Is it possible to shuffle a 3x3 Rubik's cube so that there's no more than 2 pieces of the same color in every face?

Question

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?

Thanks

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

Answer 1

You mean like this?

https://alg.cubing.net/?alg=M-_E-_S_L_B2

To find the solution just click "play".

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

M' E' S L B2

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...

Answer 2

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.