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Frnicle Standard FormA magic square remains "essentially similar" if it is rotated or transposed, or flipped so that the order of rows is reversed; the concept is named for 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 essentially similar. A magic square is in Frnicle standard form if the following two conditions apply: - the element at the top left corner is the smallest of the four corner elements; and
- the element immediately to the right of the top left corner is smaller than the element immediately below the top left corner.
Thus in the example above, only the final square is in Frnicle standard form. There are eight different magic squares with the same standard form.
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