How one goes about creating a magic square is best illustrated by a specific example. The magic square below is the first one that I found (on Dec 4).
I started by filling the rows of the bottom left quarter with the sums at the top of the lists for 9 and its complement 25. The order was arbitrary but I switched the 9 and 16 about so that the vertical sums had the lowest maximum. The bottom right quarter also needed row sums which added up to 9 and 25 so my 3rd and 4th choices were 7 + 2 and 14+11 again arranged to product the lowest maximum vertical sum. The horizontal, vertical and diagonal sums were then computed for the bottom half of the magic square. The remaining independent variable in the upper left quarter has to have a vertical sum of 20 and a diagonal sum of 13 as indicated in the lower half . The arrows in the tables for sums which equal 13 and 20 have only 12 as a common number so that was selected. The remainder of the magic square can be computed using the equal pairs of sums.
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