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07/04/2018 at 11:54
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Albert and Bernard just becone 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 then tells Albert and Bernard separately the month and the day of hey birthday respectively.

  Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not knnow too.

  Bernard: At first I don't 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?

At first, the problem seems impossible to solve. But once you use some logic, the solution is actually rather simple. Rattle your brain — or phone a friend — before I send the solution in 1+ hour 

(P/s: The question was originally thought to posed to fifth graders competing in the Singapore and Asean Schools Math Olympiads (SASMO).)



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    Lê Anh Duy 09/04/2018 at 15:23

    First we need to figure out if Albert knows the month or the day. If he knows the day, then there is no chance that Bernard knows the birthday, so it must be that Albert knows the month.

    From the first statement, we know that Albert is sure that Bernard doesn't know the birthday, so May and June should be ruled out (the day 19 only appears in May and the day 18 only appears in June). In other words, if Albert had May or June, then he cannot be sure that Bernard doesn't know, since Bernard could have had 18 or 19.

    Following that statement, Bernard knows that May and June are ruled out.

    Then, Bernard is able to know which month it is. So it must be either July 16, August 15 and August 17 (not 14th as then he can't know).

    Since Albert subsequently can also be sure of the date, he must know it's July. If it's August, he can't be sure as there is August 15 and 17.

    So the answer is July 16

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