This problem went viral after it appeared on a Math Olympiad test for talented students in Singapore. It's not a trick question! Here's the problem, which I have very slightly re-worded for clarity.
Blog post (detailed text explanation): http://mindyourdecisions.com/blog/2015/04/14/when-is-cheryls-birthday-answer-to-viral-math-puzzle/
Official Solution: http://mothership.sg/2015/04/p5-logic-question-is-actually-a-math-olympiad-question-for-sec-3-and-4-students/
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 tells Albert the month and Bernard the day.
Albert says, "I don't know when Cheryl's birthday is, but I know that Bernard cannot know either."
Bernard then says, "At first I didn't know when Cheryl's birthday is, but now I do know."
Albert concludes, "Now I know when Cheryl's birthday is."
So when is Cheryl's birthday?
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