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# Advanced Math/Rubik's Cube Game Modification.

Question

Rubik's Cube
Dear Prof Randy

http://en.wikipedia.org/wiki/Rubik's_Cube

Game Modification
-----------------

Instead of Same Color Patterns in each face, every face is identified with Identical Numbers Patterns.

Cube
----

Face 1 : Even Numbers

2  4  6
8  10 12
14 16 18

Face 2 : Odd Numbers

1  3  5
7  9  11
13 15 17

Face 3 : - Negative Numbers

-1 -2 -3
-4 -5 -6
-7 -8 -9

Face 4 : Square Numbers

1   4  9
16 25 36
49 64 81

Face 5 : Prime Numbers

2  3  5
7  11 13
17 19 23

Face 6 : Square Root

√1 √4 √9
√16 √25 √36
√49 √64 √81

Require your inputs and suggestions regarding this Modified Cube Number Puzzle.

Thanks & Regards,
Prashant S Akerkar

Prashant: These modifications would make the Rubik's Cube extremely difficult. I don't know a lot about them, but I know they are very hard to solve already. Changing the faces to have the numbers you suggest would greatly cut down on the number of configurations possible for a solution. I suppose ultra Rubik's geeks would still find it interesting but the appeal to more normal people would be very limited.

Another observation is that the numbers just serve as markers and don't actually mean anything, i.e., one doesn't combine them in any special way such as is done in Soduko. You could just as well number the sides from 1 - 54 (with some number repeated as per your sequences). Does this suggest a 3-D Soduko games?

A worthwhile math exercise would be to calculate and compare the number of solutions, compared to all possible permutations/combinations, for both the same-color-per-face and your numeric version. Note that your version has multiple solutions based on the fact that several numbers appear on more than one face (eg., 1, 3, 5, 13, etc.).

Randy
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Randy Thank you. Thanks & Regards, Prashant S Akerkar

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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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