Comment by rawling
4 days ago
> There are 3 limitations:
> ...
> 2) I can place the first 11 edge pieces onto the cube any way I want. The orientation of the last edge piece is determined by the orientation of the first 11.
> 3) I need to track how many swaps I create by placing those pieces. An even number of swaps is solvable, and odd number is not.
Would it be equivalent to say, after placing the first 10 edge pieces, the position of the 11th is mandated, and then the orientation of the 12th is too? Or if (3) is broken might it be harder to fix than swapping the 11th and 12th?
Kind of.
But it introduces an artificial difference between edges and corners. You'd get the same ability for corners if you did them after the edges.
The slightly counterintuitive “magic” is that you can trade a corner swap for an edge swap: for permutation parity, corners and edges are interchangeable.