Question

Difficult Question to Solve :

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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?

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Answer 1

HERE IS YOUR ANSWER.

CHERYL'S BIRTHDAY IS ON JULY 16.

EXPLANATION :

Following Albert's first statement, both Albert and Bernard know to eliminate all dates in May and June. If Cheryl told Albert the month of her birthday was May, Albert could not say with certainty that Bernard didn't know her birthday (if Cheryl told Bernard the day of her birthday was 19, Bernard would have known her birthday was May 19 since it's the only date with the 19th). June can be eliminated the same way (if Cheryl told Bernard the day of her birthday was 18, Bernard would have known her birthday was June 18 since it's the only date with the 18th). So Cheryl's birthday has been narrowed down to July 14, July 16, August 14, August 15, or August 17. Note that Bernard uses the same logic as Albert to eliminate the dates in May and June.

Following Bernard's statement, Albert can eliminate July 14 and August 14, because if Cheryl had told Bernard the day of her birthday was 14, Bernard would not have been able to say at this point that he knew Cheryl's birthday (it could be either July 14 or August 14). Albert now knows that Cheryl's birthday is either July 16, August 15, or August 17.

Following Albert's second/final statement, we can eliminate August 15 and August 17. If Cheryl had told Albert the month of her birthday was August, he would not have been able to say at this point that he knew Cheryl's birthday (it could be either August 15 or August 17). So Albert knows (and you do too) that Cheryl's birthday is on July 16.

HOPE THIS HELPS YOU.

Answer 2

Very easy believe me I did this in class 7

Albert and Bernand became friends with Cheryl .

Now Cheryl's birthday hmm..........

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

POSSIBILITIES OF MONTHS :

(i) May

(ii) June

(iii) July

(iv) August

POSSIBILITIES OF DATES

(i) 14

(ii) 15

(iii) 16

(iv) 17

(v) 18

(vi) 19

Albert : I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

NOTE :

Cheryl told Albert the month only .

Cheryl told Bernand the date only.

If Cheryl told 19 or 18 to Bernand then he would have guessed it ! So cancel 19 and 18.

Cancel May and June because then easily Bernand could have found the date.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

NOTE :

This means that either July or August contains the date as we have cancelled June and May .

Now if it is 14 , then no one can guess it .

Cancel 14 because then Bernand could not guess it .

There are different dates of 15 , 16 and 17 and hence he guessed it because he already knew the dates !

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

NOTE :

Now left with :

16 July

15 August

17 August

There are 3 possibilities and already Albert knows the month .

Under such circumstances if and only if Albert knew that the month was July then only he could guess it !

So month is July and date is 16

16 th July is the date !!!

16 th July ( 2 days before Mandela ) was her birthday :-)

sooo easy ..........

Hope it helps !

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