2006 Canadian MO Problems/Problem 3

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Problem

In a rectangular array of nonnegative real numbers with $m$ rows andn $n$ columns, if and only if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that $m=n$.

Solution

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See also

2006 Canadian MO (Problems)
Preceded by
Problem 2
1 2 3 4 5 Followed by
Problem 4