whatshisbucket
Member
Due to the impossibility with current computational power of having random state scrambles for many puzzles, and the inconvenience of having scrambles long enough to produce a good random state, some puzzles use scramble generators that couldn't possibly generate every position of the puzzle. I noticed this when I picked up Megaminx recently, and I am curious how the different scramble generators compare in the portion of possible positions can actually be generated as scrambles.
I know (or at least am pretty sure) for these puzzles the scrambles are random state:
3x3
2x2
Pyraminx
Skewb
Square-1
Clock?
And that due to the fact that the current scramble generators for megaminx have only 2 options for each move, there are at most 2^70=1.18*10^21 possible scrambles out of the 1.01*10^68 possible positions (this is an astonishingly tiny fraction of the possible positions).
But since I don't do larger NxN puzzles, I don't know how those scramble generators work. Could anyone shed some light on the number of possible scrambles that they can generate?
I know (or at least am pretty sure) for these puzzles the scrambles are random state:
3x3
2x2
Pyraminx
Skewb
Square-1
Clock?
And that due to the fact that the current scramble generators for megaminx have only 2 options for each move, there are at most 2^70=1.18*10^21 possible scrambles out of the 1.01*10^68 possible positions (this is an astonishingly tiny fraction of the possible positions).
But since I don't do larger NxN puzzles, I don't know how those scramble generators work. Could anyone shed some light on the number of possible scrambles that they can generate?
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