Recently, I saw a question in [see here](http://www.puzzling.stackexchange.com) which is so interesting for me. This question is as follows:



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> Is it possible to fill the $121$ entries in an $11×11$ square with the values $0,+1,−1$, so that the row sums and column sums are $22$ distinct numbers?
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This problem is interesting for me because its definition is reverse of the magic square. I think for solve this problem we must use something like design theory. Also, for $n=6$ this problem have an answer. My next question is:



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> For which integer number $n$, this problem has a solution and is this problem well known in math?
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I will be so thankful for any helpful comments and answers. 



reverse definition for magic square
This problem is so famous. For first trivial reference, you can see:[link](http://mathworld.wolfram.com/-101-Matrix.html).


$\it{R. Bodendiek}$ and $\it{G. Burosch}$ studied this problem in a paper with name:


"Solution to the Antimagic 0,1,-1 Matrix Problem."


If there is solution for integer $n$, then we have:


$1)$ $n$ is even,


$2)$ The number in $\{-n,1-n,2-n,...,n\}$ that does not appear as a line sum is either $-n$ or $n$,


$3)$ Of the $n$ largest line sums, half are column sums and half are row sums.


Also, you can search about "Alternating sum matrix", for more information.


