Enigma 8: Anti-magic square
5 December 2011
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From New Scientist #1150, 12th April 1979 [link]
Frances was trying to remember how to arrange the numbers 1 to 9 in a magic square. This was her first shot. As you see, so far from getting the 3 columns, the 3 rows and the 2 main diagonals totalling the same, she got them all different. “Look!” she said, “I have invented an anti-magic square!”
What I ask you to do is to concoct the smallest possible 3 x 3 anti-magic square with 9 whole numbers, all positive but not necessarily all different. In judging the smallest possible, the first criterion is to minimise the highest number used: the second is to minimise the total of all 9 numbers.