Volume no :7, Issue no: 1, March 2012

Journal of Algebra, Number Theory: Advances and Applications

SQUARING THE MAGIC SQUARES OF ORDER 4

Author's: STEFANO BARBERO, UMBERTO CERRUTI and NADIR MURRU
Pages: [31] - [46]
Received Date: April 11, 2012
Submitted by:

Abstract

In this paper, we present the problem of counting magic squares and we focus on the case of multiplicative magic squares of order 4. We give the exact number of normal multiplicative magic squares of order 4 with an original and complete proof, pointing out the role of the action of the symmetric group. Moreover, we provide a new representation for magic squares of order 4. Such representation allows the construction of magic squares in a very simple way, using essentially only five particular matrices.

Keywords

additive magic squares, multiplicative magic squares, normal magic squares, symmetric group.