# Birthday Puzzle

Recently, this interesting puzzle went viral on Facebook. Tackle challenges is my nature, so I’m going to give it a try.

We will analyze every piece of the conversation. Always remember : Albert knows the month, Bernard knows the day.

Albert : I don’t know when Cheryl’s birthday is.

This is obvious. No matter what month he gets, he couldn’t possibly know Cheryl’s birthday as they are more than one date in each month. We cannot get any information from here.

Albert : I know that Bernard does not know too.

Bernard knows Cheryl’s birthday if and only if the day he got only occurs once among the possible dates, which in this case 19 and 18. The dates that have 19 or 18 in it are May 19 and June 18. Since Albert is pretty sure that Bernard doesn’t know Cheryl’s birthday, the month he received must not be May nor June.

Remaining dates : July 14, July 16, August 14, August 15, August 17.

Bernard : At first I don’t know when Cheryl’s Birthday is, but know I know.

Remember that Bernard also knows what we’ve concluded (he’s intelligent!). After he get the conclusion, he is then confident about Cheryl’s birthday. Again, Bernard knows Cheryl’s birthday if and only if the day he got only occurs once among the possible dates, which is 15, 16, 17.

Remaining dates : July 16, August 15, August 17.

Albert : Then I also know when Cheryl’s Birthday is.

Albert is also very clever, and his information (remaining dates) are as same as ours. Among the dates, there is only one with July, but two with August. He couldn’t know which is Cheryl’s birthday if the month he received is August. Hence, the month is July.

Cheryl’s birthday is July 16!