Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.
- May 15
- May 16
- May 19
- June 17
- June 18
- July 14
- July 16
- August 14
- August 15
- August 17
Chely 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 does not know too.
Bernard: At first I don’t 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 ?
Hover to show the answer.
It is the July 16
- Albert (A) knows the month.
- Bernard (B) knows the day.
- If A knows the month and knows that B doesn’t know, it means that it is a month that only contains day that you can also find in other proposed months. Otherwise A wouldn’t be so sure that B doens’t know. So it cannot be May because if it was May 19, B would know. It cannot be June, because if it was June 18, B would know. It can be July or August.
- B says he now knows when the birthday is. B just deduced, like us, that it could be July or August because of what A just said. If he now knows when it is, it cannot be the 14. So it is the July 16, August 15 or August 17.
- A then says that he also now knows. So it has to be the July 16, since that is the only month where A has enough information to know the exact birthdate. If it was August, A would still need more information to differentiate between August 15 and August 17.