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This paper outlines a closed solution to an open problem in Graph Theoryconcerning the classification of the successful initial distributions of kitems in N vertices, where $k = N$, that lead to the terminal set $N_k = \{n_i\} $, where $n_i=1$ and $i=1,2,3,...,k$. First, each successful initialdistribution is enumerated using an algorithm. The closed solution classifiesthe terminal set in terms of its modulus, and proves that each successfulinitial distribution can be classified by the same modulus.

A Solution for the Open Abelian Sandpile Problem of Distributing k Items in N Vertices, where k = N