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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: 4, Interesting) by bzipitidoo on Thursday April 16 2015, @04:35AM
I don't follow it. I guess we have to assume several things. First, Albert and Bernard communicate with each other in some fashion. They don't pool their knowledge, because if they did they'd know immediately. Maybe Albert only sees that Bernard is still stumped? Or knows that Cheryl would not give Bernard a clue that gives away the information? How does Albert know Bernard was told the day? Cheryl could have told them both the same information, the month. Or she could have given Bernard a formula, something like "day = month + 9" or "day = 23 - month".
But, if everyone knows that Cheryl told Bernard which day, we can eliminate May 19 and June 18, otherwise Bernard would know. June 17 can also be eliminated, because if Albert knew the month was June, and knew that Bernard did not know Cheryl's birthday, then Albert would know that it has to be June 17. But I don't yet see why May 15 and 16 are out.
(Score: 3, Insightful) by Anonymous Coward on Thursday April 16 2015, @04:51AM
The first assumption is that Cheryl was even born. How does Albert know that Cheryl was not from her mother's womb untimely ripped?
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @07:42AM
From the puzzle:
“My birthday is one of these,” she said.
This already implies that Cheryl has a birthday, because if she didn't have a birthday, none of the given dates would be her birthday.
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @08:18AM
Albert assumes Cheryl has a birthday, before she confirms that she has a birthday.
(Score: 2) by Anal Pumpernickel on Thursday April 16 2015, @02:23PM
What if she was lying?
(Score: 3, Funny) by fritsd on Thursday April 16 2015, @08:30AM
Singapore probably doesn't have room for the Forest of Dunsinane.
(Score: 2) by TheB on Thursday April 16 2015, @07:42AM
Without assuming that both Albert and Bernard are aware of Cheryl whispering the month to one and the day to the other this puzzle is unsolvable.
Given that the reader is given this information it is reasonable to assume that both Albert and Bernard also know this.
May 15th and 16th are out for the same reasoning you used to eliminate June 17th.
If Cheryl's birthday was May 19th then Albert's statement "I know Bernard doesn’t know, either." would be invalid.
Since there is only one 19th Bernard could deduce it must be May 19th. Albert must know the month is not May for his statement to be correct.
(Score: 4, Insightful) by bzipitidoo on Thursday April 16 2015, @02:16PM
Oh, I see it now. Albert knows that Bernard does not know, not because Bernard or Cheryl told Albert that, but because Albert was told a month for which Cheryl did not give unique days. I was thinking that Albert saw only that Bernard did not know, which eliminates only June. So all of May and June are out. After Albert announces that he knows Bernard does not know, Bernard can also make that connection.
Then, the 14th is out, because Bernard would still not know which month Albert was told if the day was the 14th, and he says he does know after hearing Albert. We're down to July 16, Aug 15, and Aug 17.
Finally, August is eliminated because Albert says that because Bernard now knows, he knows too. If Albert knew the month was August, he still could not tell if it was the 15th or 17th. So Albert must have been told that the month was July, for him to be able to announce (truthfully) that now he knows too.
(Score: 0) by Anonymous Coward on Thursday April 16 2015, @07:48AM
Yes, you have to assume they both know that Bernard was told the day and Albert was told the month. The only other communication between them is in what they explicitly said in this problem.
Now if Albert can say he knows Bernard doesn't know when Cheryl was born, then as Both May and June have unique days in it, Albert knows it is neither May nor June, that lets Bernard know it isn't May or June, now Bernard says he does know with this new information, which leaves only one option.