Puzzle From Singapore
This puzzle was presented to some high school students in Singapore:Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates:
May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17
“My birthday is one of these,” she said.
Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day.
“Can you figure it out now?” she asked Albert.
Albert: I don’t know when your birthday is, but I know Bernard doesn't know, either.
Bernard: I didn't know originally, but now I do.
Albert: Well, now I know, too!
When is Cheryl’s birthday?
= new reply since forum marked as read
but not for everyone. I called it a math problem because the reasoning you use to solve this problem is similar to that in mathematics, but it's really a problem in logic.
Albert said: "I don’t know when your birthday is, but I know Bernard doesn't know, either."
He wouldn't have said that if the month (which Albert knows) were May, because then the day (which Bernard knows) could be the 19th, in which case Bernard would deduce that Cheryl's birthday is May 19th. (The list does not include the 19th of any other month.)
One other month is excluded by similar reasoning.
Thus as soon as Albert spoke, Bernard knew that the month was one of the remaining two months.
Now maybe you can figure out what of the rest of the conversation implies.