On the Construction of Pandiagonal Magic Cubes

Fucheng Liao () and Hao Xie
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Fucheng Liao: School of Mathematics and Physics, Hechi University, Guangxi 546300, China
Hao Xie: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Mathematics, 2023, vol. 11, issue 5, 1-23

Abstract: This paper investigates the construction method of pandiagonal magic cube. First, we define a pandiagonal Latin cube. According to this definition, the cube can be constructed by simple methods. After designing a set of orthogonal pandiagonal Latin cubes, the corresponding order pandiagonal magic cube can be constructed. In addition, we give the algebraic conditions of the universal diagonal Latin cube orthogonality and the strict theoretical proof. Based on the proposed method, it can be shown that at least 6 ( n ! ) 3 pandiagonal magic cubes of order n is formed through a pandiagonal Latin cube. Moreover, our method is easy to implement by computer program.

Keywords: magic cube; Latin cube; pandiagonal magic cube; pandiagonal Latin cube (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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