So here is the question I copied from the Internet:
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?
At the first glance the question is very difficult.
How can Bernard get the answer by Albert's seemingly irrelevant clue?
After a little bit thought, and observing the dates more carefully, we found that Albert actually gave out a very important clue that was clearly enough to eliminate quite a few dates. Then Bernard's clue, combined with what Albert already knew, led to the right answer.
What is the logic?
Keep reading, on the next page,
Observe the days first, there were two 14s, 15s, 16s, 17s, but only one 18 and one 19. Therefore, if Albert was told the month and he was SURE Bernard did not know the answer, the month would not be May nor June. Because if he heard May or June, then it was POSSIBLE that the birthday was May 19th or June 18th, in which case Bernard would know the birthday immediately by hearing the day. Albert was sure Bernard did not know the birthday. So, the month Albert heard could not be May or June. It must be July, or August.
Now Bernard knew the month could be either July or August. Let's look at the dates:
July 14 — July 16
August 14 — August 15 — August 17
Since Bernard knew the birthday, the day could not be 14 because it occurs twice. Until now, my dear reader, if you think "Oh, then it can be 15, 16, or 17, how can we know which one? ", then you are falling to the same trap I have. You missed the fact that Albert KNEW the month!
The question we should answer is: how come Albert knew the birthday after Bernard knew!?
Because he heard July!
If he had heard August, he would not say "Now I know"!
Therefore, the birthday is July 16th.
