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12 black unit squares in a 8x8 all white chessboard

Source: Greece JBMO TST 2019 p4

April 29, 2019
combinatoricsgridtableChessboardsquare grid

Problem Statement

Consider a 8×88\times 8 chessboard where all 6464 unit squares are at the start white. Prove that, if any 1212 of the 6464 unit square get painted black, then we can find 44 lines and 44 rows that have all these 1212 unit squares.
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