Why Do The Centers Matter? 3x3x3

[RobDude]

I'm hoping someone can give me a straight forward answer to this. I was putting together my first 'speed cube' and I didn't know how to attach the center pieces. I (incorrectly) assumed that the center pieces didn't matter - after all, they can't move.

While trying to solve my new, centerless cube, I found that I ended up in an unsolvable situation.

Using my regular cube - I found that, ignoring the center pieces - I could solve the cube completely as long as I started with the white pieces around the white, red, orange, or yellow centers. But I couldn't solve it with white around blue or white around green.

Can anyone explain why this is? I don't understand it at all.

 

[Toad]

The simple answer is that certain cases with the centers moved ARE possible and others aren't possible... eg:

 

[Zarxrax]

You should be able to just change the center caps.
I can't really explain it... but yea, if you have the centers wrong, its unsolvable.

 

[maggot]

same for n x n even cube have moving center need correct center orientation or unsolved.:fp

 

[jms_gears1]

same for n x n even cube have moving center need correct center orientation or unsolved.:fp

even cubes center orientation does not matter, if you dont count the center piece as part of the solve state...

so you sir deserve :fp

 

[Toad]

same for n x n even cube have moving center need correct center orientation or unsolved.:fp

even cubes center orientation does not matter, if you dont count the center piece as part of the solve state...

so you sir deserve :fp

No, what he means is that this how parity is created. By the centers being solved in different locations to how they were before.

 

[Meisen]

Using my regular cube - I found that, ignoring the center pieces - I could solve the cube completely as long as I started with the white pieces around the white, red, orange, or yellow centers. But I couldn't solve it with white around blue or white around green.

Can anyone explain why this is? I don't understand it at all.

I think maybe i misunderstood you, but if not:

Take yout solved cube, have white as up, and orange as front and do this algorithm: M' Z M' Z M' Z M'. Now white is around blue. If you do M' Z' M' Z' M' Z' M' you get white around green.


Edit: Btw, when you put in the center caps it does not matter where you put in the first one, lets use white as an example, but it is important that the opposite center piece is the opposite color of your first piece, in other words yellow in this case.

Now, for the third piece, you can put on either of the four you have left, it does not matter. Lets say you choose green. Again it's important that the opposite piece of green is the correct color, in this example blue.

Now you are left with 2 center caps, but this time you can't put the next one in randomly. IF white is up and blue is front, then red is to your left, and orange is opposite of that ofcourse

 

[RobDude]

The simple answer is that certain cases with the centers moved ARE possible and others aren't possible... eg:

Yeah - totally.

Using my cube - the white pieces can be around Red, Orange, Yellow, and (of course) White.

But not Blue or Green.

I'm just having trouble understanding what makes Blue different from Orange in this regard.

 

[Jude]

FWIW here is a simple and easy to remember parity fixing alg for centreless cubes:

Spoiler

M

 

[Toad]

FWIW here is a simple and easy to remember parity fixing alg for centreless cubes:

Spoiler

M

And if you're not sure what that means it goes from this:

To this:

 

[RobDude]

FWIW here is a simple and easy to remember parity fixing alg for centreless cubes:

Spoiler

M

Much appreciated....but that doesn't really answer my question

 

[Meisen]

I thought i answered your question in my first post?

Did you try that alg?


Edit: well, the answer would be "you're wrong", and the proof would be in my first post

Again, if i didn't misunderstand anything that is....

 

[Innocence]

The answer I think you're looking for is that on a 3x3x3 cube, pieces can only be rearranged with either 3 cycles, or an even number of swaps. The only reason the parity case shows up on a centerless cube is that the wrong centers(or lack thereof) act as a "second swap". As it is impossible to tell whether the centers are correct when there are none, it creates the illusion that there is an odd number of swaps.

As it is 3:00 AM, I have no idea whether this is coherent information or not, or whether what I just said made sense. Heck, I can't even remember whether coherent means what I think it means.

 

[bwatkins]

I'm hoping someone can give me a straight forward answer to this. I was putting together my first 'speed cube' and I didn't know how to attach the center pieces. I (incorrectly) assumed that the center pieces didn't matter - after all, they can't move.

While trying to solve my new, centerless cube, I found that I ended up in an unsolvable situation.

Using my regular cube - I found that, ignoring the center pieces - I could solve the cube completely as long as I started with the white pieces around the white, red, orange, or yellow centers. But I couldn't solve it with white around blue or white around green.

Can anyone explain why this is? I don't understand it at all.

Hello,

I have done what you said and solved the cube with all the white around the BOTH the green and blue sides. The end result of white around green looks like this:

Side Center
W G
G O
R Y
B R
O W
Y B

So if i understand you correctly you are ignoring ALL the centers but still trying to solve ALL the EDGES and CORNERS "correctly" with respect to each other?

 

[rahulkadukar]

Well the point is if you are solving without centers then when u say the cube is unsolvable basically what you are saying is that u may have a 2 Edge cycle or a 2 Corner Cycle.

This is known as "Parity on Void Cube" and it can be solved. If you can tell me how your center less cube is unsolvable I can tell you how to completelt solve it.

 

[qqwref]

No, what he means is that this how parity is created. By the centers being solved in different locations to how they were before.

Obligatory :fp. This is not how parity is created.

 

[Caedus]

I think this entire thread is a mass of bad explanations and misunderstandings. It deserves this. :fp

I will not add another bad explanation of how parity works to this thread, as I doubt I can explain it very well. I will leave that to Google/someone more experienced.

 

[blah]

I think this entire thread is a mass of bad explanations and misunderstandings. It deserves this. :fp

Yes.

Check out a void cube thread.

I'm just having trouble understanding what makes Blue different from Orange in this regard.

It's not. If you have the standard BOY color scheme, it's not. Try again. How you align the cross matters.

 

[RobDude]

I think this entire thread is a mass of bad explanations and misunderstandings. It deserves this. :fp

Yes.

Check out a void cube thread.

I'm just having trouble understanding what makes Blue different from Orange in this regard.

It's not. If you have the standard BOY color scheme, it's not. Try again. How you align the cross matters.

My cube is...

F- Green
L - Orange
R - Red
B - Blue
U - White
D - Yellow

Using the online Rubik's Cube Solver to check my work (http://www.wrongway.org/cube/solve.html - click advanced and you can solve it to a specific finished state) I am only able to solve the the white pieces around the White, Red, Yellow, and Orange center.

You say that Blue is no different than Orange - but - I'm unable to solve the cube with white around the blue center.

These four examples demonstrate what I'm talking about. The online solver was able to generate a solution to all these.

But any solution I entered that had the white pieces around the blue center resulted in an error/unsolvable state. If I'm mistaken and Blue/Green is not a special case - could you use the cube solver to generate the turns I'd need to do to get my cube from the traditional solved to 'White around Blue'?

 

[Litz]

Start with the cube solved. Blue on top, red on front. Do this algorithm:

M y M y M y M

Do it so M is like L or R' and y is a cube rotation to the right. You now have white around blue center.