Publication Date


Document Type


First Advisor

Beach, James W.||Miller, Herbert (Professor of mathematics)

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematics


Magic squares


The purpose of this paper was to find necessary conditions for a 3 X 3 magic square. In a similar manner, the conditions for a variation of the square were found, and the two sets of conditions were compared. The dimension of the system of equations formed by the magic square was found. From this we found suitable bases for the system. Using one of the suitable bases for the system, the forms for the solutions of the nine variables were obtained. Special conditions, such as size and position, were found to exist for several of the variables. General series relationships wars found to exist among the nine variables. Using these series and the equations of the system, we found conditions necessary for the assigning of arbitrary values to some of the variables so that solutions for the remaining variables could also be found. By changing the operation to subtraction, we formed a variation of the magic square and proceeded to obtain the necessary conditions for it. Finally, we compared the conditions for a magic square and this variation and arrived at the conclusion that a square can not satisfy both sets of conditions simultaneously.


Includes bibliographical references.


28 pages




Northern Illinois University

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