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Pandiagonal magic square information


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 diagonals, 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 or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an pandiagonal magic square can be regarded as having orientations.

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Pandiagonal magic square

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A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional...

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Magic square

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even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect...

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Pandiagonal magic cube

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generalize pandiagonal magic squares to three dimensions. In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are...

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Pantriagonal magic cube

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of magic cubes may contain some simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications. The magic constant...

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Magic hypercube

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magic square we commonly call pandiagonal and often call perfect. He then demonstrated the concept with an order-7 cube we now class as pandiagonal,...

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Magic cube

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cube has gradually come into use. It is based on the fact that a pandiagonal magic square has traditionally been called "perfect", because all possible lines...

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Magic cube classes

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magic cube. Minimum correct summations required = 7m2 + 6m Pandiagonal: All 3m planar arrays must be pandiagonal magic squares. The 6 oblique squares...

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Associative magic square

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associative magic squares of odd order can be singular or nonsingular. Frierson, L. S. (1917), "Notes on pandiagonal and associated magic squares", in Andrews...

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Perfect magic cube

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does not require that the planar and diagonal squares be a pandiagonal magic cube. For example, a magic cube of order 8 has 244 correct lines by the old...

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Broken diagonal

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columns, and diagonals is called a pandiagonal magic square. Examples of broken diagonals from the number square in the image are as follows: 3,12,14...

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Diagonal magic cube

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+ 6 simple magic squares. The new definition perfect magic cube has a total of 13m2 correct lines and 9m pandiagonal magic squares. Magic cube classes...

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Kathleen Ollerenshaw

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pandiagonal magic squares", in: Mathematics Today, 1998, vol. 34, pp. 139–143. ISSN 1361-2042. D. S. Brée and K. M. Ollerenshaw, "Pandiagonal magic-squares...

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Sriramachakra

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can easily verify that the magic square represented by the Sri Rama Chakra is a strongly magic square. Pandiagonal magic square Vijaya Samvatsara Vakya Panchanga...

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Bohemian matrices

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S2CID 242158547. Ollerenshaw, Kathleen; Brée, D (1998). Most-perfect pandiagonal magic squares. IMA. Higham, Nicholas J; Lettington, Matthew (2022). "Optimizing...

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