GAIC Math 2024 Problem 131

Alice and Bob are playing hide-and-seek. Initially, Bob selects a point $B$ inside a unit square (without informing Alice). Then, Alice sequentially selects points $P_0, P_1, \ldots, P_n$ on the plane. After each selection of a point $P_k (1 \leq k \leq n$, and at this point, Alice has not yet chosen the next point), Bob informs Alice which of the points $P_k$ and $P_{k-1}$ is closer to point $B$. After Alice selects $P_n$ and receives Bob's response, she chooses a final point $A$. If the distance between $A$ and $B$ does not exceed $\frac{1}{2020}$, Alice wins. Otherwise, Bob wins. When $n=18$, which of the following options is correct? A. Alice cannot guarantee victory. B. Alice can guarantee victory.