MathDB
1 of n symbols in n x n square

Source: Switzerland - 2009 Swiss MO Final Round p4

December 26, 2022
combinatorics

Problem Statement

Let nn be a natural number. Each cell of a n×nn \times n square contains one of nn different symbols, such that each of the symbols is in exactly nn cells. Show that a row or a column exists that contains at least \sqrt{n} different symbols.
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