Alice and Bob are perfectly logical and super intellegent. Their professor decides to play a game with them, and he tells them: "I have chosen two numbers (integers) $x$ and $y$ with $2\le y \le x\le 100$. I will tell Alice the value of their difference $d=x-y$ and Bob the value of their ratio $r=x/y$. I stress that the ratio $r$ is an integer, too."
After the professor has told the difference to Alice and the ratio to Bob, the following exchange occurs:
- Alice: I don't know the numbers.
- Alice: You might though. Do you know them?
- Bob: No, I don't know them.
- Alice: Too bad, if you did I would know them too.
- Alice: I still don't know them though.
- Bob: Me neither.
- Alice: Oh really? Then I do.
- Bob : Dang it; I still don't.
What is the value of $r$?
What are the possible values for $x$ and $y$?