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Unit squares with the same color - ILL 1990 USS2

Source:

September 19, 2010
combinatorics unsolvedcombinatorics

Problem Statement

Given a 10×1010 \times 10 chessboard colored as black-and-white alternately. Prove that for any 4646 unit squares without common edges, there are at least 3030 unit squares with the same color.
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