# Cheryl's Birthday

Discussion in 'Math' started by Roderick Young, May 3, 2015.

1. ### Roderick Young Thread Starter Member

Feb 22, 2015
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This has been going around the internet virally for a while. I found it to be an entertaining puzzle.

Code (Text):
1.
2. 24. Albert and Bernard just become friends with Cheryl, and they want to know
3.     when her birthday is.  Cheryl gives them a list of 10 possible dates.
4.
5.                   May 15         May 16         May 19
6.                  June 17         June 18
7.                  July 14         July 16
8.                August 14       August 15     August 17
9.
10.     Cheryl then tells Albert and Bernard separately the month and day of her
11.     birthday respectively.
12.
13.     Albert:  I don't know when Cheryl's birthday is, but I know that Bernard
14.              does not know too.
15.     Bernard: At first I don't know when Cheryl's birthday is, but I know now.
16.     Albert:  Then I also know when Cheryl's birthday is.
17.
18.     So when is Cheryl's birthday?
19.

Last edited: May 3, 2015
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2. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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I'll bite. I came up with July 16.

Will you let us know the answer?

John

3. ### Roderick Young Thread Starter Member

Feb 22, 2015
408
168
This puzzle is supposedly from a math competition in Singapore. I won't post the answer here and spoil it, but the answer can be googled.

There is a principle that some call the "Eureka Principle" that doesn't help solve puzzles, but does an excellent job of verifying answers, at least for me. It helped me on the SAT test years ago, helped me in debugging circuits, and helped me debug software. It's simply this: when I have the right answer, I just know. Everything falls into place. When I think maybe, kinda, it could be the answer, usually it's not.

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4. ### BR-549 Well-Known Member

Sep 22, 2013
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I saw this a while back. Only I did not have the benefit of knowing about Singapore. I wished I had.

This is not a math problem to me. It's an English problem.

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5. ### WBahn Moderator

Mar 31, 2012
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It IS a math problem, just not an arithmetic problem. It is a logic problem involving sets and set operations such as intersection. It is not an English problem any more than it would be a Chinese problem if presented in Chinese.

It's also a very straight forward and simple logic problem.

EDIT: Confirmation of jpanhalt's answer removed to address GopherT's complaint that the giving an answer isn't a problem but confirming it is unacceptable.

Last edited: May 3, 2015
6. ### Roderick Young Thread Starter Member

Feb 22, 2015
408
168
I hesitated to add that detail, because I'm really not trying to say that people from there use bad English, but remember that they have several national languages, and one of them is Chinese, which doesn't have tenses for verbs. When I originally read the problem, I could hear the voices of some of my friends from that area. It's very much how they speak in casual conversation.

7. ### WBahn Moderator

Mar 31, 2012
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Okay. Let's see. Post #2 gave the answer and you have no problem with that, but you are bitching at me for confirming an answer given nine hours earlier.

8. ### WBahn Moderator

Mar 31, 2012
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@GopherT I removed my confirmation of jpanhalt's answer since you obviously feel that confirming an answer is such a terrible sin as to justify denigrating someone's personality. I guess the thinking is that if someone gives an answer that no one will take note unless someone else confirms it. Interesting theory.

9. ### GopherT AAC Fanatic!

Nov 23, 2012
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@WBahn
I deleted my post as well.

10. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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My answer was just an "educated guess," so to speak. I was absolutely sure what months it wasn't at the start (i.e., May or June), but my reasoning for the latter part was a little less certain -- maybe because of the hour. I didn't mean to spoil anyone else's fun, hence, I expressed that doubt.

Anyway, I think it is fun for individuals to take a stab at solving such questions without consulting Google in any way. I used to devour the math puzzle section by Martin Gardner in Scientific American when I was younger. He also has a couple of compilations called "ah ha" or something to that effect.

One puzzle of his in particular comes to mind about pirates and deciding who one should make walk the plank. I don't recall enough of the details to repeat it here, but the solution was simple enough once you realized to work backwards from the end state most desirable to yourself. That lesson was not lost on me.

John

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11. ### strantor AAC Fanatic!

Oct 3, 2010
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I'm stumped. I've seen the problem on facebook already but did not try to solve it. I'm not sure how you got that answer John and I refuse to google it. Maybe I will change my mind and google it later, but I would like to sleep on it first and see if it comes to me. I plotted the dates on a graph paper; the range spans 6 days and 4 months; a 6X4 block. I do not see any pattern in the block, and I'm not at all sure I'm approaching it in a logical way. It does not even seem like a logical question to me. It seems Albert & Bernard would have to share some information with each other, but if they did that, then they both would know the date immediately (which apparently they did), but we still wouldn't know; and the problem does not state that they shared information, so I assume that they did not.

Anyway, I must move along. I have other things with which to punish my poor overworked, ill-equipped brain today.

12. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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@strantor

Here is a clue. Remember that Albert only knows the month, but he can confidently say that he knows Bernard does not know the date. There are two unique day numbers, May 19 and June 18. Thus, in order for him to be certain Bernard does not know the date, the months of June and May must be excluded.

John

Last edited: May 4, 2015
13. ### Roderick Young Thread Starter Member

Feb 22, 2015
408
168
Sounds like a good approach to me. That's the first thing I did, plot out a grid like you did, then decide which rows or columns could be eliminated based on the statements.

14. ### ErnieM AAC Fanatic!

Apr 24, 2011
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I can see how Bernard could know the date but not how Albert can also infer this.

15. ### WBahn Moderator

Mar 31, 2012
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You need to alternate and put yourself in the other person's shoes and examine the possibilities from their perspective.

If you know the month, then you know the subset of dates that the other person could know.

If you know the date, then you know the subset of dates that the other person could know.

If the other person makes a claim about what you do or don't know, then you put yourself in their shoes, knowing the subset that they have to be working from, and ask which of those possibilities would allow them to make that claim given what that person would then know about the subset that you have to be working from.

16. ### Roderick Young Thread Starter Member

Feb 22, 2015
408
168
You're almost there. Bernard could know if it's a certain date. But Albert, knowing only the month, is able to positively exclude those dates... What does that tell you about what month it cannot be?

17. ### atferrari AAC Fanatic!

Jan 6, 2004
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Sorry Roderick, but how they manage to tell stories or say what they hope to be doing in their future?

Necessity of conveying sense of time passed or to pass is real.

18. ### WBahn Moderator

Mar 31, 2012
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The information can be conveyed, it is just done in a different way. Different words entirely are used and there are also particles that are tacked on that change the meaning of words.

Chinese also doesn't have gender pronouns such as he/she and him/her and so people Chinese speakers often use the masculine pronoun when speaking English regardless of the gender of the person they are talking about. But that doesn't mean that when they talk to someone in Chinese that the conversation is missing that information. It is just conveyed differently (albeit more weakly).

Mar 6, 2009
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