Classic - sum of rows and columns nonnegative
Source: 1961 All-Soviet Union Olympiad
August 4, 2015
combinatoricsinvariantmonovariantextremal principle
Problem Statement
Consider a table with one real number in each cell. In one step, one may switch the sign of the numbers in one row or one column simultaneously. Prove that one can obtain a table with non-negative sums in each row and each column.