Frenicle’s 880 Magic Squares

Abstract

This chapter discusses magic squares. A magic square of order n is an arrangement of the numbers from 1 to n 2 in an n × n array so that the two diagonals and all the rows and columns have the same sum. This sum is called the magic constant. Bernard Frenicle de Bessy's work on magic squares appears in two papers published in the book Divers ouvrages de mathematique et de physique par Messieurs de l'Academie Royale des Sciences. In his first paper, “Des Quarrez ou Tables Magiques,” Frenicle quotes a rule for constructing magic squares of odd order. However, Frenicle is more famous for his second paper, “Table Generale des Quarrez de Quatres,” in which he enumerates the 880 magic squares of order four. His enumeration has been repeated many times. These later enumerations they have confirmed the remarkable fact that he was correct.