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 or 16 or 19.
June: 17 or 18.
July: 14 or 16 .
August: 14 or 15 or 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 doesn't know too.
Bernard: At first I did not 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?"
If Albert was told May, he wouldn't know whether Bernard knew (if 19th, which is unique), or didn't know (if 15th or 16th, non-unique). The same is true for June as regards 17 (non-unique) and 18 (unique).
If Albert was told July or August, he'd know of Bernard's lack of initial knowledge, but that would not clue Bernard in if Bernard had 14.
But if Bernard had 15, 16 or 17, that would clue Bernard in to the appropriate one of these two months, as these two are the only two where Albert could be sure of Bernard's lack of knowledge initially.
So the birthday could be July 16 or August 15 or 17.
However, if it were August, Albert would not have been able to tell whether it was the 15th or the 17th. So it would have to be July 16.
Posted by Charlie
on 2015-09-24 10:16:36