Science Frontiers ONLINE No. 138: NOV-DEC 2001 Issue Contents

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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 blas� of us. (SF#127) Take, for example, the 8 x 8 extra-magic square displayed below.

17	47	30�	36	21	43*	26	40
32	34	19	45�	28*	38	23	41
33	31	46	20*	37�	27	42	24
48	18	35*	29	44	22�	39	25
49	15	62*	4	53	11�	58	8
64	2	51	13*	60�	6	55	9
1	63	14	52�	5*	59	10	56
16	50	3�	61	12	54*	7	57

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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