Cheryl’s Birthday

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:

May 15 16 19
June 17 18
July 14 16
August 14 15 17

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?

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