This question appeared in the 2015 Singapore and Asian Schools Math Olympiad, a competition for 14-year-old students from Singapore, Thailand, Vietnam, China, and the U.K. (I’ve amended the language a bit):
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:
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 it either.
Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
Singapore TV presenter Kenneth Kong posted the question online, and it went viral in a matter of days. The competition organizers had intended it to “sift out the better students” and expected that 40 percent of the competitors would find the solution. What is it?