If you already have trouble remembering the birthday dates for your friends, relatives, or (God help you) your significant other or children, then this math/logic puzzle isn't for you. That's because it asks the very simple question, "When is Cheryl's birthday?"
This problem came up in the Singapore and Asian Schools Math Olympiads contest. A TV presenter put it online and since then it's spread like crazy as everyone tries to figure it out. So, can you do it?
Here's the full question:
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 them 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 [sic.] 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?
Aside from the fact that Cheryl sounds like a terrible friend, the entire problem isn't phrased quite as clearly as it should be. I'll help you out a bit by clarifying that Albert knows the month and Bernard knows the day. Also, Albert and Bernard are speaking out loud to each other there at the end.
So, do you think you have the answer?
The answer is (drum roll, please) July 16. Surprised? Not sure how to get that answer? Here's the solution.
When Albert looks at the list he says that Bernard won't be able to figure out the birthday. That rules out May and June as possibilities because both have unique numbers (18 and 19). If they were possibilities, Bernard could know the birthday just from the number Cheryl gave him.
Bernard, knowing that May and June are out, says he knows the birthday. That means the number can't be 14 because there are two of them, July 14 and August 14. So it has to be 15, 16 or 17.
Once Albert realizes that the number is 15, 16, or 17, he says he knows the birthday, too. If the month was August he wouldn't know because there are still two options, August 15 and August 17.
Therefore, the answer has to be July 16.
If you didn't get it, that's OK. This was problem 24 out of 25 for the contest and it was meant to stump hardcore math students. The Math Olympiad creators flat out said, "SASMO contests target the top 40% of the student population and the standards of most questions are just high enough to stretch the students."
Given how many people online are arguing the answer, or actively not caring, I would be surprised if Cheryl has ever had a birthday party.
So, did you get it right? Let me know in the comments.