The Problem Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives 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 16

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

Albert: I don’t know what her birthday is but I know for sure that Bernard does not know.

Bernard: At first I didn’t know what Cheryll’s birthday is but now I know for sure.

Albert: Now I know Cheryll’s birthday too.

##Solution

Lets approach the problem with an individual knowledge based examination approach.

When Cheryll gives the list of 10 possible dates, we can infer some results immediately.

• If the date is 18th, then the birthday will be on June 18 as there is no other month with date 18th in the list of choices.
• If the date is 19th, then the birthday will be on May 19 for the same reason as above

This is our initial knowledge of the situation

Now, Albert’s statement says that he knows for sure that Bernard does not know. Now the question is how can Albert know this for sure.

Albert knows the month of Cheryl’s birthday but this does not help him as for each month, there is more than one possible case which might be Cheryl’s birthday. Albert also knows that Bernard knows the day and that Bernard can tell accurately the entire birthdate of Cheryl if the date is 18th or 19th. But he knows the month which is not May or June, so it will be impossible for Bernard to use the initial knowledge and tell the birthdate. So, we can eliminate all dates of May and June of our list.

• The updated knowledge is that the birthdate is in either July or August

Now, Bernard says that after hearing Albert’s statement, he knows Cheryll’s birthdate for sure.

After Albert’s statement, Bernard knows for sure. Now, Bernard knows the date of the birthday. If the date was 14, then he would still have confusion between July 14 and August 14 but since there is no confusion, July 14 and August 14 can’t be Cheryl’s Birthday.

• So, the updated knowledge is that the birthday is in either July 16, August 15 or August 16

Now, Albert says that after hearing Bernard’s statement, he knows Cheryll’s birthdate for sure.

Albert knows only the month. Among the choices left, the only way Albert can tell the birthdate with only the Month is July 16 since there is only one choice in July. If the month was August, then he would have had confusion between August 15 and August 16.

So, in conclusion, Cheryl’s birthdate is July 16

Solved by me and Aditya Kumar

So, the moral of the problem is

If someone tells you don’t know something, you can learn from that instead of getting depressed because you don’t know it.