Abstract
본 논문은 홀수, 이중 짝수와 단일 짝수 마방진 알고리즘을 제안하였다. 홀수 마방진은 de la <TEX>$Loub{\grave{e}}re$</TEX>가 제안한 방법으로 <TEX>$O(n^2)$</TEX>회를 수행하는 단점이 있다. 이중 짝수 마방진은 2가지의 교차 알고리즘이 제안되었다. 단일 짝수 마방진은 <TEX>${\frac{n}{2}}{\times}{\frac{n}{2}}$</TEX>의 홀수 마방진에 기반하여 여러 가지 방법이 제안되었지만 Strachey 알고리즘이 적용이 가장 쉽다. 본 논문에서는 홀수 마방진에 대해 3회 수행, 이중 짝수 마방진에 대해서는 4회 수행으로 마방진을 얻는 방법을 제안하였다. 또한, 단일 짝수 마방진에 대해서는 홀수 마방진에 기반을 두지 않고 직접 구하는 알고리즘을 제안하였다. This paper proposes an algorithm for odd, doubly even, and singly even magic squares. In constructing an odd magic square, de la <TEX>$Loub{\grave{e}}re^{\prime}s$</TEX> method is widely known and used, but it has an inherent defect of executing <TEX>$O(n^2)$</TEX> 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 <TEX>${\frac{n}{2}}{\times}{\frac{n}{2}}$</TEX>, 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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