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 Post subject: An odd question that came to me this afternoon
PostPosted: Thu Dec 01, 2011 12:00 am 
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I happened to pull out my Eastsheen Super 5x5 to take a look at it in very dim light. It was nearly impossible to distinguish between opposite faces' colors (so blue and green looked identical, as did red/purple and white/yellow).

If I were to "solve" the cube in light like this, of course it might not actually be solved. However, because of the super stickering, each misplaced piece would end up where it could be moved into the correct position using only half-turns.

So, would you be guaranteed to be able to get from this state to truly solved by only making half-turns? And if it was not guaranteed, what would the chances be of being able to do it?


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 Post subject: Re: An odd question that came to me this afternoon
PostPosted: Thu Dec 01, 2011 3:06 am 
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Location: Bay Area, California
The answer is no, there are additional parity restrictions for halfturns and it is possible to put the puzzle into a state that has blue-green, white-yellow, red-orange all nicely solved but is a parity for the halfturn solve.

I'm sure Jaap has written about this but I can't find where.

For example, you can swap two corners diagonally (ignoring what happens to the edges) and it is very easy to manually verify that you can't achieve this state with half-turns.

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