Given dates are:
May 15
May 16
May 19
June 17
June 18
July 14
July 16
August 14
August 15
August 17
18 and 19 are the distinct numbers in the given list and these days are in May and June respectively.
If Albert was told one of these month, then there is a possibility that Bernard might know the answer straight away. But he was told a month other than May and June, so he knows that Bernard also does not know the answer.
So, Bernard understands that the month is either July or August.
The day is distinct so that Bernard gets the answer, so it is not July 14 or August 14.
That leaves us with July 16, August 15, August 17
Now, from above dates if Albert can get the correct answer only if the month is distinct. If it is August there are 2 possibilities.
So, the answer is July 16
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