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When a rubik's cube is solved, will the tiles always be in the same position?

For example, if you were to write the number 1-9 on one of the sides before scrambling it, will the numbers always be in the same order once the cube is solved on all sides?

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  • $\begingroup$ I believe the question (in the second sentence) is "will the numbers always be in the same order...". $\endgroup$ – oleslaw Dec 1 '16 at 8:41
  • $\begingroup$ yes, thats what i meant. $\endgroup$ – Avilan Dec 1 '16 at 9:55
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You shouldn't think about the cube in terms of tiles, but on the mini-cubes it is split into, sometimes called cubies or cubelets. There are 26 of these (3*3*3 minus the center), and there are 3 types. The centers (1 color), the edges (2 colors), and the corners (3 colors). For instance, it is not just a blue tile, it is a blue-red edge piece, which there is only one of.

the center pieces can't be moved, so you solve the cube around these. For instance, the the orange-white-green corner has to be placed in the corner between the orange, white, and green centers. It also has to be rotated so the colors match.

To answer your question, then yes, every piece, and therefore every tile on them, has a single unique position on a solved cube. The only thing that can change is the center pieces. While they cannot be moved, they can be rotated, and since they are symmetrical, you can't tell if they have been. For some variations of the cube, the centers have to be oriented too.

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    $\begingroup$ might be worth noting in bigger than 3x3 there are more options for change, but probably not interesting this op $\endgroup$ – user19641 Dec 1 '16 at 14:29
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    $\begingroup$ Specifically, there are 2048 solved configurations of a standard cube that differ only in rotations of the central squares. (This makes a cube with pictures on the sides significantly more difficult than one with solid colors, as these 2048 configurations are now visually distinct!) There are an additional 2048 configurations that cannot be reached by standard moves, you'd have to disassemble & reassemble the cube to get into this alternate orbit. $\endgroup$ – jasonharper Dec 1 '16 at 14:48
  • $\begingroup$ You could tell if you wrote the numbers 1-9 on each face. $\endgroup$ – Dave Kanter Dec 1 '16 at 17:59
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    $\begingroup$ @jasonharper Do you have a source for that? I'd love to read more. $\endgroup$ – John Feminella Dec 1 '16 at 20:55
  • $\begingroup$ @JohnFeminella don't recall exact source, I read it many years ago. Basically, there are 4096 possible center configurations (4 orientations ^ 6 sides). For the same sort of reasons why only 1/12 of possible cube configurations can be solved with standard moves, you can only reach half of these possibilities (those with an even number of center twists) from a given starting state. $\endgroup$ – jasonharper Dec 1 '16 at 21:16

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