Can you solve this maths question posed to children in Singapore?

You —

Maths question posed in an exam paper to weed out the top students aged 14/15

This question has gone viral, but unlike the myth, it was not in an exam paper for primary school children, but one of the last questions in a paper for 14/15 year olds.

Itst a logic problem and its quite intriguing:

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 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 her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know 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?

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You — Thu, 30 Apr 2015 - 22:38

Nope not that simple.

First step is how can Albert know for sure that Bernard doesnt know?

If albert was told it was May, Bernard could have been told the number 19. Then Bernard would know the date.

So it wasn't May. Same for June.

Both those numbers have a unique number.

By Albert making his first statement with such confidence, Bernard knows that the birthday was either in July or August.

Second step: How does Bernard find out?

We now know Bernard was given the numbers of 14, 15, 16 or 17.

From those as 14 is in both months, if he was told 14, he still could not figure out the month, so its not 14.

15, 16 and 17 only occur once in these months, so with any of these numbers, Bernard now knows and Albert can calculate that it was one of these numbers.

The last step is going backwards.

Albert already knows the month. He has one number left in July and two in August.

If Albert was told August, as it could be one of two dates, he cannot say that he now knows.

He must have been told that it was July because there is only one date it could be in there and that is the only time Albert can say with certainty that he knows the date too.