>>11603313Albert knowing Bernard doesn't know means Albert has a month which doesn't contain a unique date.
So Bernard now knows Albert can't have:
May - due to 19
June - due to 18
So Bernard knows Albert has either July or August, which is enough for him to know the full date. If he had the number 14, Bernard wouldn't have been able to choose between July or August. So he must have one of 15, 16, or 17.
Knowing that Bernard knows the full date allows Albert to also know the full date. If the month were August, Albert wouldn't have been able to choose between 15 and 17.
So this must mean the full date of Cheryl's birthday is July 16.
