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k chips of two colors on cells of a nxn board

Source: Ukraine TST 2014 p7

May 1, 2020
combinatoricstableColoring

Problem Statement

For each natural n≥4n \ge 4, find the smallest natural number kk that satisfies following condition: For an arbitrary arrangement of kk chips of two colors on n×nn\times n board, there exists a non-empty set such that all columns and rows contain even number (00 is also possible) of chips each color.
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