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 Post subject: 3x3x3 edge parity questionsPosted: Fri Nov 29, 2013 7:46 am

Joined: Mon Mar 30, 2009 5:13 pm
1. Can a single flipped edge cancel out any pair of swapped edges, and vice versa? For example:

a) If you take out and swap round a single pair of edge pieces in a solved 3x3x3, can you re-solve the puzzle so that everything is in place except for a single flipped (inverted) edge piece?

b) And conversely, if you take out and flip a single edge piece in a solved 3x3x3, can you re-solve the puzzle so that everything is in place except for a single pair of swapped edge pieces?

2. How many edge flips and/or edge swaps are required to ensure that the puzzle can be solved after random assembly? Do you need one of each (1 edge flip AND 1 edge swap), or either one (1 edge flip OR 1 edge swap), or 2 of either (2 edge flips OR 2 edge swaps)?

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 Post subject: Re: 3x3x3 edge parity questionsPosted: Fri Nov 29, 2013 9:51 am

Joined: Fri Apr 01, 2011 10:58 am
Location: Stockholm, Sweden
1: a,b) Not possible.

2: After random assembly, the most you possibly have to do is one edge twist, one corner twist, and one edge or corner swap.

Sorry for the not so elaborative answers

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 Post subject: Re: 3x3x3 edge parity questionsPosted: Fri Nov 29, 2013 9:54 am

Joined: Mon Mar 30, 2009 5:13 pm
OK, thanks, so these forms of parity are non-equivalent and can't substitute or cancel each other, right?

I guess this explains why only one in 12 (2 x 2 x 3) randomly assembled configurations can be solved...

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