Re:The Mathematics of the Rubik’s Cube (2009) [pdf]
by perfect_wave on Monday February 11, 2019 @06:56PM
(#19139731)
Except that simply isn't true. When randomly performing rotations you're much more likely to end up in certain states (as I mentioned in my other comment). Whether you make 10k random rotations or 20 random rotations you're still more likely to end up in a certain state.
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Re:The Mathematics of the Rubik’s Cube (2009) [pdf]
by Retric on Monday February 11, 2019 @07:33PM
(#19139928)
In theory I agree with you, in practice I don’t.
Sum 20 coin flips mod 3 and you can find the bias in the output. It’s hard with a small sample set, but you could do it. Sum 10k coin flips and it’s a different situation.
Eventually you fall through the noise floor for any reasonable sample size.
Re:The Mathematics of the Rubik’s Cube (2009) [pdf]
by bunderbunder on Monday February 11, 2019 @07:47PM
(#19140002)
It's almost certainly less effort (though arguably also less fun) to write a valid state checker than it is to prove that N random cube operations will yield something that's within some tolerance of a uniform distribution across all legal cube states.