When Is The Birthday Of Cheryl ?

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Puzzle 1: When is Cheryl's birthday?

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    16    19
         June       17    18
         July        14    16
         August   14    15    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 does not know, too.
Bernard: At first, I didn't 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?

The answer to the Puzzle 1: 

This had been one of the famous puzzles on social media such as Facebook, Google+ and Twitter a few months back and become one of the commonly asked puzzles during interviews. Let's find out the solution:

Step 1:

First, you have to figure out what Albert knows that Bernard doesn't.

Cheryl gave the pair 10 possible dates. The combinations are made up of four possible months and dates falling between 14 and 19. Only 18 and 19 appear once across the 10 combinations.

If Bernard was told either 18 or 19, he would know Cheryl's birthday — either May 19 or June 18.

Albert says he doesn't know when Cheryl's birthday is, but neither does Bernard. If Cheryl had told Albert she was born in either May or June, it would be possible for Bernard to know when her birthday is (assuming she told him either 19 or 18). 

If Bernard can't know Cheryl's birthday with this information alone, we know Cheryl told Albert she was born in either July or August.

Step 2:

After Albert says his piece, Bernard announces he now knows when Cheryl's birthday is.

At this point, he has also been able to deduce the months down to July or August. From the potential dates in those two months, only 14 appears twice.

To know Cheryl's birthday, Bernard must have been told a number other than 14.

Step 3:

Albert then announces he also knows Cheryl's birthday, having eliminated two months and the number 14. This leaves him with three potential dates: July 16, August 15 and August 17.

If Cheryl had told Albert August, he would not know because he would still be missing the date — either 15 or 17.

Cheryl must have told Albert July, leaving him with only one possible date to celebrate his new friend's birthday: July 16.

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