# The Cheryl’s Birthday problem solved

Cheryl’s Birthday

The Problem

Albert and Bernard meet Cheryl and ask her when is your birthday ?

She tells them it is one of the following 10 dates

May 15th,May 16th-May 19th.June 17th,June 18th july 14th,July 16th,August 14th,August 15th,August 17th my birthday is one of these.

Cheryl then whispered the month only into Alberts ear , and the day only into Bernards ear .

Can you figure it out she asked Albert?

Albert I don’t know when your birthday is ,but I know Bernard does not know either.Bernard say I didn’t know originally ,but I do know.

Albert well I know now too.

What is Cheryl’s birthday?

The first thing to do is make a Diagram

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

Bernard has been given one of the following dates

14th ,15th ,16th ,17th ,18th ,19th

If Bernard had been given 18th he would immediately have known that the date was June 18th as there is only one 18th The same reason applies to 19th as there is only one 19th

We can exclude May and June for this reason.

Albert if he has figured this out now sees the following table.

 July 14th 16th August 14th 15th 17th

Bernard also sees this table and says he knows the date

But he would not know the date if he had been given the 14th as it could be 14th July or 14th August. We can eliminate 14th of July and 14th August.

The Table has now been reduced to

 July 16th August 15th 17th

Bernard now says he knows the birth date as he has been given the day .

Albert has to figure out whether 16th July, 15th August or 17th of August is the correct date.

Then  Albert says he also knows the date (it cannot be August as there are two options) and because he knows the month then July16th   is the only option.

Cheryl’s Birthday is the 16th July

Comment :Getting to the first table is a good first step , then eliminating the 14th  also reduces the question to a more manageable form .We are looking at the tables  and using what Bernard and Albert are saying .