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bw unit squares in nxn table

Source: 2014 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST)

October 3, 2020
combinatoricstableColoring

Problem Statement

In a table n×nn\times n some unit squares are coloured black and the other unit squares are coloured white. For each pair of columns and each pair of rows the four squares on the intersections of these rows and columns must not all be of the same colour. What is the largest possible value of nn?
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