Plenty of Franklin magic squares, but none of order 12
Cor A. J. Hurkens · TU/e Research Portal · 2007
We show that a genuine Franklin Magic Square of order 12 does not exist.This is done by choosing a representation of Franklin Magic Squares that allows for an exhaustive search of all order 12 candidate squares.We further use this new representation (in terms of polynomials) to generate large classes of true Franklin Magic Squares of orders 8 and multiples of 16.Next we show how Franklin Magic Squares of orders n = 20 + 8k can be constructed.Finally we indicate how almost-Franklin Magic Squares of order 20 can be constructed in a general way.