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How can you transform a given magic square into a square where all the lines are invariant under multiplication?

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2 Answers 2

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Replace each number in the grid with $2^x$ (or $3^x$, etc).

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  • $\begingroup$ Ok, this is way better than what I was thinking $\endgroup$ Commented Apr 22, 2023 at 13:57
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The most trivial is to:

Multiply every cell by zero. But I'm pretty sure that's not the intended solution.

Partial solution involving another thought process:

I tried with a few examples for 3x3 and 4x4 and it worked. I didn't manage to find a generalization for any nxm magic square. I just don't know how to proof it: You sum it with itself rotated twice when it's 3x3.
You sum it with itself vertically mirrored when it's 4x4.
3x3

4x4

4x4 other

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