Analysis of the Game "2048" and its Generalization in Higher Dimensions

Abstract: We theoretically analyze the popular mobile app game `2048' for the first time in $n$-dimensional space. We show that one can reach the maximum value $2<sup>{n_1n_2+1}$ and $$2^{{\left({\prod_{i=1}^{d}} n_i}\right)+1}$$ for the two dimensional $n_1\times n_2$ board and $d$ dimensional $n_1\times n_2\times \ldots \times n_d$ board respectively. We also present a strategy for the computer and a winning strategy for the human player in certain conditions.