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Rubik's minimal operator set (Posted on 2019-05-23) Difficulty: 3 of 5

It's pretty simple to see that you can reach any possible configuration of a Rubik's cube (check Wikipedia if you're not sure what that is!) with just six basis operations. Namely, a counterclockwise quarter rotation around each of the axes: +x,-x,+y,-y,+z,-z.

But perhaps all six operations aren't necessary, so that it is possible to reach the same configuration following from a turn around +x by some combination of turns around the other five faces?

Explain why rotations around all six faces are independent or, alternatively, come up with a sequence of rotations about -x,+y,-y,+z,-z which mimic the effect of a rotation about +x.

  Submitted by FrankM    
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Solution: (Hide)

The six rotations are independent.

To see this, consider the boundary between the edge +x+z and the centre face +z. These are adjacent when the cube is in its pristine state, but is disrupted by the rotation about +x. On the other hand, none of the other rotation operators disrupt this border. So it is impossible that any combination of them will effect the same change on the cube as the +x rotation.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Hint from the author tonny ken2019-10-04 01:55:12
Hint from the author FrankM2019-05-27 12:56:09
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