  In recreational mathematics, a normal magic square is an $n \times n$ square
matrix whose entries are distinctly the integers $1 \ldots n^2$, such that each
row, column, and major and minor traces sum to one constant $\mu$. It has been
proven that there are 7,040 fourth order normal magic squares and 2,202,441,792
fifth order normal magic squares, with higher orders unconfirmed. Previous work
related to fourth order normal squares has shown that symmetries such as the
dihedral group exist and that (under certain conditions) normal magic squares
can be categorized into four distinct subsets. With the implementation of an
efficient backtracking algorithm along with supervised machine learning
techniques for classification, it will be shown that the entire set of fourth
order normal magic squares can be generated by expanding the symmetry groups of
95 asymmetric parents. Discussion will suggest that methods employed in this
project could similarly apply to higher orders.
