On the magic squares census problem

L. U. Uko

School of Science and Technology, Georgia Gwinnett College

Abstract. 

A magic square is a square array of order greater than two whose entries are taken from a

set of consecutive whole numbers { beginning from 1 { with the property that the numbers in any row,

column or diagonal of the array add up to the same sum. For centuries, they have been a source of exciting

mathematical amusements and challenging unsolved problems. One of the latter is the census problem of

determining the number of magic squares of order six and above. In this paper we discuss some progress

that have been made in the census problem, namely the magic squares census formulas obtained recently

by Kathleen Ollerenshaw and David Bree for most perfect magic square of doubly even order, and the

census formula derived by Uko for uniform step magic squares of odd order. We also present a result

obtained by parametrizing magic squares and show how it can be used in the study of the general magic

squares census problem.

Keywords: magic square, census problem.