[math-fun] diameter of Rubik's cube puzzle
Has the diameter of the Rubik's cube puzzle been established yet? We now have enough computing power to find & prove the distance- to-start for any particular position, using the obvious square-root meet-in-the-middle algorithm and a big disk. We can search for edge positions by generating random positions and using the exact distance algorithm to guide a hill-climb away from the start position. But this is only heuristic. Rich
On 7/7/06, Schroeppel, Richard <rschroe@sandia.gov> wrote:
Has the diameter of the Rubik's cube puzzle been established yet?
... Later a number of variations on the original 3x3x3 puzzle appeared, including 4x4x4, 5x5x5, and 2x2x2. It must be quite easy to find the diameter of the last example --- does anybody know what it is? Another of Rubik's puzzles involved a rectangle comprising 3x2 square pieces, looped together by an elastic cord following a cyclically diagonal path in such a manner that the pieces could flip individually. I can't now recall the name; only my utter failure to model the symmetries of the wretched thing mathematically. Fred Lunnon
Later a number of variations on the original 3x3x3 puzzle appeared, including 4x4x4, 5x5x5, and 2x2x2. It must be quite easy to find the diameter of the last example --- does anybody know what it is?
11 if you count half turns, 14 if you only allow quarter turns. http://www.research.att.com/~njas/sequences/?q=2+X+2+X+2 +Rubik&sort=0&fmt=0&language=english&go=Search erich friedman
On Sun, 9 Jul 2006, Fred lunnon wrote:
Another of Rubik's puzzles involved a rectangle comprising 3x2 square pieces, looped together by an elastic cord following a cyclically diagonal path in such a manner that the pieces could flip individually. I can't now recall the name; only my utter failure to model the symmetries of the wretched thing mathematically.
I believe you're referring to Rubik's Magic: https://secure.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=produc&lvl2=rubbr... Although it might also be the Rubik's Homer Simpson Head: https://secure.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=produc&lvl2=rubbr... But in case it's in fact the Rubik's Jango Fett/Clone Trooper Head, here's the (rather amusing) complete product lineup: https://secure.rubiks.com/lvl3/index_lvl3.cfm?lan=eng&lvl1=produc&lvl2=rubbr... -J
participants (4)
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Erich Friedman -
Fred lunnon -
Jason Holt -
Schroeppel, Richard