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152 THE FASCINATION OF NUMBERS

The number 3, for instance, is transferred to the last sub-
square in the second row.
The following magic square results:

o le [w]e]e
s 1 ]9 127 >
oot 10 5[z 2 [5¢
Lo [T 53]
e s o[ [s2] o 10
il 6 [ w[ss[
2] s [ 15150 1 [

Magic squares are by no means confined to the use of con-
secutive integers. They may, in fact, be composed from any
set of integers which conform to certain rules. A square may
be made from nine integers (a) if these integers can be
written in three sets of integers, each set being an arithmeti-
cal progression with a common difference of 1, and () if the
relative terms in these sets can be extracted to form new pro-
gressions with a common difference of 6. The following nine
integers may be so arranged:

 
       
 
    
     

ok N R g R Lt
and their arrangement is:

o bt
(1) I e g
(i1 ¥ 10800
(111) 08 AT s