Can You Solve This Math Problem For 14-Year-Olds?

(FOX 11) When is Cheryl's birthday?

A TV presenter in Singapore recently posted a math problem on Facebook -- and the Internet is having trouble with the answer.

The logic problem was reportedly part of the Singapore and Asian Schools Math Olympiad, which is a competition for teens. After it was posted on Facebook, the puzzling math problem has been shared all over the world with people trying to solve it (and failing).

Here's the question:

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 do not 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?

Here's the answer (via 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."


Did you answer correctly?

Here's another answer sheet on mothership.sg
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