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Rectangle containing no black squares

Source: Greece JMO 2018, pr 2

March 5, 2018
rectanglecombinatoricsColoring

Problem Statement

A 8×88\times 8 board is given. Seven out of 6464 unit squares are painted black. Suppose that there exists a positive kk such that no matter which squares are black, there exists a rectangle (with sides parallel to the sides of the board) with area kk containing no black squares. Find the maximum value of kk.
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