Cheryl's birthday (see 15th April)

OK - here we go.  Remember, Albert knows what month it is and Bernard knows what date it is. Albert's first statement is that he doesn't know her birthday, but he knows that Bernard doesn't know either.  This tells Bernard that the month cannot be May or June - because as far as Albert knows, Bernard may have been given the 18th or 19th as the date.  It therefore follows that the month is July or August. So Bernard (who knows the date) now declares he knows her birthday.  Albert (who knows the month) can now work out that the date can't be the 14th (because if it was, Bernard wouldn't know if it was July 14th or August 14th) so her birthday must be July 16th. Easy when you know how, isn't it - or is it??