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I have the following magic square but cannot determine how the square is actually "magic".

It's a 3x3 as seen below in red with the green showing a few examples of row sums.

Each vertical and horizontal multiplication, for example AxBxC = 120, however, the diagonals do not.

magic square

DT.DTDG
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  • What's your question? Because a magic square is per definition a square for which each row, column and diagonal sum to the same value. So it's not a magic square. – Eric S. Mar 08 '16 at 11:07
  • @EricS. This is a grade 6 question whereby the teacher has explicitly asked, "Why is this square Magic"? From my understanding it is not, although they seem quite adamant that it is. – DT.DTDG Mar 08 '16 at 11:09
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    This is a multiplicative semimagic square (semimagic means one no longer enforce the constraint that diagonal sum/multiply to same value). – achille hui Mar 08 '16 at 11:10
  • @achillehui Thank you! Exactly what I was looking for. Please add this as an answer so I can accept. – DT.DTDG Mar 08 '16 at 11:14

1 Answers1

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The square of numbers at hand is not a magic square but a multiplicative semimagic square.

In the common definition of a magic square, we demand:

the sum along the rows, the columns and the two diagonals are all the same.

If we replace sum by product, it will be called a multiplicative magic square.

If one relax the constraint and the sum/product only require to be the same along rows and columns, it becomes a semimagic square.

achille hui
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