Solution to the math problem from Singapore that went viral on the internet

Here is our solution to the math problem from Singapore that went viral on the internet. It is a question from a global math Olympiad for high school children in Singapore.

Check this image for the question

What we need to find is the birthday of Cheryl. Cheryl tells them separately the month and day of her birthday and gives them 10 possible dates.

So, Albert knows the month and Bernard knows the day. 

From the first line of the conversation, 

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

He says Bernard doesn't know too. Why?

Let us say, if Cheryl told Bernard the day is on 19th, he would have easily got the answer as May without Albert revealing the month. The same applies for the date 18th. Since he says Bernard doesn't know, then she must have told him either July or August, so we can eliminate all the dates from the month May and June.

Now we are left with 5 possible dates and just two months.

Now Bernard says,

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Remember Bernard knows the date and he mentions this.  Out of these 5 options, if the day was 14th, Bernard would not be still knowing but he says, "but I know now." 

Therefore we can eliminate July 14 and August 14. Now we're left with three options July 16, August 15 and August 17.

Now if Cheryl has told Albert that the month was August, he wouldn't be still knowing as there are two dates in August and he just knows the month. But he says, in the last line of the conversation,

Albert:    Then I also know when Cheryl’s birthday is.

That means it must be July 16th.

If you still did not understand, comment us below. We would be glad to help!