# Six colors on each face



## satya (Jul 30, 2010)

Hi all,
I was thinking of a nice way to get all the six colors 
of the cube on each of the six faces from the 
solved state.
For eg. do this on a solved cube: U F U2 R L' B2 D F2 R2 F B U2 L U B2 R2 F2 
can you guys suggest a better way to do this??
thanks in advance.


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## rubiknewbie (Jul 30, 2010)

1 color on each face looks better to me.


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## cuBerBruce (Jul 31, 2010)

While fairly long, I noticed that Satya's alg works for the void cube, not just the regular Rubik's cube. Tord's alg works for the regular Rubik's cube, but does not put 6 colors on each face on a void cube.

So I wondered what are optimal maneuvers for this for both the regular and the void cube. Assuming my computer code worked correctly, here are the answers I got (in spoiler):


Spoiler



For both regular and void cube, 6 face turns is the shortest maneuver to generate 6 colors on all sides.

Example: U F U2 D2 F D

For quarter-turn metric, 7 quarter-turns is the shortest maneuver to generate 6 colors on all sides (regular cube).

Example: U F D R' B U F

For the void cube, 8 quarter-turns is shortest.

Example: U D F2 L R U D' 



(I note that I probably wouldn't have seen this "question" if it were in the one answer question thread. IMO, it was a good thing not to post this in that thread.)


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## satya (Jul 31, 2010)

thanks a lot....
I never thought that it could be done in 6 moves.
and its a coincidence that it works for void cube.
just to share with you,this is how I got the algo.:
by doing a super flip each face gets all the adjacent 4 colors,
now each face has 5colors.Now the missing 6th color on each face is the
color of the face,opposite to that face.So by swapping two corners of 
opposite faces (which i did with T-permutation + suitable setup moves)
we get the 6th color,I did this for all the 3 pairs of opposite faces.
reaching a state with all the 6colors I used cube explorer to find 
the optimum solution for that state.Finally i got the answer as 
U F U2 R L' B2 D F2 R2 F B U2 L U B2 R2 F2 
but all this seems ridiculous now 
@cuBerBruce: will you please share your computer code?


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## mrCage (Jul 31, 2010)

satya said:


> thanks a lot....
> I never thought that it could be done in 6 moves.
> and its a coincidence that it works for void cube.
> just to share with you,this is how I got the algo.:
> ...


 
I'm sure it's nothing but brute force search. How is quite trivial knowing a bit about computer algorithms. Call it bruce force if you like

Per


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## Cride5 (Jul 31, 2010)

@Bruce, cheers for the optimal solution, but could you use spoiler tags next time. It's kinda fun working on these sort of puzzles when you don't know the optimal solution.


Anyway, I found this 8-mover (HTM).
R L U D R L E2


EDIT: An interesting sub-problem, fewest moves to get any two opposite colours on all sides


Spoiler



(U/D colours)
R L2 D2 F


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## cuBerBruce (Jul 31, 2010)

mrCage said:


> satya said:
> 
> 
> > thanks a lot....
> ...



Yes, my search was a brute force approach.

I used some program code I wrote quite awhile ago that does a breadth-first search of Rubik's cube positions out to 6f or 7q, and in the routine that stores the positions that are found, I added a call to a new routine that checks if each face has all 6 colors. For 8q, I had to add an extra loop to apply each quarter-turn to each 7q position. I took the first position found for each case, and entered it into Cube Explorer to generate the maneuver.

I note that there are multiple solutions for each case. So you can still look for alternate optimal solutions, that aren't merely isomorphic to the ones I gave.

I could share the code, but I would like to trim the code down to what I was actually using before doing so. That's not going to happen before US Nationals.

(I added a spoiler tag as suggested by Cride5.)


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## nitay6669 (Aug 12, 2010)

i dont know if someone noticed but the original post alg also makes a 12 bad edges situation


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