Published September 23, 2025 | Version v1

Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 8

  • 1. Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Description

This work brings self-made algebraic magicsemi-magic and pandiagonal magic squares of order 8. By self-made or reduced or less entries, we understand that instead of normal n^2 entries of a magic square order n, we are using less numbers, where the magic square is complete in itself. This is just put any integer values for the less entries, one will get always a magic square. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and negative numbers. In some cases, these may be decimal or fractional values depending on the way of chosing the entries. Sometimes to avoid decimal or fractional entries we apply certain conditions. These conditions depends on the types of magic squares. The name self-made is not known in the literature of magic squares.  The work is based on different types of magic squares, i.e., pandiagonalblock-wisecorneredsingle-digit bordereddouble-digit bordered, etc. It is not necessary, but we worked with magic rectangles with equal width and length for the same category within a magic square. If we relax this condition, i.e., by considering only equality of width, still we have good results. For more details refer author’s previous works. Previously, the author brought similar kind of work for the orders 3 to 12, specially for the for the dates and days of the year 2025, where the dates are few entries and days are the sums of magic squares. Total there are 26 magic squares, out of them 8 are just magic squares, 5 are semi-magic and 13 are pandiagonal magic squares. This work is available online at the following links: link1link2

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