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2 Russian Scientist & Japan & pi

Topic closed. 51 replies. Last post 13 years ago by johnph77.

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Cleveland,Oh
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July 16, 2003
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Posted: December 29, 2003, 7:03 pm - IP Logged

Rubik cube!

color=#0000ffBRubik s/B online Home Page IMG height=12 alt=icon src= http://aolsearch.aol.com/gr/pw.gif"> - ... Solving the Cube! Rubik's Club. Rubik's Cube. Try online Rubik's Challenges! ... Try online Rubik's Challenges! Where to buy? FAQ and Cube info. Rubik's Promotion. ...
http://www.rubiks.com/

ask them?

    johnph77's avatar - avatar
    CA
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    December 10, 2003
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    Posted: December 30, 2003, 2:24 am - IP Logged

    Thought about it after I posted. Here's where I erred.

    The cubes on the edge show two faces at the same time and have but four orientations. That math stands. But the corner cubes have six exposable faces. Think of them as dice, with each color representing a specific number. If one color (assume it represents the number 1) is in a specific position then there are four different possible orientations on the cube as the cube is rotated on the 1-6 axis - 1-2-3, 1-3-5, 1-5-4 and 1-4-2. The color representing the number 6 will never be exposed as it is on the opposite side of the color representing the number 1. Given this, with no mechanical limitations, there would be 24 different orientations of each corner cube. Having never disassembled a cube I have no idea what those mechanical limitations are, so I guess I'll have to stand by the 43 trillion number of possibilities.

    Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

    Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

     =^.^=


      China
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      December 16, 2003
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      Posted: December 30, 2003, 3:30 am - IP Logged

      you can have a different view with a wheeling system concept.

        Prometheus1's avatar - trace9

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        Posted: December 30, 2003, 12:42 pm - IP Logged

         Johnpm77,

                                             895,833,333,333,333,333  

                        Isn't it about 43 quintillion divided by 48 or just under a quintillion.  What the heck ....what's 895,833,333,333,333,333  quadrillion among friends?

         This is not an exact answer, because some patterns exhibit symmetry, and do not actually have 48 distinct representations. I suspect the exact calculation entails the use of the Bernside Polya counting theorem, but it's been a long time since I took combinatorics. Any help would be appreciated.

        Although the cube has not been completely analyzed, we can place a lower bound on its complexity. After one move, the cube can be in any of 12 different configurations. After two moves, the cube can attain, at most, 12^2 = 144 patterns (the actual number is 129). The number of configurations that lie within k moves of start is
        1 + 12 + 12^2 + 12^3 + ... + 12^k = (12^(k+1) - 1) / 11.
        When k = 18, the result is less than 43 quintillion. Therefore, some configurations are 19 moves from start. If 180 degree turns are considered moves, the base of the exponential function changes from 12 to 18, and some configurations are 16 moves from start.

          PROMETHEUS       

          WIN  D's avatar - q05Q0
          Stone Mountain*Georgia
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          Posted: December 30, 2003, 1:46 pm - IP Logged

          Prometheus, don't you mean, "what's 895,833,333,333,333,333 among friends?" (quadrillion is redundant) LOL

           

           

          The only real failure .....is the failure to try.                               

                                        Luck is a very rare thing....... Odds not so much. 

                                        Odds never change .....but probability does. 

                                                                                                 Win d    

            Prometheus1's avatar - trace9

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            Posted: December 30, 2003, 1:57 pm - IP Logged

            LOL  Good man Win d . You are very right. Hope you emptied your mail box. I have what we talked about ready to go. Let me know asap so I can re-send...   

              p.s. that was just in case someone fell asleep before they got to the end. LOL 

              PROMETHEUS       

              johnph77's avatar - avatar
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              Posted: December 30, 2003, 11:09 pm - IP Logged

              Ahhhhh, what the heck - since there are 8 cubes with 24 possible configurations and 12 cubes with 4 possible configurations, disregarding mechanical limitations I get ((24 x 24 x 24 x 24 x 24 x 24 x 24 x 24) = 110,075,314,176) x ((4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4) = 16,777,216) = 1,846,757,322,198,614,016 - 1.8 quintillion possibilities.

              HNY, a - gl

              Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

              Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

               =^.^=