An algorithm for constructing magic squares

“…[1][2][3] 단일 짝수 마방진은 Madjig 를 이용하는 방법 [1], Strachey [3,4] 방법과 Conway [2,3,7] 의 LUX 방법이 있다. 이외에도 Kim과 Yoo [8] 은 곱셈법을 적용하였으며, Jacob과 Murugan [9] 은 이중 짝수 마방진 을 구성하는 방법을, Chen et al [10] …”

Section: ⅰ 서 론unclassified

The Magic Square Algorithm

Lee¹

2017

JIIBC

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This paper proposes an algorithm for odd, doubly even, and singly even magic squares. In constructing an odd magic square, de la Loubère's method is widely known and used, but it has an inherent defect of executing     steps. 2 types of cross algorithms have been proposed to the double even magic square, and more to the singly even magic square based on the odd magic square of    ×    , the most popular and simple of which is one proposed by Strachey. The algorithm proposed in this paper successfully constructs odd and doubly even magic squares by undergoing 3 steps and 4 steps respectively. It also directly constructs a singly even magic square without having its basis on the odd magic square.

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“…Magic Polygons are objects that had its inspiration on the classics Magics Squares, and these are known from a long time ago, and there are algorithms to build Magic Squares of different orders, as we can see in [1,2,3,4,5,6]. Furthermore, such objects has applications in fields like Computer Science Physics and Cryptography according to [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Magic Polygons and Combinatorial Algorithms

Augusto¹

2022

ARJOM

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In this work, we study the Magic Polygons of order 3 (P(n; 2)) and we introduce some properties that were useful to build an algorithm to find out how many Magic Polygons exists for the regular polygons up to 24 sides. The concepts of Equivalents Magic Polygons and Derivatives Magic Polygons which allowed to classify, and avoid ambiguity about the representations of such elements, are also introduced.

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An algorithm for constructing magic squares

Cited by 10 publications

References 8 publications

Existence of Yang Hui Type Magic Squares

Existence of Yang Hui Type Magic Squares

The Magic Square Algorithm

Magic Polygons and Combinatorial Algorithms

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