Questions tagged [rubiks-cube]

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Does Chu and Hough's solution to the mixing time of the 15-puzzle carry over to the Rubik's cube?

In his 1988 book Group Representations in Probability and Statistics , Diaconis considers mixing times of the 15-puzzle. He states: Here is a simplified version: Consider the blank as a $16$th ...
13
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0answers
356 views

Geometric (smooth) Rubik's cube

I and my friend are thinking about a smooth analog of Rubik's cube. One idea is the following: Consider the 2-dimensional sphere $S^{2}$. We choose three parameters: $(L, H, \theta)$. Here $L$ is a ...
13
votes
1answer
2k views

Number of positions of Rubik's cube grows with multiplier 13 with the distance - what are explanations and groups with similar growth pattern?

Rubik's cube and its generalizations attracts certain attention of mathematical community. It is somehow "noteworthy" that it has been proved that diameter of the Rubik's cube group is 20, i.e. ...