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from the it-seemed-like-the-logical-thing-to-do-at-the-time dept.
A couple of months ago, it was a color-changing dress that blew out the neural circuits of the Internet. Now Kenneth Chang reports in the NYT that a problem from a math olympiad test for math-savvy high school-age students in Singapore is making the rounds on the internet that has perplexed puzzle problem solvers as they grapple with the simple question: "So when is Cheryl's birthday?"
Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates:
May 15 — May 16 — May 19
June 17 — June 18
July 14 — July 16
August 14 — August 15 — August 17
“My birthday is one of these,” she said.
Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day.
“Can you figure it out now?” she asked Albert.
Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!
When is Cheryl’s birthday?
Logical puzzles like this are common in Singapore. The Singapore math curriculum, which has a strong focus on logic-based problem solving, has been so successful that it's been adopted around the world. According to Terrance F. Ross, US students have made strides in math proficiency in recent years, but they still lag behind many of their peers internationally, falling at the middle of the pack in global rankings. In the same PISA report the U.S. placed 35th out of 64 countries in math. "And even though the "Cheryl's Birthday" question may be atypical of the average Singaporean classroom, perhaps it's still worth asking: Are you smarter than a (Singaporean) 10th-grader?"
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @08:40PM
Incorrect.
Albert knows the month.
Albert knows that Bernard knows the date.
Albert makes the statement "I don’t know when your birthday is, but I know Bernard doesn’t know, either" and passes critical information to Bernard.
By saying that "Bernard doesn't know, either", Albert affirms that for the month that was spoken by Cheryl, all the days in the month are replicated in other months.
Let's take the answer as an example. July has two dates: 14th and 16th. The 14th is replicated in August, and the 16th is replicated in May. Therefore Albert knows that Bernard has no idea what Month the birthday is just by Bernard using his private information (16th).
This is also true of August as all the days (14th, 15th, 17th) are repeated in other months.
Albert could not have made the absolute statement "Bernard doesn't know, either" if the month was either May or June. Both of these months contain a unique day, thus Bernard could have known the birthday using just his private information if he was given 18th or 19th as the day.
If May or June was the correct month, Albert would have said "Bernard could know the birthday" and a different logic path would follow.
(Score: 2) by EQ on Thursday April 16 2015, @09:46PM
What most folks miss is this : By saying that "Bernard doesn't know, either", Albert affirms that for the month that was spoken by Cheryl, all the days in the month are replicated in other months.
It doesn't necessary follow - its a matter of semantics to get that much inference (affirms) out of such a simple statement. The broadest meaning does NOT include that information, and requires a contextual jump that may not be justified in normal conversation. "doesn't know" could be stating the simple fact that he does not know the birthday meaning the month AND day -- which is an allowable and perfectly lgical semantic interpretation of the statement. In that case you cannot draw the inference which the problem assumes that you do. Once you get past this, and make the non-colloquial semantic change in the processing of the statements, the problem is easy. Its not making the logic that's tough, its the contextual jump. For many, this isnt a logic problem, its a trick of semantics problem.