Clue to Puzzle #48: When is Cheryl's Birthday

48. Albert and Bernard just 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 the 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?
Twice before we have looked at puzzles where the clues came indirectly via what other people were able to deduce from information known only to them rather than directly, firstly in the much easier three men in different colored hats and secondly in the somewhat easier man with three daughters riddles. It's a special class of puzzle and you must always remember that the person knows something you do not. You are looking for what that information could be in order that they make the statements they do.

It's helpful to lay the dates out in a table so we can identify what is special about different dates.

MayMay 15May 16May 19
JuneJune 17June 18
JulyJuly 14July 16
AugustAugust 14August 15August 17

The first real clue is that in addition to not knowing the full date himself Albert declares that he knows for certain that Bernard, who has only been given the day can not deduce the full date.

If you think that is enough of a hint stop there, else I have a little bit more:

Continue eliminating the dates until only one is left.

Where next?
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