When is Cheryl’s Birthday?

Problem:-

So when is Cheryl’s birthday? That’s a question confounding thousands of people around the world Monday as a test question from Singapore goes viral.

Puzzle: Albert and Bernard just became friends with Cheryl, 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: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

Solution:-

Dates Given :
——————————–

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

——————————–
Say Albert=A ; Bernard=B ;Cheryl=C
———————————————————————————————-

A says: B doesn’t know the date

This means:B has more than one options,that’s why he doesn’t know
Ex.Say B has 17 , A says he can’t deduce the month as 17 appears in Juna as well as in August

So,If the date were 18 or 19 then there would not have been any confusion for B,as
these dates doesn’t repeat in given data and B would have known the month to be May/June.
Therefore 18,19 are ruled out.

A says:He doesn’t know too

It means the month is not June(18th date)/May(19th date)
Because if the months were June/May then A could have told that B doesn’t know.
That’s why these months are also ruled out.
———————————————————————————————–
Now the data becomes :

July |14| |16| | | |
August |14|15| |17| | |

B says: Now he knows

It means , for B to know the birthdate, the dates he knows,doesn’t fall in more than one month
That’s why he says confidently that he has no confusion now

So both occurences of 14 are ruled out as they fall in July as well as August.

————————————————————————————————
Now the the data becomes

July | | |16| | | |
August | |15| |17| | |

NOW B says :Now I know

:-) It means there is no confucion for A now, which means the month which A knows has only one date left.
That’s why he has no confusion anymore.

Here Only July has one date left i.e. 16th

Therefore the month is “July” AND date is “16″