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I was reading up on 2 x 2 Rubik's cube. Wikipedia says that

Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (37 positions).

I cannot visualize the second half of this statement. Can somebody please help?

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    $\begingroup$ Instead of 37 positions I believe you mean $3^7$ positions? $\endgroup$ – timidpueo Apr 9 '14 at 20:40
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Each corner consists of three faces. The second statement means that seven of the corners can themselves be "rotated" so that the faces are pointing in whatever direction you prefer, without forcing you to change anything else about the other corners.

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  • $\begingroup$ Hi, thanks for answering. But how we know the one 'odd' corner, since it seems to be all symmetrical ? $\endgroup$ – Josephus Apr 9 '14 at 20:20
  • $\begingroup$ There's no specific 'odd' corner. You can rotate any of the seven corners, but the rotation of the remaining corner will be decided (forced) based on the rotation of the others. $\endgroup$ – naslundx Apr 9 '14 at 20:21
  • $\begingroup$ ok. cool! Thanks. $\endgroup$ – Josephus Apr 9 '14 at 20:23

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