Question 76
Define $M_n = \{1, 2, \dots, n\}$, for any $n \in \mathbb{N}$. A collection of 3-element subsets of $M_n$ is said to be *fine* if for any coloring of elements of $M_n$ in two colors there is a subset of the collection all three elements of which are of the same color.
For any $n \ge 5$ find the minimal possible number of the 3-element subsets of $M_n$ in the fine collection.
For any $n \ge 5$ find the minimal possible number of the 3-element subsets of $M_n$ in the fine collection.