Earticle

초록

영어

Like the Sudoku puzzle, the magic square involves recreational mathematical contexts and has attracted considerable attention. Although there are many researches available, few of them could provide an efficient solution for constructing all magic squares of order four. In this paper, we firstly formulate constraints of magic squares of order four by a collection of linear equations and provide an intuitive but computationally infeasible solution to these equations. Then, we propose an efficient algorithm for constructing all magic squares of order four. The algorithm transforms solving these equations into finding all possible permutations of seven free variables from sixteen consecutive natural integers based on the Gaussian Elimination method. Furthermore, we show the effectiveness of the proposed algorithm by 48 magic squares in the experimental section.

목차

Abstract
 1. Introduction
 2. Magic Squares of Order Four
 3. An Infeasible Solution
 4. Methodology
  4.1. Gaussian Elimination
  4.2. Optimization Algorithm
 5. Experiment
 6. Conclusion
 References

키워드

저자

• Changyu Liu [ College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China, School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China ]
• Tiezhu Zhao [ Computer College, Dongguan University of Technology, Dongguan 523808, China ] Corresponding Author
• Bin Lu [ School of Computer Science, Wuyi University, Jiangmen 529020, China ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Control and Automation

• 간기

  월간

• pISSN

  2005-4297

• 수록기간

  2008~2016

• 십진분류

  KDC 505 DDC 605