Question 59
Let $A_1, A_2, \dots, A_{20}$ be 20 distinct subsets of size 3 of the set $X = \{1, 2, \dots, 10\}$. We say that a subset $S$ of $X$ is a covering subset if for every $1 \le i \le 20$, it holds that $S \cap A_i \ne \emptyset$. What is the minimum possible value of $k$, such that there always exists a covering subset of size $k$?