Question 78
Let $n \ge 4$ be a positive integer. Prove that among any $n$ numbers from the set
$$
\{1, 2, \dots, 2n - 1\}
$$
there are some of them with the sum divisible by $2n$. (Ratko Višak)
$$
\{1, 2, \dots, 2n - 1\}
$$
there are some of them with the sum divisible by $2n$. (Ratko Višak)