Do you know the answer to this logic problem? Interesting to say the least, especially since this questions was first asked to children:

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?

Well Cheryl Cole, she use to be known as Cheryl Cole, but then she insisted on being called Cheryl (like Prince, or Cher) and her birthday is on the 30th June, so none?

Interesting problem, indeed. Took me while to figure it out.

The problem is awkwardly worded, but once you understand what they are looking for it is easy to solve.

The key is to break it into sets by date in addition to the sets by month given in the problem.
date 14: { july 14, aug 14 }
date 15: { may 15, aug 15 }
date 16: { may 16, july 16 }
date 17: { june 17, august 17 }
date 18: { june 18 }
date 19: { may 19 }

The first line relies on the sets with a single data point to eliminate months. With those eliminated, rebuild the tables and rely on the per-month table to eliminate days, and finally rebuild the by-date tables and again remove the single answers. You are left with a single result.

Still don't get it.

1. A is asserting that his knowledge of the month means that B can't possibly know the answer. This eliminates two entire months because those two months include unique dates that B could possibly know.

2. B uses A's assertion to eliminate those two months, which gives him the answer. He asserts this.

3. A uses B's assertion that he knows the answer to eliminate the 14th of the month, since this would still be ambiguous if it were the date that B knows. This reduces the sets enough for A to know what the answer is as well, so we can deduce which date it is from the intersection of A's and B's remaining sets that only have one entry.

Still don't get it.

Albert and Bernard are Holmes and Watson.

While I did successfully solve it, I'm man enough to say that my head hurts enough that I don't like Cheryl.

Still don't get it.

The problem is poorly stated. A "normal" Albert would say "I don’t know when your birthday is, but I know Bernard doesn’t know, either." in every case no matter what month he knew without further thought and that doesn't really reveal any information. What's missing here is that Albert and Bernard are both perfect logicians who always tell the truth based on all the information they currently know. Then it should make sense.

This is basically the same as en.wikipedia.org/wiki/Impossible_Puzzle