# Puzzles:When is the birthday

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## When is the birthday

Albert (A) and Bernard (B) just become friends with Cheryl (C), and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

 May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

 Albert[A] I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too Bernard[B] At first I don’t know when Cheryl’s birthday is, but I know now. Albert[C] Then I also know when Cheryl’s birthday is.

So when is Cheryl’s (or C’s) birthday?

nswer : 16th July

Okay, to explain why the answer is 16th July I will need your full attention for next 5 minutes. Lets go one by one statements made by A and B. It is also important to know that A only knows the month while B only knows the day.

• A said “I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too”

At this point of time we only know that A was told either May, June, July or August but hold on, why is A saying I “know that Bernard does not know too”. If he was told May he would have not said this confidently because there is a unique day 19 in that row/month. Similarly A was not told June either because there is another unique day (18) in that row/month.

Note : If its still not clear, assume you are A and you was told May. Now try to think whether B would know the birthday by going each day (15, 16, 19) of May month. If its 15th May B will not know as there are two entries, Similarly if it is 16th May B will not know because again there are multiple entries but if its is 19th May B will know because there is only one 19 so you would be in no position to make statement that “I know that B dosent know too“, likewise you can try for June.

So from the A’s statement its very clear that C’s birthday falls in either July or August and possible days are 14, 15, 16, 17

now lets move to second statement, statement by B

• B said “At first I don’t know when Cheryl’s birthday is, but I know now.”

By now we know that B was only told either 14, 15, 16 or 17. And as soon asB heard A he made this statement.  If B was told 14 he would have been in no position to say that now I know as there are two 14s (14th July and 14th August). So from the B‘s statement we can only deduce that he was either told 15, 16 or 17.

From the B’s statement it is clear that C’s birthday is either on 15th August, 16th July or 17th August

Now lets move to final statement made by A

• A said “Then I also know when Cheryl’s birthday is.”

As of now the only possible dates are 15th August, 16th July and 17th August and remember A was only told month. Assume you are A and try to think when would you be able to make the statement that I also know when is C’s birthday. If A was told August he would have not in the position to say this because he will not know what day B was told as there are to days in August (15 and 17). A would be able to say this only if he was told July.

So from the second statement of A its clear that C’s birthday is on 16th July.