I'm not sure if this question belongs here but I see lots of Rubik Cube's questions around so here it goes:

Can I take a standard $3 \times 3$ Rubik's Cube and shuffle it so that, for every face, there are no more than $2$ pieces with the same color?


Please answer if you have managed (or failed) to solve the question using an actual cube. No guessing here, thanks.

  • $\begingroup$ I would add the tag "group-theory" $\endgroup$ – Sylvain Biehler Mar 5 '14 at 14:59
  • $\begingroup$ Did you try it? It seems very easy to do... $\endgroup$ – Karolis Juodelė Mar 5 '14 at 15:15
  • $\begingroup$ Did YOU try it, @KarolisJuodelė? It's not a matter of seeming easy but of actually doing it. $\endgroup$ – Adrian Mar 6 '14 at 9:53
  • 2
    $\begingroup$ @Adrian, yes, I did. "seems" might have been a poor choice of wording. $\endgroup$ – Karolis Juodelė Mar 6 '14 at 14:36
  • $\begingroup$ I have answered this here. No more then two colors per side $\endgroup$ – Saloaty Jun 29 '17 at 20:39

You mean like this?


To find the solution just click "play".

EDIT: By the way, the movements to get this setup are:

L R' F' B M' E' U B B

Anyway the question is quite interesting because I think there are not tons of solutions to this problem... so now I have two new questions...

Does anyone knows a shorter way?

How many different combinations of this setup exists?

Protip: In ruwix.com to get the M' and the E' you have to extend the panel by clicking on ">" button

Edit2: This is the shortest algorithm I can imagine...

M' S E M' R U U

The last two steps can be done with U U, D D, F F or B B...

  • $\begingroup$ You're much likelier to get responses to your two follow-ups if you post a new question, linking to this one as appropriate. :) $\endgroup$ – Andrew D. Hwang Mar 7 '14 at 12:36
  • $\begingroup$ You are surely right, but I don't know if this questions deserve a new topic, may be does not... $\endgroup$ – DaniRG Mar 7 '14 at 13:52

I believe this works. Rotate diagonally opposite pairs of corners so that the front faces move to the sides. Rotate the vertical center slice by a half-turn. Interchange the four edge cubies around the equator.

  • $\begingroup$ I have tried to reproduce your solution. No luck. Had a cuber friend try it and same result. Have you positively managed to achieve the required result using an actual cube or just guessing ? $\endgroup$ – Adrian Mar 6 '14 at 9:52
  • $\begingroup$ Or please provide instructions on how to reproduce using an online rubik's like ruwix.com/online-rubiks-cube-solver-program $\endgroup$ – Adrian Mar 6 '14 at 10:10
  • 1
    $\begingroup$ @Adrian: I just guessed it. I thought you could twist any pair of corners as described. I have lost track of my algorithms for manipulating the cube, so used a rigid cube and looked at where the faces go. $\endgroup$ – Ross Millikan Mar 6 '14 at 14:01

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