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January 17th, 2017, 10:46 PM  #1 
Newbie Joined: Jan 2017 From: Romania Posts: 1 Thanks: 0  Calculate all possible moves of m distinct balls into a N points space
We have a ndimensional 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 ndimension, layer by layer, in the way that in 2dimension formed equilateral triangles, in 3dimension 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. 

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balls, calculate, distinct, moves, points, space 
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