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bw cells in 200x200 table - All-Russian MO 2000 Regional (R4) 9.8

Source:

September 26, 2024
combinatoricsColoring

Problem Statement

The cells of the 200×200200 \times 200 table are painted black and white so that there are 404404 more black cells than white ones. Prove that there is a 2×22 \times 2 square in which the number of white cells is odd.
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