Agglomeration of Spheres
An artist wants to create a sculpture by gluing together uniform spheres. She creates a rough rectangular base that has 50 spheres along one edge and 30 spheres along the other. She then creates successive layers by gluing spheres in the grooves of the preceding layer. How many spheres will there be in the sculpture?
The answer is 18755.
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1 solution
The base is 50x30. Second layer is 49x29. Third is 48X28 and so forth..and the final layer is 21x1. Hence, the number of balls is Sum (20x+x^2) from 1 to 30.