The Anti-Magic Square Project: Construction

Madachy asks "Are there any systematic methods by which antimagic squares may be constructed?" It seems that up until now, no such method was known. Here, we present several constructions discovered this summer.

Constructing an AMS(4k+3)

This construction is essentially the same as the 4k+1 case. Use the same permuted Cayley table as the high order square but the low-order square is slightly different. We need three staircases of red along the back diagonal instead of one. This necessitates a slight change in the pattern of blues and a different arrangement of greens and turquoise.

Differences between odd types Type 4k+1 Type 4k+3

  • Three staircases of reds instead of just one.

  • Construct blues with 1s below and right of the center entry

  • Green & turquoise pattern is different.

Otherwise, the construction is the same. Please (see examples of orders 7, 11, 15 & 19)

Composed by John Cormie Updated: July 21 1999

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