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: 5, Insightful) by KilroySmith on Thursday April 16 2015, @04:32AM
Your logic is lacking.
Albert doesn't know anything other than what Cheryl told him ("To Bernard, she whispered the day, and only the day"). As far as Albert is concerned, Cheryl could have told Bernard the exact month, day, hour, and second. When he says "I don’t know when your birthday is, but I know Bernard doesn’t know, either", he's making a statement that has no basis in logic, and as a result gives no information to Bernard.
Albert doesn't know that Cheryl told Bernard the day. Any conclusions you draw can't assume that knowledge.
(Score: 1, Insightful) by Anonymous Coward on Thursday April 16 2015, @05:53AM
Yes, yes, I thought of that objection too, but it's also easy figure out what the people who designed the question wanted you to answer.
(Score: 3, Interesting) by TheB on Thursday April 16 2015, @07:11AM
You are right that without an assumption this puzzle is unsolvable.
It is a common error in puzzles and tests. I've seen similar "must read between the lines" questions on college entrance exams. According to one instructor, it was an intentional omission to test ability to make reasonable conclusions of intent.
(Score: 2, Funny) by Anonymous Coward on Thursday April 16 2015, @08:02AM
Well, here's what actually happened:
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @08:04AM
Err ... s/Alice/Cheryl/ of course …
(Score: 1, Funny) by Anonymous Coward on Thursday April 16 2015, @08:25AM
More like they looked it up on facebook etc even if cheryl doesn't list it on facebook, sometimes you can tell from the birthday greetings in her timeline ;).
(Score: 2) by wonkey_monkey on Thursday April 16 2015, @09:49AM
Any or all them could also have been lying at any point, since that's not explicitly stated.
Cheryl's birthday could be August 15, May 16, or January 4.
She might even be a fictional character, and this entire thing is just a tissue of lies, in which case she doesn't even have a birthday.
systemd is Roko's Basilisk
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @04:35PM
Technically you are correct. Also note https://xkcd.com/1475/ [xkcd.com]
(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.