An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identi…ed. Treated as matrices these squares possess just two nonzero eigenvalues. The construction of these squares has been automated by writing Maple r code, which also performs tests on the results. A rather more trivial set of pandiagonal non-magic squares consisting of the monotonically ordered sequence of integers existing for all orders has also been found.
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