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No. 138: NOV-DEC 2001

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Bent Magic

Magic squares cannot be anomalous since they challenge no paradigms, but they can certainly be intriguing. Those that are "extra-magic" can surprise the most blasé of us. (SF#127) Take, for example, the 8 x 8 extra-magic square displayed below.

174730°3621 43*2640
32341945°28*382341
33314620*37°274224
481835*294422°3925
491562*  45311°58  8
64  25113*60°  655  9
  1631452°  5*591056
1650  3°611254*  757

All rows and columns add up to 260, although the two diagonals do not. This deficiency would seem to greatly diminish the square's magickness. But get out your calculator and add up the numbers in those two blunt chevrons marked by ° and *. They add up to 260, so does an (uncoded) S-shaped column beginning with 36. Its mirror image beginning with 21 also yields 260. But wait, there's more, as the TV adds I!] shout, the four "bent" columns can each be slid to right or left, by as many squares as you wish, maintaining their shapes, and still add up to 260!

(Holden, Constance; "Number Fun with Ben," Science, 292:843, 2001.)

From Science Frontiers #138, NOV-DEC 2001. © 2001 William R. Corliss

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