Alice and Bob Cheat

We have always seen Alice and Bob playing fairly. Little do we know they are serial cheaters. There are $N+1$ classrooms, numbered $0$ to $N$. Each classroom has a test. Classroom $i$ has a question paper of set $S_i$. Initially, Bob is in the $N^{th}$ classroom. You are allowed to put Alice in any classroom other than the $N^{th}$. Both Alice and Bob have a secret device to communicate during t