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MAGIC SQUARES 151

the required square drawn inside the first square so that the
sides of the first square are bisected by the corners of the
smaller square. Numbers are then written consecutively in
the first square, as follows: ;

      
   
 
 
 
 
   

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It will be seen that some of the integers automatically
appear in the smaller square, because the sub-square of the
two main squares partly coincide in places. The numbers
which appear in the smaller square are left in their respective
positions, but the numbers which appear outside the smaller
square are transferred to positions within that square. Each
such number is, in fact, moved to the furthest vacant sub-
square along the same row or column of the larger square.

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