4x4 algorithm

[Feanaro]

Does anybody know an algorithm that will swap only two pieces on a 4x4? For example, on a solved american colour scheme cube it would be like swapping a blue yellow piece and a green white piece on the same slice. Thanks for your help.

 

[Johannes91]

r U2 r U2 F2 r F2 l' U2 l U2 r2

Lower case means inner slice only. That swaps UFl and UBl (and also some centers, but I hope that doesn't matter).

 

[Feanaro]

That one is good but I am looking for one that would swap a blue yellow and green white. Thanks for the algorithm, it is quite usefull.

 

[Lucas Garron]

r' U2 r2 U2 r U2 r U2 (l r2') U2 r' U2 r U2 l' U2

 

[Jason Baum]

You can use those algs to swap any two edge pieces, just do set up moves to bring the two pieces to UFl and UBl and undo the set up moves when you're done.

 

[Feanaro]

r' U2 r2 U2 r U2 r U2 (l r2') U2 r' U2 r U2 l' U2

YES!!! Thank you so much, this is exactly what I have been looking for! I am forever in your debt. At leat until you ask me to do something.

 

[deadalnix]

r' U2 r2 U2 r U2 r U2 (l r2') U2 r' U2 r U2 l' U2

Yeah ! That's great !

Where have you found this alg ? If you found it by yourself, how ?*

(I'm very curious )

 

[Lucas Garron]

r' U2 r2 U2 r U2 r U2 (l r2') U2 r' U2 r U2 l' U2

Yeah ! That's great !

Where have you found this alg ? If you found it by yourself, how ?*

(I'm very curious )

ACube... (domino def)
And handpicking.

(Not entirely true, I actually got this alg from CE, but that was chance.)

 

[Feanaro]

Does anyone also know a move that will swap two face pieces on a 4x4 without messing up any other faces?

 

[MistArts]

Does anyone also know a move that will swap two face pieces on a 4x4 without messing up any other faces?

Do you mean Centers? Just set up for a 3-cycle. Like:

Lower case = slice

r l F' l b2 l' F l b2 l2 r'

 

[joey]

I think he meant two whole centres?

 

[Feanaro]

I think he meant two whole centres?

No I meant two individual center pieces. Is is possible to only swap two?

 

[andrewvo1324]

nevermind he was banned already. *talks about the spammer 2 posts aobve me*

 

[tim]

I think he meant two whole centres?

No I meant two individual center pieces. Is is possible to only swap two?

No, you have to use a 3-cycle to "swap" them.

 

[joey]

It's possible to swap two, by cycling three!

 

[tim]

It's possible to swap two, by cycling three!

Awesome post!

 

[cmhardw]

I think he meant two whole centres?

No I meant two individual center pieces. Is is possible to only swap two?

Yeah, practically during a solve use a 3-cycle to appear to swap 2 pieces.

You can actually swap just two centers on a 4x4, but you must also swap two corners to do so. On a 4x4x4 supercube the parity of the corners *must* match the parity of the x-centers.

Chris

 

[Lucas Garron]

On a 4x4x4 supercube the parity of the corners *must* match the parity of the x-centers.

That is certainly true for simple mortal cubers like us.

However, I would like to note that this certainly does not hold for Frank Morris.

 

[blah]

@Chris: I don't quite get what you mean, does this mean that on a 4x4x4 supercube, the edges, centers and corners are not 'independent'? i.e. there's a possibility/probability that each 'piece type' cannot be solved by cycling 'within' itself?

Also, if there's an alg that swaps 2 center pieces and 2 corners, wouldn't it be more move-efficient to use this alg rather than solving the centers and corners independently? (which I think most people do, at least that's what I do...)

 

[deadalnix]

On a normal cube, center can interchange if they are the same color. So you can do like you permute two center using a third of the same color and cycing 3.

It is the practical side of the thing (Sorry, i think i'm not very clear, but i'm not a native english speaker and i find this idea difficult to explain with my vocabulary).

Mathematicaly :

On a 333, when you rotate a face, you permute 4 corner and 4 edges. cycling pieces 3 by 3, you end with 2 corner and 2 edges to permute. On a megaminx, as you cycle 5 edges and 5 corner, you can't have parity

On a 444/555, it's more complexe because you have two type of moves : a slice move and a face move. I will deal with 444, the idea is the same for 555.

A face move cycle 2*4 wing, 4 centers and 4 corners. A slice move 2*4 centers and 4 wings. The important thing is in the 2*4.

You can solve 2*4 cycle of the same type of pieces using standard 3-cycles. So a slice move generate a parity on wing and a face move generate a parity on corner and a parity on center.