Form standard of Frénicle

In Mathématiques, a magic square remains “primarily similar” if it is transposed, or permuted i.e. if the order of the lines is reversed; the concept is named thus in the honor of Bernard Frénicle de Bessy. Thus magic squares

8 1 6 8 3 4 4 9 2 4 3 8 6 7 2 6 1 8 2 9 4 2 7 6 3 5 7 1 5 9 3 5 7 9 5 1 1 5 9 7 5 3 7 5 3 9 5 1 4 9 2 6 7 2 8 1 6 2 7 6 8 3 4 2 9 4 6 1 8 4 3 8

are all primarily similar. A magic square is in a standard form of Frénicle if the two following conditions are applied:

  1. the element with the left higher corner is smallest of the elements of angle.

  2. the element immediately on the right of the left higher corner is smaller than the element immediately under the left higher corner.

Thus in the example above, the last square is in a standard form of Frénicle.

There exist eight different magic squares with the same standard form.

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