Cheryl gives them a list of 10 possible dates:
May: 15 or 16 or 19.
June: 17 or 18.
July: 14 or 16 .
August: 14 or 15 or 17.
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.
Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too.
Bernard: At first I did not know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.
So when is Cheryl's birthday?"