


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 3n^{2} 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?
Submit a solution
Go to the Challenge Problem Archive
Back to the Math Department Homepage
Back to the Problem Corner
This page is maintained by Les Reid. Last updated January 8, 2015.