Second part: http://www.youtube.com/watch?v=qN46KsjUUa8
Unfortunately, Maxim continued cheating.
There is big controversy in the Russian-speaking communities about if it had brought benefits or harm to the community.
I think that despite the advantages, it is a great...
Using dynamic algorithm, suggested by Stefan, I recalculated the histograms for 1-19 moves. Now they are complete and absolutely exact.
1 move: :)
Thank you, I understand the idea.
The number of possible scrambles, that have length 11, is relatively small. 9*6^10=544195584. So we need't use Monte Carlo method. OK, I'll try to do complete calculation for number of moves <=15.
Scrambles are in FTM (moves U2, R2, F2 are included) and do not allowed to repeat the face in next move.
BTW, if we allow such a repetition (for example U U', R2 R sequences), the distribution becomes much worse. If i'm not mistaken, the peak of the histogram increases 100 times or something...
I think we will get some kind of average histogram for histograms for 10-14 moves. Because in all cases the same positions have more probability to appear, with slight differences. The most common position for any length of scramble - solved state. Further there are positions that can be solved...
Recently I got interested in such a question: if we scramble a puzzle using random sequence of moves, do we really get an "absolutely random" position? How many moves should we perform, before we scramble puzzle really well?
Obviously, the ideal scramble should give the discrete...
I have developed a program that on my home computer is able to find one Devil algorithm for the RU subgroup in ~5 minutes. I have not used too much theory, mainly used Warnsdorff's rule, in conjunction with Euler's method, plus a variety of optimizations under this specific problem. I did not...