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That 'Primary 5' logic question is Sec 3 Maths Olympiad question

AsiaOne | Monday, Apr 13, 2015

Dear all who scratched your head,I know Cheryl has caused enough trouble with her mysterious birthday.I got the...

Posted by Kennethjianwen on Monday, April 13, 2015

That 'Primary 5' mathematics question that made its rounds in Facebook and caused lots of speculation as to its answer has now been revealed to be a question from a maths competition for Secondary 3 and 4 students.

It was one of the 25 questions posed to students who took part in the Math Olympiad on April 8, which was organised by the Singapore and Asian Schools Math Olympiad.

Mr Henry Ong, founder of the Singapore and Asian Schools Math Olympiads sent out a clarification after the question went viral. In it, he explained it was not a primary school level maths question "so that Singapore parents will not worry unnecessarily."

He said this was the 24th question, and "is a difficult question meant to sift out the better students."

The Straits Times reported that Mr Ong was surprised that the question was being circulated online, because "students were not allowed to keep their mobile phones on them."

He said questions have never been leaked in his 10 years of organising such competitions.

Students from more than 30 secondary schools took part in the April 8 competition.

The questions are set by a team of mathematics experts, including professors here and overseas.

The same set of questions are given to participants from 14 other countries, including Britain, Malaysia, Brunei and Uzbekistan. Cambodia has yet to run the competition, and will do so on May 4. The leaked question will be replaced.

And if you are wondering about the correct answer, Cheryl's birthday is on July 16.

Here is the explanation from the Singapore and Asian Schools Math Olympiads:

Out of the 10 dates, the day ranges from 14 to 19, with only 18 and 19 each occurring once. If the day of Cheryl's birthday is 18 or 19, then Bernard would have known when Cheryl's birthday is since she has told him the day of her birthday.

But why is it that Albert know that Bernard does not know? If Cheryl has told Albert that her birth month is May or June, then it is possible that her birthday may be May 19 or June 18. This means that Bernard may know when Cheryl's birthday is. The fact that Albert knows that Bernard does not know means that Cheryl has told Albert that her birth month is either July or August.

Initially, Bernard has no idea when Cheryl's birthday is. So how did he know after Albert has first spoken? Out of the five remaining dates in July and August, the day ranges from 15 to 17, with only 14 occurring twice. If Cheryl has told Bernard the day of her birthday is 14, then Bernard would not have known. The fact that Bernard knows means the day of her birthday is not 14. So now we are left with three possible dates: July 16, Aug 15 and Aug 17.

After Bernard has spoken, Albert now knows when Cheryl's birthday is. If Cheryl has told Albert her birth month is August, then Albert would not have known because there are two possible dates in August.

So, Cheryl's birthday is on July 16.


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