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Let's say you fill in a 6 by 6 square with the numbers 1, 2, ..., 36. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the second row is equal to the product of the second column, ..., etc?

So far I had already ask the n=4 and n=5 here.

Fill in a 5x5 multiplicative magic square

Fill in a 4x4 multiplicative magic square

I apologize if this topic is repetitive. But I am very interested in this problem and I cannot figure out 𝑛=6 case.

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I think the following grid will work

19 25  36  9  6 13
 5 23  16 15 14 17
18  3  29 32  2 22
10  4  12 31 24 21
27 28   1  8 35 20
26 34  11  7 30 33

Method

I followed almost exactly the same path of reasoning as given here, an approach to the previous problem. Obviously, the parameters are different here but the approach is still as effective.

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