Can anyone tell me about the Rubiks cube. What I mean is, how many different combinations are possible? I came up with an answer that is like in the Quintillions, can this be right?

I could be wrong, because Im not totally sure how to do the math, but I get the number- 60,466,176 i think its too low...

Yeah, it's some factorial problem. I can't think that hard right now.

I havent fully thought out the problem (I am extremely busy this week), but here is a quick attempt...

There are 26 small cubes of a rubiks cube. The 8 corners can be placed in any orientation, so there are 8! ways for them.

There are 6 middle pieces, 6! ways for them.

There are 12 "middle of edge pieces", each independent, so 12! ways for them. This leaves the total number of ways to be 6!12!8!, which is about 1.39 x 10^16 different ways to arrange the cube. However, there is more than one solution using this counting scheme... there are I believe 24 solutions using this scheme, not just 1.

I might not have taken all the variables or contraints into consideration in this formulation of the problem, but it should suffice for now.

Nate

it's fun having a resident genius :)

Sorry.......I try not to do any math that makes my brain hurt!! Will have to buy videos to teach my kids algebra........

Originally posted by Momof6
Sorry.......I try not to do any math that makes my brain hurt!!

Well, we have something else in common, anyway...

Mechanical Engineer, imagine the headache at the end of the day...

43,252,003,274,489,856,000

Originally posted by Cosmo
43,252,003,274,489,856,000

That’s about the amount of possibilities in 64bit encryption.

..actually somewhere between 65 and 66bit encryption.

Uhh, is that good ?

Surely you have to divide by six.

If you turn it over it's the same cube just upside down. There are six ways the cube can be turned around, therefore you have to divide by six.

I was playing around with this question yesterday and I found out it if you did one combination a second it takes 441 +/- million years to do all the combinations.

Originally posted by Cosmo
Uhh, is that good ?

Depends on what side you are on, I guess :)

I don't think you divide by six, all sides are a differnt color right? i thought for sure you guys would have all had the answerby now. Maybe I'm not as dumb as I look, or as dumb as the masked avenger says i am. Or maybe I am!

I found an article on the Rubik's cube. The professor didn't show the math, but here's his quote.

"there are more than 43 quintillion (4.3252 x 10**19) different states that can be reached from any given configuration."

http://www.engineer.ucla.edu/press/1997/korfcube.html

I actually learned to solve that thing with a procedure in a guide book.

Here is better discussion:

http://mathforum.org/dr.math/problems/glapa.4.11.01.html

It confirms Cosmo's 4 x 10^19 post;

I wish I understood it! :o

Cosmo doesn't understand it either. I tried to solve it on a bet, but no one seems to know the right answer. By best Math subject was geometry, to give you an idea.

I read that article and I understood it OK, but I couldnt explain it any better than that article does. For those of you who read my previous post and understood that, what that counting did not take into account were the multiple orientations of each small block in the cube. I only considered their positions. Thus, if you correct my answer for the multiple block rotations then you get the correct answer. The difficult part comes in counting the number of block positions.

Thutmose, I am glad there are poeple like you to make up for peeeople like me. All part of gods plan I reckon.

Originally posted by Thutmose
I read that article and I understood it OK, but I couldnt explain it any better than that article does. For those of you who read my previous post and understood that, what that counting did not take into account were the multiple orientations of each small block in the cube. I only considered their positions. Thus, if you correct my answer for the multiple block rotations then you get the correct answer. The difficult part comes in counting the number of block positions.

I think you explained it much better, b/c they are taking into the fact that you could peel off the stickers and out them in any order.. while if you didn't the corner pieces would never change.. they would just simply rotate.. in other words take a rubix cube and see if you can make the three corner color change.. you can't they have to be beside each other.. just my train of thought.. :)

so...according to a mathamatician (Spelling?) that i know...


you can never be more than 52 moves away from solving a rubics cube....

cool huh?:D

Originally posted by Scott
so...according to a mathamatician (Spelling?) that i know...


you can never be more than 52 moves away from solving a rubics cube....

cool huh?:D

well according to my mathmatician.. it's 20..

I guess my math guy likes to peel off the little stickers... LOL