Some days back the above maths problem in Singapore maths Olympiad was being passed around. Here is my solution. And yes, I solved it on my own before confirming the solution from elsewhere on Internet.
Take a look at the 10 possible choices Cheryl gave. Let’s put them in the tabular form
====== | 14 | 15 | 16 | 17 | 18 | 19 |
May | | x | x | | | x |
June | | | | x | x | |
July | x | | x | | | |
August | x | x | | x | | |
At first Albert says he does not know, but he knows that Bernard does not know as well. Is it even possible for Bernard to know the birth day just by knowing date? Looking at the table above, it is indeed possible. If the date Bernard knew was 19, it happens only one month in given choices, May. So Bernard could have guessed the birth date just by knowing the date. Same is hte case for date 18. It happens only on June 18.
How can Albert say that he knows Bernard does not know? He can say that only if based on the month he knows, he can eliminate the dates being 18 or 19. That is possible only if the Month is not May or June.
So Albert knows the month is no May or June. So we can eliminate 5 out of the 10 choices.
At this point Bernard says he knows the date. He knows that if Albert is making such a statement, that means the month is not May or June. Now Bernard says he knows the birth day. That means out of the choices left, Bernard can guess the date by knowing just the date. Clearly the date cannot be 14 because it has two possible month choices and Bernard would have to know the month to eliminate one of them.
At this point we know that the Months are not May and June and date is not 14.
Now after knowing this much, Albert says he knows the date. Since he knows only month, it must be a month which has only one possible choice of dates. If the month was August, it still has two possible dates. But if the month is July, then it has only one date.
That is our choice. July 16 is the answer we want.