Singapore high school math problem stumps the internet

Apr 14, 2015 1:56 PM by News Staff, Photo Courtesy Facebook/kennethjianwen

A math question given to high school students in Singapore has gone viral after a media personality posted it to his Facebook page.

Can you figure this one out? Social media users around the globe have been stumped:

Albert and Bernard just become 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 fist 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?

It seems nearly impossible when you first read the question. But the answer may be reached with more common sense than you think.

The question was originally on a test given to the Singapore and Asean Schools Math Olympiads.

Read the solution, courtesy of Singapore's Study Room Facebook page:

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.


Most Popular