Problem

Source: Vietnam TST 2023, P6

Tags: combinatorics



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