There are two distinct positive integers $a,b$ (i.e. $a\neq b$) such that $a < 7$ and $b < 7$.
Alice has been told the sum of $a$ and $b$. Bob has been told the product of $a$ and $b$.
Both Alice and Bob are aware of all the information mentioned above.
This is their conversation:
Alice says, "I am not sure if you know the sum that I have been told."
Bob says, "Actually, even before you spoke, I knew the sum that was told to you."
What are the possible values of $a$ and $b$ ?
Inspired by a Ted-ed video that I saw.