Remember the 1st Singaporean problem that went viral? Try this!
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them two unknowns: $M$ and $D.$
$M$ is the month of Cheryl's birthday (1-12).
$D$ is the day of Cheryl's birthday.
Cheryl then tells Albert the sum $M+D$ and she tells Bernard the product $M \times D$.
So they strike a conversation.
Albert: "I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
Bernard: "I could not figure out when Cheryl's birthday is, but I can now."
Albert: "Then I also figured out when Cheryl's birthday is.".
What is the earliest Cheryl's birthday could be?