When is Cheryl's Birthday?
I saw this question on Facebook:
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 16 19
June 17 18
July 14 16
August 14 15 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 didn't know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.
When is Cheryl's birthday?
There is an official solution which is explained in the link below, but I don't understand the logic.
July 16, as explained here. https://www.facebook.com/kennethjianwenz/posts/386479228197631
What is wrong with the logic in the answer I posted below (I put it in spoilers if others want to try)?
@JoeZ. there's one which is exactly the same but with different numbers, it was about 2 students guessing the birthday of their professor with about the same dialogue. It's convoluted logic but fun none the less. I'll see if i can find the question
Can someone suggest a website or book that has bunch of such questions? EDIT: http://puzzling.stackexchange.com/questions/tagged/logic-puzzle is a good source. More suggestions are welcome.
I will try to help you understand the answer. It is important to note that Albert and Bernard both know the answer before we do.
With Albert's first statement, it is clear to us that Albert was told either July or August. Had he been told May or June, he would not be able to state definitively that he knew Bernard didn't know. (May 19 and June 18 both could be uniquely identified immediately by Bernard without Albert's help, so in order for Albert to know that Bernard doesn't know, the month he was told must not be May or June.)
Because Bernard has been able to identify Cheryl's birthday after Albert's statement, he must not have been told 14. Because Albert's statement revealed July and August, had Bernard been told 14, he would still be unclear on the date. (If he said he didn't know, then Albert would know the birthdate, but Bernard would never be able to deduce it.)
We still don't know whether it is July 16, August 15, or August 17.
However, since Albert (who was only told the month) is able to state that he also knows the birthday, he must not have been told August. Had he been told August, he would be unable to decide if Bernard was told the 15th and 17th.
It is only after the third statement that we (as outsiders) can deduce the birthday. Bernard knew after the first statement and Albert knew after the second.
Even though this isn't the highest rated answer, and a lot of them were similar, I picked this one because after reading it, I can finally understand why July 16 is the answer.
Thanks @RichardKennethNiescior, I don't know why I thought his name was Bertrand. How odd.
@IanMacDonald I am sorry but I still having problem understanding your answer,How are we so clear that Albert was told July or August `Had he been told May or June, he would not be able to state definitively that he knew Bernard didn't know. (May 19 and June 18 both could be uniquely identified immediately by Bernard without Albert's help` 18,19 are unique but we also have 15 and 16 of May and 17 of June.
@SurajSingh the trick is not that there are dates available, but rather that he stated that he *knew* that Albert didn't know. Since Bernard was only told the month, suppose that he was told "May". Looking at the set of dates that it could be, Albert could have been told 15, 16, or 19. Bernard doesn't know which number Albert was told, but he is able to confidently say that it wasn't 19. The only way he can confidently say this is if he were not told May as the month. A similar argument is made for June.
@SurajSingh in fact, let's suppose that her birthday *is* May 16. This means Bernard was told "May". With three possibilities for the day (and one of them unique), Bernard's first statement would be "I don't know if Albert knows the birthday." (The logic table then proceeds to resolve with May and June being the only possible months.)