MMO 349 Moscow MO 1957 sum 1 or all numbers=0 in a rectangle table
Source:
August 20, 2019
geometryrectangle tabletableSumcombinatorics
Problem Statement
For any column and any row in a rectangular numerical table, the product of the sum of the numbers in a column by the sum of the numbers in a row is equal to the number at the intersection of the column and the row. Prove that either the sum of all the numbers in the table is equal to or all the numbers are equal to .