Tim Reynolds
Premium Member
Hi puzzle theory people,
Lots of WCA competitions have adopted the policy of "use a reverse scramble on an extra attempt". I'm interested in whether this is, puzzle-theoretically, a good option. [note: in contrast to the inverse scramble, I'm talking about the reverse scramble. For instance, the reverse scramble of F R U is U R F, not U' R' F']
For now I'm just thinking of 3x3, but I guess we can extend it to other puzzles too.
The questions I'm asking are:
-Are there any relationships between the regular scramble and the reverse scramble? I can see that permutation parity must be the same.
-Is there any statistical problem with the distribution of positions reached by reverse scrambles?
If it helps, we could assume that we're dealing with the first scramble that Cube Explorer stops on (usually 21 moves). I guess technically, if CubeExplorer is deterministic, then a person could memorize the cube during inspection, cause a timer malfunction, run to their computer and plug the cube into Cube Explorer, take the scramble it gives, and reverse it. Are there any other conceivable issues we can see with reverse scrambling?
Thanks,
Tim
Lots of WCA competitions have adopted the policy of "use a reverse scramble on an extra attempt". I'm interested in whether this is, puzzle-theoretically, a good option. [note: in contrast to the inverse scramble, I'm talking about the reverse scramble. For instance, the reverse scramble of F R U is U R F, not U' R' F']
For now I'm just thinking of 3x3, but I guess we can extend it to other puzzles too.
The questions I'm asking are:
-Are there any relationships between the regular scramble and the reverse scramble? I can see that permutation parity must be the same.
-Is there any statistical problem with the distribution of positions reached by reverse scrambles?
If it helps, we could assume that we're dealing with the first scramble that Cube Explorer stops on (usually 21 moves). I guess technically, if CubeExplorer is deterministic, then a person could memorize the cube during inspection, cause a timer malfunction, run to their computer and plug the cube into Cube Explorer, take the scramble it gives, and reverse it. Are there any other conceivable issues we can see with reverse scrambling?
Thanks,
Tim