MathDB
Removing 990 rows or columns to get at least one 1 or 0...

Source:

February 19, 2011
geometryrectanglecombinatorics unsolvedcombinatorics

Problem Statement

Each cell of a 1000×10001000\times 1000 table contains 00 or 11. Prove that one can either cut out 990990 rows so that at least one 11 remains in each column, or cut out 990990 columns so that at least one 00 remains in each row.