A Travelling Salesman Paths within nxn (n = 3, 4, 5) Magic Squares
General Mathematics
2025-04-02 v3
Abstract
Intriguing symmetries are uncovered regarding all magic squares of orders 3, 4, and 5, with 1, 880, and 275,305,224 distinct configurations, respectively. In analogy with the travelling salesman problem, the distributions of the total topological distances of the paths travelled by passing through all the vertices (matrix elements) only once and spanning all elements of the matrix are analyzed. Symmetries are found to characterise the distributions of the total topological distances in these instances. These results raise open questions about the symmetries found in higher-order magic squares and the formulation of their minimum and maximum total path lengths.
Keywords
Cite
@article{arxiv.2306.08123,
title = {A Travelling Salesman Paths within nxn (n = 3, 4, 5) Magic Squares},
author = {Peyman Fahimi and Walter Trump and Cherif F. Matta and Alireza Ahmadi Baneh},
journal= {arXiv preprint arXiv:2306.08123},
year = {2025}
}
Comments
14 pages, 7 figures