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A problem in IMC 2012 in which i'm interested but I have no answer. Can you help me? Many thanks.

Problem : Let $n$ be a fixed positive integer. Determine the smallest possible rank of an $n\times n$ matrix that has zeros along the main diagonal and strictly positive real numbers off the main diagonal.

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    It has been discussed [here](http://www.artofproblemsolving.com/Forum/viewtopic.php?f=79&t=491031]), with a nice solution.2012-08-01
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    Thank Davide Giraudo. I'll see the solution. I would like to thank also Xoff and joriki for your participation :-).2012-08-01

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