In the annoying Cheryl’s birthday problem part 2 (go here if you haven’t read it), we have additional member; David. So it’s getting more complex than the previous one.

And here is my answer: (apologize ahead for grammatical errors)

To get the conclusion of the problem, we have seven important points from the conversation:

- Albert knows that Bernard does not know
- Bernard still does not know even after point 1 is known
- Albert still does not know even after point 2 is known
- Albert now knows that David does not know
- David knows the month after point 4 is known, but not before
- Bernard knows the answer after point 4 is known, but not before
- David now knows the answer

As what we did in the previous Cheryl’s problem, we also can do elimination to solve this.

From the initial options:

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

we can eliminate al May and June options because if Albert got May or June, he would not sure that Bernard does not know the answer, since both May and June has unique day; 19 and 18 respectively.

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

But then Bernard still does not know the answer. Means he got a day that is not unique even after the elimination. Therefore we can eliminate the remaining unique days:

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

Then, Albert still does not know the answer. Had he has July, he must have known the answer.

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

Albert now knows that David does not know. Why? Had he has August, he would not be sure, because David could have Sep 14 or Sep 20 and know the answer. So Albert must have been told that the month is September.

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

Bernard knows the answer after point 4 revealed, and not before. Had he been told 16, he would have known the answer after point 3 is known.

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

Finally, David now knows the answer. So he has either 14 or 20. Let say he has 14 then it must be Aug 14. But let see again point 5. Had he has Aug 14, he must had known the correct month after point 3 revealed. So Aug 14 is impossible and so 14. (Also, for the same reason as Aug 14, Aug 20 is impossible.) So he got 20 means 20 is not the correct date.

May 15 May 16 May 19

Jun 17 Jun 18 Jun 20 Jun 22

Jul 15 Jul 16

Aug 14 Aug 20 Aug 22

Sep 14 Sep 16 Sep 17 Sep 20

And yay, we got the answer: Cheryl’s birthday is Sep 14 and Cheryl told David Jun 20.

Please Cheryl, just say that you don’t want to invite them to your birthday party. It is less cruel.

(Anyway, I hope the name of the person who made this problem is not Cheryl, because I respect her/him)