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A Magic Square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a nested magic square is the order 7 square illustrated above (i.e., the order 7, 5, and 3 squares obtained from it are all magic).
See also Magic Square
References
Kraitchik, M. ``Border Squares.'' §7.7 in
Mathematical Recreations. New York: W. W. Norton, pp. 167-170, 1942.