Table of zeros and ones with special property
Source: 2007 Bulgarian Autumn Math Competition, Problem 10.4
March 17, 2022
combinatoricstable
Problem Statement
Find all pairs of natural numbers , , such that there exists a table with rows and columns filled with the numbers 1 and 0, satisfying the following property: If in a cell there's a 0 (respectively a 1), then the number of zeros (respectively ones) in the row of this cell is equal to the number of zeros (respectively ones) in the column of this cell.