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## IMC 2012 Problem 2

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

It is easy to see that if $n \geq 3$ then the rank of the matrix is at least $3$. The main difficulty is to find an example of a matrix with rank exactly $3$.