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exists a column colored in n colors - All-Russian MO 2002 Regional (R4) 11.4

Source:

September 17, 2024
combinatoricsColoring

Problem Statement

Each cell of the checkered plane is colored in one of n2n^2 colors so that in any square of n×nn \times n cells all colors occur. It is known that in some line all the colors occur. Prove that there exists a column colored in exactly nn colors.
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