# Given a scrambled cube...



## Rinfiyks (Apr 25, 2010)

If you can only see the stickers on the up, front and right faces, what can you deduce about the other stickers on the sides of the cube that you can't see?
Are there positions where you cannot correctly deduce the position and orientation of all the corners?

Also, given a cube where you can only see the stickers on the up, front and right faces, _and these stickers are all solved_ (stickers, not cubies), how many possible positions could the cube be in?


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## trying-to-speedcube... (Apr 25, 2010)

Every corner is already determined, there is no ambiguity for that.

So if all the stickers are solved, the last corner is also solved, there are 3 edges that are invisible, (3!*2^2), and every pair of edges (UB and UL, FL and FD, RD and RB) can be swapped (2^3). 

3!*2^5/2 = 96 possible positions.


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## Rinfiyks (Apr 25, 2010)

trying-to-speedcube... said:


> Every corner is already determined, there is no ambiguity for that.
> 
> So if all the stickers are solved, the last corner is also solved, there are 3 edges that are invisible, (3!*2^2), and every pair of edges (UB and UL, FL and FD, RD and RB) can be swapped (2^3).
> 
> 3!*2^5/2 = 96 possible positions.



Don't forget you can swap DL DB, LB LD, LB BD


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## trying-to-speedcube... (Apr 25, 2010)

Those are the 3 invisible edges I was talking about.


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## Sakarie (Apr 25, 2010)

trying-to-speedcube... said:


> Every corner is already determined, there is no ambiguity for that.
> 
> So if all the stickers are solved, the last corner is also solved, there are 3 edges that are invisible, (3!*2^2), and every pair of edges (UB and UL, FL and FD, RD and RB) can be swapped (2^3).
> 
> 3!*2^5*/2* = 96 possible positions.



To make clear, the /2 part is because you have to have an even permutation, because it can't be just two edges swapped.


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## Rinfiyks (Apr 25, 2010)

trying-to-speedcube... said:


> Those are the 3 invisible edges I was talking about.



Ah, fair enough.

Is it 96 different possible positions for any scramble then? If not, what's the most/least?


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## qqwref (Apr 25, 2010)

In general two stickers are enough to tell which corner something is, but one isn't. Since there are four corners you know (at most) one sticker about each, you can't unambiguously figure those corners out except in special circumstances (such as solved corners).

If three faces of the cube are solved, for instance, the corners must be solved. There are indeed 96 positions.

This isn't the most for any possible scramble, though. I don't know what would be, but if you move only the corners around you can get at least 24 possible corner positions (where you see all the yellow corners, and then three white stickers on the others).


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## Lucas Garron (Apr 26, 2010)

5 sides are not enough.


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## Jaspar (Apr 26, 2010)

I deduce that the three visible sides have stickers and that the three hidden sides may or may not have stickers.


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## kunz (Apr 26, 2010)

how do we know that the three sides are comlete if we can only see three faces? or am i missing somthing?


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## trying-to-speedcube... (Apr 26, 2010)

We can see that the faces are complete.


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