When is Cheryl's birthday? How to solve the maths problem that has stumped the world

It has infuriated thousands - yet is surprisingly doable

Adam Withnall
Thursday 16 April 2015 12:25 BST

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Louise Thomas

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A TV presenter in Singapore has sparked an unlikely viral craze after posting a maths problem that was posed to the nation’s children.

Initially confusing but very doable, it has sparked thousands of comments and shares – particularly when it was initially thought to have been posed to 10-year-olds.

"Hello Singapore" presenter Kenneth Kong has since clarified that it was actually a problem set to 14-year-olds in the Singapore and Asean Schools Math Olympiads (SASMO).

But that hasn’t stopped people testing their mettle against Singapore’s youngest and brightest.

So can you solve the question? Here it is - and don't read on below the image if you don't want to be told the answer:

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?

'Hello Singapore' presenter Kenneth Kong
'Hello Singapore' presenter Kenneth Kong (Facebook)

After Mr Kong's post attracted such interest, he was contacted by the executive director of SASMO who clarified that the "supposedly P5 (primary school) question" was posed to maths Olympiad contestants on 8 April.

Henry Ong also stated that it was the 24th of 25 questions - in other words "a difficult question meant to sift out the better students". Mr Ong said he was nonetheless pleased "that this question has generated so much interest and 'solutions' on the internet".

And here's the true 'solution', courtesy of a debate on Singapore's Study Room:

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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