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Coloring square

Source: Moscow Olympiad 2018, Grade 10, P2

July 13, 2018
combinatorics

Problem Statement

In there 2018×20182018\times 2018 square cells colored in white or black. It is known, that exists 10×1010 \times 10 square with only white cells and 10×1010\times 10 square with only black cells. For what minimal dd always exists square 10×1010\times 10 such that the number of black and white cells differs by no more than dd?
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