Albert and Bernard have 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.
Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.
- Albert knows the month.
- Bernard knows the day.
Then they have the following conversation:
- Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know either.
- Bernard: At first, I didn’t know when Cheryl’s birthday was, but I know now.
- Albert: Then I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
👁 cheryl_s_birthday
Check if you were right - full answer with solution below.
Solution:
Step 1: Albert’s Statement
- Albert knows the month and says Bernard does not know the birthday.
- If the month were May or June, Bernard could have known ,since 19 and 18 appear only once in May and June respectively.
- Therefore, eliminate May and June.
Remaining dates: July 14, July 16, August 14, August 15, August 17
Step 2: Bernard’s Statement
- Bernard now says he knows the birthday.
- As Bernard is unaware of the Month, if the day were 14, there would still be two possibilities (July 14 and August 14).
- Therefore, eliminate 14.
Remaining dates: July 16, August 15, August 17
Step 3: Albert’s Final Statement
- Albert now says he also knows the birthday.
- If the month were August, there would still be two options (15 and 17), so he would be unsure.
- Therefore, the month must be July.
Cheryl’s birthday is July 16.
