Hi,
according to Chris´ calculations and Christopher´s calculations, I perceive the 3x3x3 cube as having 43 252 003 274 489 856 000 / 2 parity problems and the same number of parity problem free positions. There are two parity states for 3x3x3, namely (in Christopher´s notation) C(3,0,0) and C(3,0,1). Similarly, for 4x4x4 there are 4 parity states: C(4,0,0), C(4,0,1), C(4,1,0) and C(4,1,1).
Now, I am wondering if it is also possible to describe parity problems and parity states this way in case of square-1? Even in cube shape alone it seems to be kind of complicated because of a combination of both "slash" move (which behaves as R2 on 3x3x3 cube, i.e. always an even permutation of corners and even permutation of edges) and "numbered" moves (which behave as quarter moves on 3x3x3, i.e. sometimes an even permutation for both corners and edges and sometimes an odd permutation for both corners and edges)...
according to Chris´ calculations and Christopher´s calculations, I perceive the 3x3x3 cube as having 43 252 003 274 489 856 000 / 2 parity problems and the same number of parity problem free positions. There are two parity states for 3x3x3, namely (in Christopher´s notation) C(3,0,0) and C(3,0,1). Similarly, for 4x4x4 there are 4 parity states: C(4,0,0), C(4,0,1), C(4,1,0) and C(4,1,1).
Now, I am wondering if it is also possible to describe parity problems and parity states this way in case of square-1? Even in cube shape alone it seems to be kind of complicated because of a combination of both "slash" move (which behaves as R2 on 3x3x3 cube, i.e. always an even permutation of corners and even permutation of edges) and "numbered" moves (which behave as quarter moves on 3x3x3, i.e. sometimes an even permutation for both corners and edges and sometimes an odd permutation for both corners and edges)...
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