An Efficient Algorithm for Constructing all Magic Squares of Order Four

@article{Liu2015AnEA,
  title={An Efficient Algorithm for Constructing all Magic Squares of Order Four},
  author={Changyu Liu and Tiezhu Zhao and Bin Lu},
  journal={International Journal of Control and Automation},
  year={2015},
  volume={8},
  pages={235-244}
}
Like the Sudoku puzzle, the magic square involves recreational mathematical contexts and has attracted considerable attention. [] Key Method 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.

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References

SHOWING 1-10 OF 25 REFERENCES
The magic square as a benchmark: comparing manual solution with MIP solution and AI algorithm and improved evolutionary algorithm
TLDR
An artificial intelligence minimax algorithm is developed that imitates a human solving the magic square and it is shown that in most cases its performance, in terms of number permutations, is better than the performance of the GA algorithm.
NEW CONSTRUCTIONS FOR SPECIAL MAGIC SQUARES
Systematic methods are presented for constructing special magic squares of arbitrarily large size, including regular (or associative), pandiagonal, and most-perfect magic squares as well as
Generalization of 6×6 Magic Square
A magic square of order n is n×n matrix containing integers in such a way that each row and column add up to the same value. We generalize this notion to that of a 6×6 matrix with the help of a
The science behind Sudoku.
TLDR
The article focuses on mathematical problems inherent in solving Sudoku puzzles and provides a mathematical analysis of how the puzzles are put together and solved.
The Ehrhart polynomial of the Birkhoff polytope
The n Birkhoff polytope is the set of all doubly stochastic n × n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem
The Lost Squares of Dr. Franklin: Ben Franklin's Missing Squares and the Secret of the Magic Circle
TLDR
Franklin's squares still appear today in popular mathematics books such as Theoni Pappas's Joy of Mathematics and Jan Gullberg's encyclopedic Mathematics: From the Birth of Numbers.
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