MAGIC SQUARES 153

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Each of the horizontal sets, (i), (ii) and (iii), form progres-
sions with a common difference of 1. Each of the vertical
sets, A, B and C form progressions with a common difference
of 6.

These numbers may be formed into a magic square by
means of the procedure outlined for the construction of
squares of an odd order. The following square results:

 

Another way of forming a magic square is now shown. For
a square of the third order (i.e. where n=3), first construct
two squares, and letter the sub-squares of one as under. This
latter square is then the key square and the first square is
built into a magic square by reference to the letters in the
key square.

Key Square

 

Next, we select any three numbers. Emphasis is laid upon the
fact that it does not matter which numbers are chosen. For
our example, we shall use the numbers 5, g and 47. One of
these numbers (say, 47) is placed in the sub-square relative
to sub-square B in the key square. Add this same number to
either of the other two selected numbers (say, 5) and place