Magic Squares

[From Krantz: 235 with additions by Stephanie Wilcox.]

Imagine a 3x3 array of squares. The challenge is to put the integers 1 to 9, one in each square, so that each row and each column adds up to the same number. Can this problem also be done with 4x4 squares (16 numbers) or even larger squares and numbers? Why or why not?

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