Guess Game

An **ordered pair** $(A,B)$ is said to be *valid* iff $\max(A,B) = k\cdot \min(A,B)$, where $k \gt 1$. Let $S(N)$ denote the set of all *valid pairs* $(A,B)$ where $(1 \leq A,B \leq N)$. Carol chooses a *valid pair* $(A,B)$ from $S(N)$ **randomly** and plays `Guess Game` with Alice and Bob. She will tell: - The value $A$ to Alice; - The value $B$ to Bob; - The condition $(A,B)$ is a *valid pa