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2-colorable way for numbers

Source: Vietnam TST 2023, P6

April 14, 2023
combinatorics

Problem Statement

Let n≥3n \ge 3 be an integer and SS be a set of nn elements. Determine the largest integer knk_n such that: for each selection of knk_n 3−3-subsets of SS, there exists a way to color elements of SS with two colors such that none of the chosen 3−3-subset is monochromatic.
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