  Given a set of integers $S = \{k_1,\ k_2,...,\ k_n\}$, the Cookie Monster
Problem is the problem of making all elements of the set equal 0 in the minimum
number of moves. Consider the analogy of cookie jars with distinct numbers of
cookies, such that $k_i$ is the number of cookies in the $i$th jar. The "Cookie
Monster" wants to eat all the cookies, but at each move he must choose some
subset of the jars and eat the same amount from each jar. The \emph{Cookie
Monster Number of $S$}, $CM(S)$, is the minimum number of such moves necessary
to empty the jars. It has been shown previously that $\lceil \log_2(|S|+1)
\rceil \leq CM(S) \leq |S|$. In this paper we classify sets by determining what
conditions are necessary for $CM(S)$ to equal 2 or 3 and what effect certain
restrictions have on $CM(S)$. We also provide an alternative interpretation of
the problem in the form of a combinatorial game and analyze the losing
positions.
