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China Second Round Olympiad 2022 Test 2 P4

Source: China Second Round Olympiad 2022 Test 2

September 11, 2022
combinatorics

Problem Statement

Find the smallest positive integer kk with the following property: if each cell of a 100×100100\times 100 grid is dyed with one color and the number of cells of each color is not more than 104104, then there is a k×1k\times1 or 1×k1\times k rectangle that contains cells of at least three different colors.
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