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A solved 3x3 Rubik's Cube has red on the top face, green on the right face, and yellow on the front face. There is one corner piece belonging to these three faces, with those three colours.

I want to know if it is possible with any sequence of moves to have the corner piece end up in the same position, but now with red on top, green in front, and yellow on the right? (I know that we can bring that corner piece to that position with either red on the right, green in front, yellow on top or red in front, green on top , yellow on the right.)

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    $\begingroup$ Your question is confusing and difficult to understand. $\endgroup$ – Michael Rize Mar 3 '15 at 14:15
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The only possible orientations that corner piece can be in is:

R
YG

Y
GR

G
RY

It can only "rotate" ... so, no, you cannot have Green on front face, and red on top.

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    $\begingroup$ This answer is correct. Even if you imagined taking the cube apart and moving the corner cubie however you wanted, you couldn't get it into the desired position. You may also be interested to know that starting with a solved cube it is impossible to get to a position where only one corner cubie has been rotated and nothing else has changed. This can be proved by considering a single rotation of a corner cubie to be a quark with charge $\frac{1}{3}$ or $\frac{2}{3}$ and using the fact that total charge must remain an integer. $\endgroup$ – h34 Mar 7 '15 at 12:23
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If I understand correctly you ask if a corner piece that has red green yellow as top right front respectively to be red yellow green instead. This is impossible. You need to understand that the corner piece itself is 1 piece, you can't swap two colors of that same piece. you can only rotate the entire piece so another color is on top.

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No you cannot by any legal moves. But if you swap the centers and put it back together you will not be able to do this any ways i tried it myself and it did not work. So you can be a sticker peeler and cheat or get a cube with that color scheme. You can try it yourself it will not work.

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    $\begingroup$ Welcome to Puzzling! Can you explain why this is the answer? Answers without explanation are deleted. $\endgroup$ – Deusovi♦ Mar 8 '17 at 4:19
  • $\begingroup$ I like the alternative solution of peeling the sticker. $\endgroup$ – Masclins Mar 8 '17 at 9:20

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