Simple magic square
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A simple magic square is the lowest of two basic classes of magic square. It has the minimum requirements for a square to be considered magic. All lines parallel to the edges, plus the two main diagonals must sum to the magic constant.
The other class of magic square is most often called a pandiagonal magic square, but also sometimes it is called perfect or nasik.
Of course, within these two main classes are a great many varieties of magic squares.