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?"
(In reply to
Puzzle Answer by K Sengupta)
Albert is told one of the months May, June, July or, August. Bernard is told one of the days 14, 15, 16, 17, 18 or 19.
Albert is sure that Bernard cannot know the date.
If Bernard was told 19, he would know the birthday was on May 19.
If Bernard was told 18, he would deduce that the birthday was June 18.
Therefore, the only way Albert is sure that Bernard didn't get 18 or 19 from Cheryl was because he was NOT given May or June. Accordingly, Cheryl must have given Albert either July or August.
By Statement 2, upon hearing Statement 1 uttered by Albert, it was deduced by Bernard that the month must be July or August.
If he had been told 14, the month would still be ambiguous. Accordingly, he must have been told 15, 16, or 17.
By Statement 3, if Albert was told August he still would not be sure. Accordingly, he must have been told July.
Consequently, the required date must be JULY 16.
Edited on June 10, 2022, 9:36 am
Explanation to Puzzle Answer
