  This paper outlines a closed solution to an open problem in Graph Theory
concerning the classification of the successful initial distributions of k
items 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 initial
distribution is enumerated using an algorithm. The closed solution classifies
the terminal set in terms of its modulus, and proves that each successful
initial distribution can be classified by the same modulus.
