Nope, I am wrong, because Bernard says he didnt know at first. So it cant be the 18th or 19th. So it has got to be june 17th.
That was HARD.
The correct answer is July 16.
You have to eliminate June altogether, because if it was June, the only possible date that could be used was the 17th, as 18th would have let Bernard know immediately, without needing the month (only one 18th in the set of dates - remember, she told both of them the possible ten dates), since Albert knew Bernard didn't know at first, but then did, that has to eliminate May and June together, since May also had a unique date.