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 May 20 awarded Notable Question Sep 18 awarded Popular Question Sep 7 awarded Nice Question Dec 20 revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” added 220 characters in body; added 254 characters in body Dec 20 comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” @Gerhard Paseman Do you think those cube states are random samples of all possible cube states, or somehow biased? Dec 20 revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” added 43 characters in body Dec 20 comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” @Francois Brunault Well, I'm allowing rotations of the face, so 4^3 = 64 states are possible once we fix one face, but you're absolutely right. What I'm trying to understand is, what is the probability that the solved cube is one of those states? Or are those states more or less a random sample of all possible cube states? Dec 20 comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” @Brendan McKay Version (1) is what I had in mind. I don't want to condition on the cells being in the correct positions for a solved cube. Dec 20 awarded Commentator Dec 20 comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” @Francois Brunault I'm looking to make a statement of just how frequently you can solve the cube when you fix one or more faces. The answer, no doubt, will be "very infrequently". Dec 20 comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” @Greg Martin :) Dec 20 revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” deleted 6 characters in body; edited title Dec 20 asked Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved” Dec 5 revised Manhattan distance vs. absorption time on an unbounded integer lattice added 257 characters in body Dec 5 revised Manhattan distance vs. absorption time on an unbounded integer lattice Incorrectly placed decimal position for percentage values. Dec 5 revised Manhattan distance vs. absorption time on an unbounded integer lattice deleted 99 characters in body Dec 5 comment Manhattan distance vs. absorption time on an unbounded integer lattice @Alexandre Eremenko Right, I'm having some trouble understanding how this problem works in the continuum limit, so I keep talking about Manhattan distances instead of Euclidean distances (where I'm not sure why it makes sense to talk about them on a lattice). Small $L$ means $L \leq 100$ or so. Dec 4 revised Manhattan distance vs. absorption time on an unbounded integer lattice Added a data point at (0, 0, 30) for walker initialization; added 17 characters in body Dec 4 revised Manhattan distance vs. absorption time on an unbounded integer lattice added 1460 characters in body Dec 4 revised Manhattan distance vs. absorption time on an unbounded integer lattice added 324 characters in body; added 42 characters in body