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Pandiagonal magic square
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{{Short description|Magic square with extra constraints}} A '''pandiagonal magic square''' or '''panmagic square''' (also '''diabolic square''', '''diabolical square''' or '''diabolical magic square''') is a [[magic square]] with the additional property that the [[broken diagonal]]s, i.e. the diagonals that wrap round at the edges of the square, also add up to the [[magic constant]]. A pandiagonal magic square remains pandiagonally magic not only under [[Rotation (mathematics)|rotation]] or [[Reflection (mathematics)|reflection]], but also if a row or column is [[Translation (geometry)|moved]] from one side of the square to the opposite side. As such, an <math>n \times n</math> pandiagonal magic square can be regarded as having <math>8n^2</math> orientations.
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