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Title
A generalization of Trenkler's magic cubes formula
Authors
Livinus U. Uko, Terry L. Barron
Abstract
A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1,2,..., p3} such that all rows, columns, pillars and space diagonals have the same sum. In this paper, we show that a  formula introduced in The Mathematical Gazette 84(2000), by M. Trenkler, for generating odd order magic cubes is a special case of a more general class of formulas. We derive sufficient conditions for the formulas in the new class to generate  magic cubes, and we refer to the resulting class as regular magic cubes. We  illustrate these ideas by deriving  three new formulas that generate magic cubes of odd order  that differ from each other and from the magic cubes generated with Trenkler's rule.
Keywords
magic cube, regular magic cube, magic cube formula, Trenkler's formula
Milestones
Published: 2018/01/11
Author Details
Livinus U. Uko
luko@ggc.edu
School of Science and Technology, Georgia Gwinnett College

Terry L. Barron
tbarron@ggc.edu
School of Science and Technology, Georgia Gwinnett College

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