ABSTRACT
Under the basic definition of a magic square (a square number array in which the sum of each row, column, and diagonal is the same), a onecelled square could exist, in theory. Of course, any square consisting of one number would be a magic square, but a trivial and uninteresting one. Richard Webster in his book Talisman Magic notes that medieval Christians employed a one-celled magic square as a symbol for God, while a magic square of order two, being impossible, they associated with the devil.1 We can easily demonstrate that a magic square of order two is impossible. Assume that such a square exists. Let its elements be represented by the letters a, b, c, d, where each letter represents a different numerical value. Thus the square is of the form:
a b c
d e f
g h i
Let the magic sum for each row, column, and diagonal be k. So a + b = k, a + c = k, and so on. Solving just two of the possible six linear equations, simultaneously, we find:
a + b = k – (a + c = k)
b – c = 0 ⇒ b = c
This indicates that two numerical values are the same and that contradicts our definition of a magic square.
