Home Page Science Frontiers
ONLINE

No. 127: Jan-Feb 2000

Issue Contents





Other pages


Other Interesting Sites


 


 


 


 


 


 


 


 


 

 

Some Magic Squares Are More Magical Than Others

It is rather suprising that magic squares exist at all. Why should we be able to arrange 0 and the first 143 integers into a 12 x 12 square such that all columns, rows, and diagonals add up to 858? Believe it or not, there are actually more than two billion 12 x 12 magic squares! However, the particular 12 x 12 square reproduced here is more magical than most.

First off, it is "pandiagonal." This means that broken diagonals, such as those like 61-12-118 + 85-3-120-25-131 82-58-140-23 also add up to 858.

Second, this square is classified as "most-perfect" because the numbers in each and every 2 x 2 square add up to 286. How could a magic square be more perfect than this?

(Stewart, Ian; "Most-Perfect Magic Squares," Scientific American, 281:122, November 1999.)

Comment. We ask, with tongue-in-cheek: "Aren't we lucky to have such an interesting number system?"

12 x 12 pandiagonal magic square

From Science Frontiers #127, JAN-FEB 2000. 1997 William R. Corliss