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 16 19
June 17 18
July 14 16
August 14 15 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 didn't know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.
When is Cheryl's birthday?
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I would try to help but I know I'd miss it
There are only two dates with unique numbers: May 19 or June 18. If Bernard was given a date of 18 or 19, he'd know. The fact that Albert says Bernard doesn't know means the month he was given wasn't May or June. Bernard has now figured this much out, and if he had been told 14 he wouldn't know the answer as there are still two 14s left (July and August) leaving July 16, August 15 and August 17. Bernard must've been given the number 16, because for Albert to say he knows too would rule out August, which still has two remaining dates. That leaves the answer: July 16.