Number of permutations possible on a 3x3x3 super cube?

[sgtjosh]

Hey there guys -

Since you were so helpful a few months ago, I figured I'd try picking your collective minds again.

So... How would I go about finding the number of possible permutations on a 3x3x3 picture cube (or "super" cube)?

I know it's probably the same mathematics used in calculating the number of permutations in a standard 3x3, but the issue with the centers definitely has me confused. I know in a picture cube you can have a single center rotated 180° (or heck, all 6 for that matter), or two (if not more) centers each rotated 90°.

How do I account for that? Thanks a ton.

 

[AvGalen]

I won't give you to the answer directly, but you should think about how many extra possibilities there are for non-centres (hint, not many) and then for the 1st center, the 2nd center, etc. Pay special attention to the last center and you should be able to figure it out easily

 

[Coolster01]

Spoiler alert

Spoiler: The Formula

24(rubikscube combinations)

 

[TDM]

Spoiler alert

Spoiler: The Formula

24(rubikscube combinations)

are you sure it isn't

Spoiler

12, not 24? I don't think you can do a quarter turn of a centre and not change any other piece, so half of the 24 aren't reachable because of parity

 

[AvGalen]

Both wrong by a large margin and obviously disregarding my hint. Why do people post things as if they are certain when they have no idea what they are talking about?

are you sure it isn't

Spoiler

12, not 24? I don't think you can do a quarter turn of a centre and not change any other piece, so half of the 24 aren't reachable because of parity

 

[Randomno]

Why do people post things as if they are certain when they have no idea what they are talking about?

Cos it's tha internetzzzzz.

 

[TDM]

Both wrong by a large margin and obviously disregarding my hint. Why do people post things as if they are certain when they have no idea what they are talking about?

Your inbox is full, so I'll post it here:

Sorry, but I thought that what I said was right and I have read your hint. But I still can't see what's wrong with what I said, even when thinking about it further. Please could you tell me, or at least give me another hint? Because I'd like to know what the answer actually is so I don't make the same mistake again.

E: oh wow I'm an idiot.

Spoiler

4^6 doesn't equal 24 :fp
is it 2048 instead of 12? Or is there something else?

 

[AvGalen]

Your inbox is full, so I'll post it here:


E: oh wow I'm an idiot.

Spoiler

4^6 doesn't equal 24 :fp
is it 2048 instead of 12? Or is there something else?

Double winner!
More hint, a very ancient link, also useful for the future

Spoiler

http://www.jaapsch.net/puzzles/cube3.htm

 

[Antonie faz fan]

i am pretty sure it is

Spoiler

4^5 (1024) cuz the first 5 can be any way twisted but the last one has to be 1 way for it to be posible unless there is some kid of parity that i do not know of).

 

[TDM]

i am pretty sure it is

Spoiler

4^5 (1024) cuz the first 5 can be any way twisted but the last one has to be 1 way for it to be posible unless there is some kid of parity that i do not know of).

Spoiler

There are two ways to orient the last centre: you can turn it 180 degrees without affecting the rest of the cube e.g. (R U R' U)5

 

[sgtjosh]

Double winner!
More hint, a very ancient link, also useful for the future

Spoiler

http://www.jaapsch.net/puzzles/cube3.htm

Ah, yes. I should've thought to check Jaap's page... I haven't visited that site in forever. Thanks for the info!