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Polychromatic colouring of a table

Source: Bulgaria EGMO TST 2017 Day 2 Problem 2

February 3, 2023
combinatoricscellscolouring

Problem Statement

Let nn be a positive integer. Determine the smallest positive integer kk such that for any colouring of the cells of a 2n×k2n\times k table with nn colours there are two rows and two columns which intersect in four squares of the same colour.
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