RU-SPB 2022 Problem 117

Given is a set of $2n$ cards numbered $1,2, \cdots, n$ , each number appears twice. The cards are put on a table with the face down. A set of cards is called good if no card appears twice. Baron Munchausen claims that he can specify $80$ sets of $n$ cards, of which at least one is sure to be good. What is the maximal $n$ for which the Baron's words could be true?