Cheryl's Birthday Problem
Cheryl's Birthday Problem Explained
Albert and Bernard just became 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. The following conversation ensues:
Albert: I do not know when Cheryl's birthday is, but I know that Bernard does not know either.
Bernard: At first I do not know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.
As a result, Albert has determined that July 16, August 15, and August 17 are potential dates. For him to now be aware, he has likely been told in July. He would not be aware of the birthday's precise date if August had been mentioned. Because of this, July 16 is the answer.
Therefore, no matter what the sum B is, there is only one answer to our problem and two possible solutions—one in which Cheryl's brothers share the same age and one in which they do not. Also, that's basically it: Cheryl is 9. That is one precarious nine-year-old.
The birthday problem asks how many people need to be at a party for two people to have a better-than-even chance of having the same birthday. The vast majority think the response is 183, the littlest entire number bigger than 365/2. In reality, you only require 23.
Question
When is Cheryl's birthday?
Answer
Cheryl's birthday is on July 16.