Albert can only be sure Bernard is stuck if his month has no date that appears just once, so it isn’t May, with the 19th, or June, with the 18th. Bernard now knowing means his day isn’t the 14th, which is in both July and August. Albert then knowing means his month has one date left, and only July does.
Albert and Bernard want to know when Cheryl’s birthday is. She gives them ten possible dates: May the 15th, 16th or 19th; June the 17th or 18th; July the 14th or 16th; August the 14th, 15th or 17th. Then she tells Albert only the month and Bernard only the day. Albert says, “I don’t know when it is, but I know Bernard doesn’t either.” Bernard says, “I didn’t know at first, but now I do.” Albert says, “Then I know too.” When is Cheryl’s birthday?
Give me a hintThe hint
Albert’s first sentence tells you which months are impossible.
Reveal the answerHide the answer
16 July
Source: Joseph Yeo Boon Wooi, Singapore and Asian Schools Math Olympiad, 2015