ok so I got July 16th too, but Im a little confused
Bernard knows it now because hes narrowed it down to the July/August from the first clue and he has the number of the day which can only be present in one of those months.
Heres my issue: how does Albert actually know? If it was August 17th, Bernard would know that too, so should Bernard saying he knows it really be enough to make Albert sure of it?