Cheryl's Birthday

The problem
10 candidate dates — Albert knows the month, Bernard the dayMayJuneJulyAug14151617181915161917181416141517from their statements, find Cheryl's birthday

Cheryl tells Albert and Bernard that her birthday is one of these ten dates:

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

She tells Albert only the month, and Bernard only the day.

The dialogue:

  • Albert: "I don't know when Cheryl's birthday is — but I know Bernard doesn't either."
  • Bernard: "I didn't know at first, but now I do."
  • Albert: "Then I know too."

When is Cheryl's birthday?