Does Cheryl think everyone would celebrate her birthday?

#1 Albert’s statement “I know that Bernard does not know too” implies: We eliminate May and June, because it contains unique days (18 and 19).. otherwise, Bernard would have known the birthday since the beginning and this puzzle would lose its meaning.

May 15 May 16 May [19]

Jun 16 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

#2 Bernard’s statement “I did not know when Cheryl’s birthday is and now I still don’t.” implies: We eliminate Jul 15, Sep 17, and Aug 22 (unique days). otherwise, Bernard would have known the birthday at this step, and it would be way too easy to solve (but of course we couldn’t solve the date being told to David.. and David wouldn’t have the chance to speak).

May 15 May 16 May [19]

Jun 16 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

#3 Albert’s statement “I still don’t know when Cheryl’s birthday is.” implies: We eliminate Jul 16. Otherwise, we would end up at this stage giving no chance for David to even say Hello.

May 15 May 16 May [19]

Jun 16 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

Here comes the tricky part…

#5 Albert’s statement “Having said that, I am sure David still does not know too.” implies: the birthday is on Sep, if it’s on Aug then David would have the possibility to know it given the date being told to him was either Sep 14 or Sep 20.

#6 At first, David didn’t know the day nor the month because the month being told to him was another month that we have eliminated instead of Aug/Sep (otherwise he would have know the month before Albert saying his last statement). But after the last statement from Albert he knows the month but not the date, because he is smart enough to realize what the implication of Albert’s last statement is. (I am still not sure about this.. I don’t know any other explanation, I put faith in his intelligence)

#7 At first, Bernard didn’t know the date because he was told other than 16 (the only unique day left). Otherwise, we would have finished on Sep 16 and we may not be able to solve what date has been told to David (or may answer it Aug 22 for convenience purpose)

May 15 May 16 May [19]

Jun 16 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, after the last statement from Albert, he knows it is on Sep. And he knows the exact date because it is either 14, or 20.

#8 The only possible way for David to knows the date is, he was told Jun 20, so he could eliminate 20 and hence know that the birthday is Sep 14. Because there was no other month which has 14 as possible day other than Sep and Aug (and we know from the previous deduction that month being told to David was other than Sep and Aug). And it also explains why he couldn’t know the date in #6, because he still confused between Sep 14 or Sep 16 (before Bernard eliminated Sep 16 in #7)

#9 Albert knows it because he’s also smart enough to conclude what David have said.

Now guys, I don’t know if this solution is correct.. but it’s pretty fun to try this puzzle. I made some mistake along the way:

#1-st Iteration I ended up discarding the siginificance of Albert’s last statement, so I picked Sep 16 as the birthday and, I don’t know how I picked Aug 22.

#2-nd Iteration I forgot to eliminate Aug 22 in #2. I also mixed up the sequence between Bernard’s last line and Albert’s 2nd (meaning that I eliminate Sep 16 first, and then thinking about the last statement from Albert). So it left me here:

May 15 May 16 May [19]

Jun 16 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 then, I got it reversed: thinking that the birthday is on Aug. So I got the birthday on Aug 14 and Cheryl’s told David Jun 20.

On the internet, I found someone got the birthday on Sep 14. I think he did just like this 2nd iteration but he forgot to eliminate Sep 16 instead of Aug 22 in this step. So, probably he got it like this before the final deduction.

May 15 May 16 May [19]

Jun 16 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

Well, if the current solution is wrong then I’ll revise the post and put them on third iteration. So tell me if it’s wrong guys.

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