Harder Cheryl's Birthday

Logic Level 4

Albert, Bernard, and David just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 16 possible dates.

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

Cheryl tells Albert and Bernard separately the month and the day of her birthday, respectively. She then chooses one particular date from the list and tells David, and makes it known to all that the chosen date has a different day and month from her birthday.

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

Bernard : I did not know when Cheryl’s birthday is. And now I still don't.

Albert : I still don't know when Cheryl's birthday is. Having said that, I am sure David still does not know.

David : I knew neither the day nor the month right before Albert said his last sentence, but after he did, now I know what month it is.

Bernard : I did not know when Cheryl’s birthday is right before Albert said his last sentence, but after he did, now I know when Cheryl’s birthday is.

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

Albert : Now I know too.

So when is Cheryl’s birthday?

Note: Last sentence refers to “Having said that, I am sure David still does not know too.”

Aug 14 Sept 17 Sept 14 Sept 20 Jul 16 Aug 20 May 16 Sept 16

1 solution

Julian Poon
Apr 25, 2015

Take a look at this blog where my friend Damian Boh posted a solution for this.

This problem is very very hard. I took a few minutes for the original one but for this I took an hour. The problem's origins are unfortunately, unknown.

I was left with sept 14 and sept 20 and then i didnt know what to do.

So I just clicked 14 as thats my b'day.;-)

Kushal Patankar - 6 years, 1 month ago

David has either May, June or July in his hand, so it couldn't be 14. Cheryl's birthday is on 14 then.

BK Lim - 5 years, 11 months ago

no, he is jul, aug or sept, think a little better, and its onnly the beggining btw.

Strahinja Zlatanovic - 5 years, 5 months ago

@Strahinja Zlatanovic – David absolutely cannot have either Aug or Sept in his hand...

kun Paohui - 4 years, 7 months ago

Once you've solved this question. Try this one instead.

Pi Han Goh - 6 years, 1 month ago

That was crazy...

Julian Poon - 6 years, 1 month ago

I used a table and eliminated options to arrive at the answer. It did not take me an hour, but it took me longer than the original problem.

To me, the crux seems to be the fact that David gets told only a date which is given in the information. And an extension to this problem would be to guess the date that Cheryl whispered to David.

Hint: it is not Sept 14 ;)

Raghav Vaidyanathan - 6 years, 1 month ago

Yes, I eliminated certain dates each time a hint was dropped. I got the answer to be Sept 20, but apparently the accepted answer is Sept 14. Why is this?

Aran Pasupathy - 6 years ago

It is not that easy to explain, the detailed solution is in the link posted by the author of the problem.

Raghav Vaidyanathan - 6 years ago

@Raghav Vaidyanathan – I see it now; the important clue was the fact that David was not given a date in August. Thanks for your response!

Aran Pasupathy - 6 years ago

Oops, sorry.....Sept 14 is indeed the answer!

Aran Pasupathy - 6 years ago

Hm, I didn't have an hour to spare. Randomly clicked an option

Agnishom Chattopadhyay - 6 years, 1 month ago

Then that's no fun.... :(

Julian Poon - 6 years, 1 month ago

There's a timeskip logic flaw in the blog post.

[“Bernard: I did not know when Cheryl’s birthday is right before Albert said his last sentence, but after he did, now I know when Cheryl’s birthday is.” Following the same logic as explained in the first part of the solution, in the list above there is only one possible date corresponding to the day 16. If Cheryl’s birthday were in Sep 16, Bernard would have gotten the day 16 and would have known Cheryl’s birthday. However, he said that he still doesn’t know.]

I tried to explain this but it became really confusing really quick, so I'll just summarize it quick; B only states once that he doesn't know, "still doesn't know" doesn't exist. Thus, I can't justify how 16 is eliminated.

Wilhelm Wolham - 5 years, 9 months ago

Yeah, I was about ready to smash my face into my keyboard at this point, since Bernard's statement here didn't seem to be helpful in any way. But, it really does eliminate 9/16. This is my explanation:

"before Albert said his last sentence", we knew that the date had to be one of the following: 8/14, 8/20, 9/14, 9/16, 9/20. If Bernard was given "16" as the day, he would have known already that it was 9/16. Since he "did not know", we know the date could not have been 9/16.

Nathan Sproul - 4 years, 4 months ago

How was sept 16 eliminated? In the solution it says bernard doesnt know but his second statement is that he does know.

Sharvesh Patki - 4 years, 6 months ago

"Bernard: I did not know when Cheryl’s birthday is right before Albert said his last sentence"

Nathan Sproul - 4 years, 4 months ago

I don't understand how we can eliminate the months of May and June off the start. It's obvious that it can't be May 19 or June 18 but why the rest of the days in those months? Why couldn't it still be May 15 for instance?

Houston Doig - 4 years, 5 months ago

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

The only way for Bernard to know Cheryl's birthday right off the bat is if he is given a day that only appears once in the list. Therefore, the only way for Bernard NOT to know is if he is given a day that appears more than once in the list. Albert is certain that this is the case (Bernard was given a day that appears more than once in the list), because the month Albert was given contains only days that appear more than once in the list.

Nathan Sproul - 4 years, 4 months ago

Same here Julian , I also took close to an hour mainly because I didn't have a pen and a paper but it was really fun !

Ayaan Kudo - 3 years, 1 month ago

Harder Cheryl's Birthday

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