Ok, so Albert knows the day and Bernard knows the month. When Albert says that he doesn’t know AND Bernard doesn’t know, we can rule out June and May because if it was one of those months Albert would not have known for certain that Bernard couldn’t know the date, as May 19th and June 18th are the only 18ths and 19ths in the list. So that leaves us with:
14: July, August
15: August
16: July
17: August
At this point, Bernard announces that he knows the answer. This means, from the above list, it cannot be the 14th, as there are two of them. With just a 15, 16 and 17 remaining as possibilities, Bernard absolutey does know the answer at this point. And Albert, once he hears that Bernard knows the answer, ALSO announces that he knows the answer. The only non duplicated month left is July, making the date July 16th.
That only took me like 30 minutes of scribbling during a conference call. I hope I didn’t miss anything.
So A says he doesn’t know but knows that B doesn’t know, so he must have been told a month that didn’t have any unique days in it (18th & 19th) so that eliminates May and June.
B says, well now I know, so it can’t have been the 14th. So that leaves 7/16, 8/15 and 8/17.
A says, well now I know (keep in mind he knows the month). So it must have been July 16th since he would still be unsure if he was told August as there were two dates remaining.
It’s more of a sets problem than an arithematic problem.
I haven’t read any reasoning from the posts above, but I think the answer is July 16.
Albert (A) knows the month, Bernard (B) knows the date.
Quote - Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
For Albert to be sure that Bernard doesn’t know the month, the date has to be ambiguous no matter what the month is. But two months - May and June have unique dates - 19 and 18. If B knew either date, he could tell the month. But A is sure that’s not the case. So the birthday is not in May or June.
Initially, B did not know the month. But after A’s statement he does. So it is not July 14 or August 14.
We are left with July 16, August 15, August 17. Since B knows the date, he knows the birthday.
Once he says that, A knows as well, so the month is unambiguous, so August is out. And we are left with July 16.
Interesting. You solved it assuming A knows the date and B knows the month while I solved it assuming the reverse - A knows the month and B knows the date as per the OP. And yet we both got the right answer.
Makes you wonder what other info can be left out of the puzzle
