Missouri State University's Challenge Problem Page
	Mandelbrot Fractal rendered by Noel Giffin

• An n×n magic square is a square array of numbers (n > 1) such that the sum of every row, of every column, and of the two diagonals is the same. For which n is there a magic square whose entries are consecutive positive integers with a sum of 2015? For each such n, what are the largest and smallest entries in the square?

• A perfect magic cube is an n×n×n array of numbers (n > 1) such that the sums of the entries in any row parallel to an edge of the array (there are 3n² of these rows), the sums along the diagonals parallel to a face diagonal (there are 6n of these diagonals), and the sums along the four space diagonals are all equal. For which n is there a perfect magic whose entries are consecutive positive integers with a sum of 2015? For each such n, what are the largest and smallest entries in the cube?

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This page is maintained by Les Reid. Last updated January 8, 2015.