This was sent to me by a friend so I can't source it but here's the full text:
Three Mathematics students, Alice, Bob and Charlie have to find the values of $x$ and $y$, with $x, y \in \mathbb Z, 1 \leq x,y\leq 1000$. Alice is told the product $x \times y$, Bob is told the sum $x+y$ and Charlie the difference $| x-y |$. Afterwards, the three have the following conversation:
Alice: I do not know the numbers.
Bob: I already knew that.
Alice: Oh! Now I know them.
Bob: Now I know them too.
Charlie: I do not know the numbers. But I can guess one number, that is probably one of $x,y$, but I don't know for sure.
Alice: I can tell the number you're guessing, but it's not one of them.
Charlie: Then I have figured them out now.
What are the numbers?
I've been trying to figure this out the whole day but I can't even get to Charlie's part.