Wednesday, April 15, 2015

When is cheryl's birthday - Cheryl, Bernard, Cheryl birthday puzzle

Since 2-3 days this puzzle has hit the internet badly and is viral all over the internet.

It was a question to test logic skills of students participating in the Singapore and Asian Schools Math Olympiad.

Here is the question text
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Albert and Bernard just became 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 does not know, too. (Statement 1)

Bernard: At first, I didn't know when Cheryl's birthday is, but I know now. (Statement 2)

Albert: Then I also know when Cheryl's birthday is. (Statement 3)
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The image which is circulating all over the internet for this puzzle is
albert, bernard, cheryl, birthday, puzzle, math, mathematics, singa pur, guess, child, kids, teens, school, may, june, july, august, 14, 15, 16, 17, 18, 19, solved, solution, answer

Here is the solution:
We know that Albert knows the month while Bernard knows the date.

From Statement 1, it is understood that Albert is sure that Bernard don't know the Birthday. So options of 18 June and 19 May can easily be excluded from answers as dates 18 and 19 both appears only once. So if Cheryl would had told date 18 or 19 then Bernard would had known the birthday.
So now as Albert is sure that Bernard don't know the Birthday so months May and June can also be excluded because if the month would had been May or June then Bernard could had know the Birthday keeping in view that dates 18 and 19 appears only once.
So from Statement 1 we are sure that month is either July or August.

Now come to Statement 2
Bernard was not known of Birthday before but after Albert's statement he knows what is the birthday.
So from remaining 5 dates we can exclude 14 because it appears twice so if date would had been 14 then Bernard would not had known the Birthday (because 14 appears twice). So now birthday is either 16 July, 15 August or 17 August. And Bernard knows the date (told be Cheryl) so he is now sure about Birthday.

Now come to Statement 3
Here (after Statement 2 - Bernard's statement) Albert also says that now he knows the birthday as well.
As Albert knows that Bernard knows the Birthday (Albert only knows the Month till now), so he can easily conclude that the birthday is 16 July because if the birthday was 15 August or 17 August then Bernard could not had tell the birthday keeping in view he only knows the date and not month.
So now both knows that the answer is 16 July.

Answer/Solution: 16th July

Here is the official statement and answer from "Singapore and Asian Schools Math Olympiad"

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