Maths Olympiad : Puzzles

Question :

Albert and Bernard just become friends with Cheryl , and they want to know her birthday is .Cheryl gives them a lsit 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 day of her Birthday respectively

Albert : I do not know when Cheryl's birthday is , but I know that Bernard does not know too.
Bernard : At first I do not 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 is


Answer : July 16
Solution :   From first statement of Albert is is clear that birthday is in either July or August months

  From Bernard statement it is clear that day is not 14, so left out options are July 16 , August 15 and August 17

Now as Albert also know so month of birthday July so
Cheryl's birthday is  July 16



Label : Maths for Kids , Maths Puzzle , Brain Tester ,  Maths Question , series and pattern, Maths Problems , Maths worksheet , LCM HCF , Algebra, Bank PO exam, SSC Exam , number pattern , Maths Olympiad
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Comments

  1. BnT4 March 2017 at 23:47

    very nice puzzle , explain of solution is excellent .your explanation made the puzzle too easy

    ReplyDelete
  2. Unknown10 May 2017 at 09:02

    What? How does Albert being clear about the birthday being in either July or August? How does Bernard signal Albert that day is not 14? I still don't get it. Can you please clarify?

    ReplyDelete
    Replies
    1. Aishi13 May 2017 at 04:46

      From Albert's first statement to be true, the month he is given must contain no dates that are unique amongst all months. If the month were May or June, Albert cannot make the statement that Bernard does not know because the 19th only appears in the list of May dates and the 18th only appears in the list of June dates. That leaves only July and August.

      Now that Bernard knows that the month is not May or June, he can only know the birthday if the date is not the 14th. That leaves July 16, August 15 and August 17. Obviously, it is one of these and Bernard knows.
      Albert can rule out July 14 and August 14. The only way the Albert can know the birthday is if the day is not the 14th and there is only one other option for the month that he knows. That can only be July. If it were August, Albert would not be able to know.
      In summary, the first statement by Albert eliminates all of May and June. The second statement by Bernard eliminates July 14 and August 14. The third statement by Albert eliminates August 15 and August 17. That leaves July 16.

      Delete

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