Question 52
For which largest $k$ does there exist a permutation $(a_1, a_2, \ldots, a_{2022})$ of integers $(1, 2, \ldots, 2022)$ such that for some $k$ integers $1 \le i \le 2022$ the fraction $\frac{a_1 + a_2 + \cdots + a_i}{1 + 2 + \cdots + i}$ is an integer larger than $1$?
(Oleksii Masalitin)
(Oleksii Masalitin)