Pick any side as the \"top\" face... solve that 1/3 of the problem. Next the 4 middle pieces on the side. Now 2/3's of the problem is solved. Next the 4 bottom corners... then lastly the 4 non-corner pieces on the bottom face... Voila' done.

The 4 x 4 is little more complex but a similar set of methods can be used.

[AlphaDoG]

You can learn to solve any of them with a lot of patience and learning the methods to solve them.

The 3x3 there was a book out a long time ago.

The trick is to do like Computer Programming and divide and subdivide the seemingly impossible into small solvable parts. The when you do each small part properly you can solve it.

The way I solve the 3x3 cube is pretty simple.

Given that the centers don't move on a 3 x 3 cube.

First Pick any side as the "top" face... solve that 1/3 of the problem. Next the 4 middle pieces on the side. Now 2/3's of the problem is solved. Next the 4 bottom corners... then lastly the 4 non-corner pieces on the bottom face... Voila' done.

The 4 x 4 is little more complex but a similar set of methods can be used.

My momma told me that gators are unreasonable due to the fact they have so many teeth and can't use a toothbrush. She also told me, "stupid is as stupid does."

Sorry to mish-mash two separate movies together.

That being said, good thread.

[Jeff250]

This reminds me of the controversy among math nerds as to whether computer-assisted proofs are \"real\" proofs or not. There really is something less satisfying about having to brute force the verification.

[Foil]

This reminds me of the controversy among math nerds as to whether computer-assisted proofs are "real" proofs or not.

Exactly. It's not so much that computer-assisted proofs are not rigorous (IMO they are, as long as the software/algorithm can stand up to rigorous review). The debate is more along the lines of whether computer-assisted proofs should be considered as valid as a more abstract proof.

There really is something less satisfying about having to brute force the verification.

For a math nerd, you're absolutely right. Resorting to an exhaustive method because one can't find a more mathematically-elegant proof feels like a letdown.

To wit, I remember an attempt I made during my last year of undergraduate work to disprove a conjecture regarding certain types of algebraic groups. To my dismay, I ended up having to build a piece of software to run through all the billion or so possibilities I needed to check. Unfortunately, the process required more cpu time than I had available. Ended up receiving the lowest grade I ever got for a math course.

[Lothar]

Here's a robot that solves a standard cube in 12 seconds:

[AlphaDoG]

5x5x5

[Top Gun]

I always thought you solved them by peeling the stickers off and putting them back on.

[Tunnelcat]

5x5x5

That one's fun to watch, especially since the robot is made out of Lego's! I wish I had the 5 X 5 cube to add to my collection.

[Isaac]

I always thought you solved them by peeling the stickers off and putting them back on.

It's easier to pop our the pieces and reassemble it. But can you do it in 6 seconds? :p

[Gooberman]

A mathematician, physicist, and biologist observe an empty house. They see two people go in, and three people come out.

The physicist says, \"We must of made a statistical error, that is the only way to explain how two people went in, and three people came out.\"

The Biologist says, \"They must of procreated, that is the only way that two people can go in, and then three people can come out.\"

The mathematician looks at the other two and says, \"Ya know, if one of us goes in there, the house will be empty.\"

(Not relevant to the thread, but I think I got the right audience )

[AlphaDoG]

LOL

[Jeff250]

Exactly. It's not so much that computer-assisted proofs are not rigorous (IMO they are, as long as the software/algorithm can stand up to rigorous review).

I agree. It's not like even most mathematical proofs are written as formal proofs (thank the gods), so even they're not verifiable without some human intuition.

For a math nerd, you're absolutely right. Resorting to an exhaustive method because one can't find a more mathematically-elegant proof feels like a letdown.

Or for me as a CS nerd with some math nerd intersection.

edit: I suppose as a CS nerd you would think that I would find the computer-assisted proofs somewhat more satisfying...

[Gekko71]

A mathematician, physicist, and biologist observe an empty house. They see two people go in, and three people come out.

The physicist says, "We must of made a statistical error, that is the only way to explain how two people went in, and three people came out."

The Biologist says, "They must of procreated, that is the only way that two people can go in, and then three people can come out."

The mathematician looks at the other two and says, "Ya know, if one of us goes in there, the house will be empty."

(Not relevant to the thread, but I think I got the right audience )

My God - a funny Maths joke!