Quick question about Megaminx Scramble Program

[DavidCalvo]

While I'm generating the scrambles for the Spanish Championship, a question has invaded myself:

Is it possible to generate all the possible Megaminx Possitions with the Scrambling Program? I assume that the answer is yes thanks to Stefan, Jaap and Clement... but how could it be proven?

 

[hr.mohr]

There is a long thread discussing this very topic. The short aswer is NO. It's not possible to reach all possible possitions using the current scramble algorithm.

 

[hawkmp4]

That's correct: For a quick proof that we can't generate all the possible states, consider that there are 70 moves in the scramble. Each move has one of two possibilities (++/ -- or U/U'). That's 2^70 = 1.18059162 × 10^21 different scrambles (which may not produce that many unique states) whereas the number of states on a Megaminx is roughly 1.01 x 10^68. In other words, the scrambler program can at most generate about 1.700 x 10^-45 percent of the total number of Megaminx states.

 

[DavidCalvo]

Thanks! Tonight I will be able to sleep in peace...