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How to solve the math problem for children that has stumped the world

DECCAN CHRONICLE
Published Apr 14, 2015, 11:20 pm IST
Updated Mar 29, 2019, 11:16 am IST
Can you figure out when Cheryl’s birthday is?
 
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. 
 
 
Here's the puzzle:
 
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?
 
 
Can you figure out the answer? 
 
 
 
Here's the solution:
 
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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