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A square with a colourful line

Source: Romania TST 2 2009, Problem 2

May 4, 2012
combinatoricspigeonhole principle

Problem Statement

A square of side N=n2+1N=n^2+1, n∈N∗n\in \mathbb{N}^*, is partitioned in unit squares (of side 11), along NN rows and NN columns. The N2N^2 unit squares are colored using NN colors, NN squares with each color. Prove that for any coloring there exists a row or a column containing unit squares of at least n+1n+1 colors.
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