IN the interesting discourse reproduced in your issue of March 13 (p. 447), there is a statement that the number of magic squares of order 5 exceeds 60,000. Major MacMahon informs me that he gave these figures on the authority of Rouse Ball's “Mathematical Recreations.” The statement is not wrong, but viewed as a minimum limit it may be largely exceeded. I have recently investigated the total number of squares of this order, which have the additional property that the nine numbers in the heart of the square also form a magic—the well-known “bordered squares.” Fig. 1 is an example. The square itself is magic in rows, columns and diagonals, and the nine numbers in the central square show like properties.