Can you solve the maths question for Singapore school kids?

Alberts first comment that he does not know the date is obvious, because every month has at least two possible dates. However, the comment that he knows that Bernard does not know the date is significant. This means that whatever date Bernard has been told, it must show up in at least two months. This rules out May and June, since both of those months have unique dates.

Now, Bernard knows that the month is July or August, and based on this information, he says he can deduce the month. This means that it cannot be the 14th as that date occurs in both July and August. We are left with the options of July 16, August 15, and August 17.

Finally, Albert tells us that based on the information Bernard gave, he was able to deduce the exact date. If the month he was told was August, he would have no way to determine between the 15th and the 17th. So he must know the month is July, for which he has eliminated all options except the 16th.

So they both know that the date is July 16th.

Here's the other thread.

https://news.ycombinator.com/item?id=9367438