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January 17th, 2017, 10:46 PM   #1
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Calculate all possible moves of m distinct balls into a N points space

We have a n-dimensional finite space formed by N points distributed equidistant in that way:
We start from a point named origin, and then put equidistant around it points in n-dimension, layer by layer, in the way that in 2-dimension formed equilateral triangles, in 3-dimension formed regulate tetrahedral, and so on.
In that finite space there are, in the way described above, L layers of points around point of origin.
We have m number of distinct balls that occupied m points in space N. Every ball has neighbor points that can be occupied or unoccupied by other balls for a reference time step. Every ball can move to one of neighbor unoccupied points in next time step.
How can be calculated the maximum number of possible moves that all m balls can do in next time step, no matter of initial position in space N (sum of total possible moves of each ball in next time step)?
Please, I need a math formula.
If you need more details please tell me.
Khadras is offline  

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