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The Difficult Maths Problem For 14-Year-Olds That Has Baffled The World

14/04/2015 19:00 | Updated 14 June 2015

Maths question

A maths problem set for 14-year-olds in Singapore has become a worldwide head-scratcher.

The problem, which tests logical reasoning, has been shared thousands of times online after leaving thousands of people baffled.

The test- which seems impossible (or is that just us!) - was set for 14-year-olds in the Singapore and Asian Schools Math Olympiad.

Have a try yourself (or get your teenager to do it while you have a cup of tea).

THE TEST ASKED:

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?

If your answers vary from, 'No idea', to 'life's too short', to 'I'm only a parent...get me out of here', then you're not alone - it has left thousands bemused and whole threads have popped up on forums to try to crack the question.

The problem was posted on Facebook by 'Hello Singapore' television presenter Kenneth Kong, and went viral as people posted their various solutions to the problem.

Kenneth Kong told the BBC: "It's a really difficult question for younger kids, so that's why people were so shocked at first... but now that people know it's for older students, they just think it's quirky."

Organisers said the test was aimed at the top 40 per cent and aimed to 'sift out the better students', adding it was 'important to clarify so that Singapore parents will not start to worry so much'.

Singapore and Asian Schools Math Olympiads' executive director Henry Ong defended the question, saying there was 'a place for some kind of logical and analytical thinking in the workplace and in our daily lives'.

So, can it be answered?

Yes – and, thankfully, the organisers have kindly posted the answer on their Facebook page, as follows...

1. We know Cheryl has already told Albert the month of her birthday, and Bernard the day.

2. Each of the men does not know what the other has been told.

3. For Albert to be 'certain' that Bernard can't know the answer - as suggested in the first statement he makes - we can deduct that the birthday is not in May or June. This is because in the months of May and June there are numbers (dates) that only occur once across the four months - namely May 19 and June 18.

4. If Albert had been given May or June as the month, there is no way he could be certain that Bernard doesn't know the birthday. Bernard, after all, might have been the number 18 or 19.

5. For Albert to be 'certain' that Bernard doesn't know, Albert must have been given a month that does not contain one of these 'unique' dates - i.e. July or August.

6. Albert's disclosure now gives Bernard the clue he needs, and says he now knows the birthday.

7. Bernard only knows the number of Cheryl's birthday, but from Albert's statement he has now also ruled out both May and June. This is because he realises Albert has ruled out May and June because of the 'single number' aspect above.

8. So there are now just five remaining dates - July 14, July 16, Aug 14, Aug 15, Aug 17 - and Bernard says he knows which is the birthday.

9. Because he now knows the date, we can whittle it down further to three dates by ruling out the numbers that appear in duplicate.

10. If Cheryl had told Bernard that her birthday fell on the 14th of the month, then he could not have worked out the date at this stage.

11. However, as he states that he now knows the date, we can rule out July 14 or August 14.

12. This leaves just three dates to chose from - July 16, Aug 15 and Aug 17.

13. Following Bernard's statement, Albert is then apparently able to deduce the date of Cheryl's birthday.

14. This means her birthday must be the only remaining date in the month he was originally told.

15. Given that there are two dates left in August and one in July, it has to be the July date.

16. So the answer is July 16.

Piece of cake, eh?

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