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combinatorial number theory ?

Source: Kazakhstan NMO 2005 (Final round) P7

December 16, 2014
combinatorics proposedcombinatoricsKazakhstan

Problem Statement

Exactly one number from the set {−1,0,1}\{ -1,0,1 \} is written in each unit cell of a 2005×20052005 \times 2005 table, so that the sum of all the entries is 00. Prove that there exist two rows and two columns of the table, such that the sum of the four numbers written at the intersections of these rows and columns is equal to 00.
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