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
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.
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
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 .