HMIC 2019 Problem 2

Annie has a permutation $\left(a_{1}, a_{2}, \ldots, a_{2019}\right)$ of $S=\{1,2, \ldots, 2019\}$, and Yannick wants to guess her permutation. With each guess Yannick gives Annie an $n$-tuple ( $y_{1}, y_{2}, \ldots, y_{2019}$ ) of integers in $S$, and then Annie gives the number of indices $i \in S$ such that $a_{i}=y_{i}$. (a) Show that Yannick can always guess Annie's permutation with at most 1200000 guesses. (b) Show that Yannick can always guess Annie's permutation with at most 24000 guesses.