# When is Cheryl’s Birthday?

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 16 19

June 17 18

July 14 16

August 14 15 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 didn’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

When is Cheryl’s birthday?

**Cheryl’s birthday is on July 16**

From the first statement, any of the day’s in that month should not be unique, else otherwise Albert can’t be sure of Bernard not knowing the birthday.Lets take the possible answers

If it was May => Albert cant say the first statement, as if the day was 19, Bernard will know the birthday for sure.

If, it is was June => Same is the case with 18th.

If, it is in July => Albert can say the first statement.

If it is in August => Albert can say the first statement.

Now after hearing first statement, Bernard can clearly figure out that the month of birthday is either July or August.

So, if the day was 14 => It can be July 14 or August 14 =>as bernard know now, it is not possible

If the day was 15 => It can be Aug 15

If the day was 16 => it can be July 16

If the day was 17 => it can be Aug 17

Only three days possible are Aug 15, July 16 or Aug 17, bernard knows the day so he know the birthday.

From the third statement, Albert knows the birthday as well, so it can only be July 16, as if the month was Aug, Albert can not figure it out.

Thus the Cheryl’s birthday is on July 16.

### Your Answer

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