Great question! Initially, I didn't quite understand the premise of the question which is why I couldn't get the right answer but after googling around I found

Great question! Initially, I didn't quite understand the premise of the question which is why I couldn't get the right answer but after googling around I found the correct premise and the correct solution in this article: http://www.independent.co.uk/news/world/asia/singapore-maths-problem-can-you-solve-the-viral-maths-question-that-was-set-to-children-in-singapore-10173090.html http://www.independent.co.uk/news/world/asia/singapore-maths... But, I think some people still won't understand the solution without visualisation! So, here it is: Well, I started of by setting a table like this: https://i.imgur.com/VhJ1gSZ.png https://i.imgur.com/VhJ1gSZ.png Next we are told: "Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively." Great! Now we know: * Albert knows the month * Bernard knows the date "Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too. The only way Albert (he knows the month remember) can say "but I know that Bernard does not know too." for definite is if the month he knows is a month that has a date which clashes with other months! Why? Because if the month he knew had a unique date then there's a possibility that Bernard could know the month hence he couldn't know for definite that Bernard didn't know the birthday. For example if Bernard knew the date was the 19th then obviously the only month with 19th date in it is May hence we would know the date of birth is the 19th of May. Because, of the information above we can completely disregard both the months wholly with the unique date in them which are May & June. So, we now have a new table which we can update the hit, misses and clashes on: https://i.imgur.com/LoBJWa1.png https://i.imgur.com/LoBJWa1.png "Bernard: At first I don’t know when Cheryl’s birthday is, but I know now." At this point Bernard knows that the choice is either between July or Aug and he goes ahead and says he now knows what the full date of birth is! This tell's us that the date is a unique from the updated table because if it wasn't a unique date then he couldn't have possibly known the month! So we can update our table again: https://i.imgur.com/UUyNQQC.png https://i.imgur.com/UUyNQQC.png "Albert: Then I also know when Cheryl’s birthday is." So, now because Albert knows the month is July is can say for definite that the full date of birth is 16 July because there is no other date in that month left. Explanation: Because if it was August then Albert wouldn't know the date of birth as there two date for him to choose between (the 15th and 17th) but because Albert does know the date; we know the month is July and the only date left in July is the 16th! Hence the correct answer is 16th July! Hope that helped!