rectangular array of nonnegative reals
Source: Canadian Mathematical Olympiad 2006, problem 3
January 28, 2007
inductioncombinatorics proposedcombinatorics
Problem Statement
In a rectangular array of nonnegative reals with rows and columns, each row and each column contains at least one positive element. Moreover, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that .