Cheryl's Birthday

Question:

Albert and Bernard became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

 May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month and day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?

Eliminate round I

If Cheryl told Bernard the day 18 or 19, then Bernard would immediately know the day (June 18 or May 19) since those are the only days with that particular date. However, Bernard says he doesn't - therefore we can eliminate the months May and June.

 May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Eliminate Round II

Now the day can't be the 14th since Bernard said at first he didn't know at first. Since he knows now, the day must be the 16th since that's the only unique date.

Thus the answer is July 16.

 May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Came up with a better solution or have a question? Comment below!